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Influence of physiological sources on the impedance cardiogram analyzed using 4D FEM simulations
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Institute of Physics and Engineering in Medicine Physiol. Meas. 35 (2014) 1451–1468
Physiological Measurement
doi:10.1088/0967-3334/35/7/1451
Influence of physiological sources on the impedance cardiogram analyzed using 4D FEM simulations 2 Mark Ulbrich 1 , Jens Muhlsteff ¨ , Steffen Leonhardt 1 1 and Marian Walter 1
RWTH Aachen University, Philips Chair for Medical Information Technology, Pauwelsstrasse 20, D-52074 Aachen, Germany 2 Philips Research, High Tech Campus 34, 5656 AE Eindhoven, The Netherlands E-mail: [email protected] Received 26 December 2013, revised 25 March 2014 Accepted for publication 13 May 2014 Published 5 June 2014 Abstract
Impedance cardiography is a simple and inexpensive method to acquire data on hemodynamic parameters. This study analyzes the influence of four dynamic physiological sources (aortic expansion, heart contraction, lung perfusion and erythrocyte orientation) on the impedance signal using a model of the human thorax with a high temporal resolution (125 Hz) based on human MRI data. Simulations of electromagnetic fields were conducted using the finite element method. The ICG signal caused by these sources shows very good agreement with the measured signals (r = 0.89). Standard algorithms can be used to extract characteristic points to calculate left ventricular ejection time and stroke volume (SV). In the presented model, the calculated SV equals the implemented left ventricular volume change of the heart. It is shown that impedance changes due to lung perfusion and heart contraction compensate themselves, and that erythrocyte orientation together with the aortic impedance basically form the ICG signal while taking its characteristic morphology from the aortic signal. The model is robust to conductivity changes of tissues and organ displacements. In addition, it reflects the multi-frequency behavior of the thoracic impedance. Keywords: impedance cardiography, ICG, finite element simulations, lung perfusion, erythrocyte orientation, characteristic points, stroke volume
S Online supplementary data available from stacks.iop.org/PM/35/1451/mmedia
(Some figures may appear in colour only in the online journal)
0967-3334/14/071451+18$33.00
© 2014 Institute of Physics and Engineering in Medicine Printed in the UK
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1. Introduction In Europe, the ever-increasing numbers of geriatric patients and associated diseases are leading to increasing costs and burden on medical resources. Therefore, methods to treat elderly persons more (cost-)effectively are needed by improving the diagnostic processes and monitoring those diseases prevalent among the elderly. A common cause of death in western Europe is heart failure. Measures for its severity are hemodynamic parameters, including stroke volume (SV) or cardiac output (CO). Until now, the gold standards to measure these parameters are the thermodilution technique using pulmonary artery catheters and echocardiography using ultrasound imaging. However, the risks associated with estimating CO by means of catheters include infections, sepsis and arrhythmias, as well as increased morbidity and mortality (Darovic 2002). For echocardiography, expensive devices and trained personnel are needed. In addition, this technique bears a higher inter-individual variation for repeated measurements compared to impedance cardiography (ICG) (Northridge et al 1990). At present, ICG is not commonly used as a diagnostic method because it is not considered reliable (Cotter et al 2006, Raaijmakers et al 1999). One reason for this is the controversially discussed accuracy of the technology concerning the calculation of SV, especially in critically ill patients (Critchley 1998). Another reason is that contributions of processes such as certain conductivity changes in the human body to measured impedance changes are largely unknown. One way to analyze where the electrical current paths run, and which tissue or organ makes a significant contribution to the measurement result, is to use computer simulations based on the finite element method. Many research groups have already worked with FEM models to analyze various issues concerning ICG which cannot be analyzed in vivo. Different models were used to analyze effects of electrode positions (Wang et al 2002) and electrode type (Kauppinen et al 1998) as well as contributions of organs to the ICG (Sakamoto et al 1979). The question of preferred electrode type and positions could thus be solved, but contradictory results were discussed concerning the contribution of dynamic sources to the ICG signal. Kim et al (1988) reported a linear relationship between aortic blood volume change and impedance change and the highest impact of ventricular blood volume change. The effect of lung resistivity change and blood resistivity change are supposed to be even smaller (only 40% of the aortic blood volume change) (Kim et al 1988). In contrast, Wang and Patterson identified blood resistivity changes as major contributor to the signal, lung conductivity change as secondary contributor and volume changes as last important influence on the ICG (Wang and Patterson 1995). Another research group (Wang et al 2002) stated that the volume change due to heart contraction is the major contributor to the signal whereas other dynamic sources contribute equally. One possible reason for these inconsistent statements is that only discrete points in the cardiac cycle were analyzed in these studies. The simplest approach is to simulate end-systolic volumes (Kim et al 1988), other works used end-systolic and end-diastolic (Wang et al 2002) or additionally end-inspiratory and end-expiratory volumes (Sakamoto et al 1979). Besides temporal resolution, the aforementioned models differ in geometry and implemented tissue parameters which might be other reasons for opposing results. Earlier works used cylinder models (Raaijmakers et al 1997), simple plumbers models (Sakamoto et al 1979), three-dimensional representations of the thorax using anatomical maps (Kim et al 1988) and static models derived from static MRI scans by segmentation (Wang et al 2002). In general, a model which comprises all possible and known sources for dynamic and static impedances should be used for simulations. The best solution would be of course to use dynamic MRI data to create a model which we tried in an earlier project (Ulbrich et al 1452
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2013). In clinical practice, one can get good dynamic images of the heart but it is not possible to get an ECG gated representation of major blood vessels, such as aorta, since this would include a huge amount of contrast agent to be injected in the subject. In addition, even if it would be possible to get scans of a thorax with a high temporal resolution, these geometries would be far too complex to be solved in a reasonable amount of time. Another limitation is the amount of memory (RAM) of computers for this problem which again suggests the implementation of simplified geometries. To be more precise: an MRI thorax model with 11 million mesh cells consumes 48 GB of RAM and takes weeks to be simulated with only providing a temporal resolution of 10 frames per heart cycle. This is also due to the restriction of the chosen simulation software to use only one core for calculations. As described in section 2.3, only one reliable dataset of human tissue parameters exists in literature. Unfortunately, none of the previous works used this dataset. Mixed parameters of different research groups, often in combination with parameters from varying animal studies (pigs, dogs, cows) were used, making it difficult to interpret and to transfer the simulation result. To sum up, none of the aforementioned models provide the possibility to generate timecontinuous impedance curves with adjustable temporal resolution based on physiological measurements, including reliable human datasets of tissue parameters and reflecting volumetric and conductivity-based dynamic changes in the human thorax, to analyze the ICG by extracting characteristic points with available algorithms used in practice. This aim is realized in this work by simulating the impact of four dynamic sources (aortic expansion, heart contraction, lung perfusion and erythrocyte orientation) on the ICG signal including a sensitivity analysis of the contribution of tissue conductivity and organ movement on the measured signal. By establishing such a model, it will be possible to identify reasons for the inaccuracy of ICG in combination with pathologies and to improve measurement techniques in the future. 2. Background Since the aim of this work is to analyze the impact of specific sources on the impedance cardiogram, we first present some information on bioimpedance measurements and physiological sources for impedance measurements. 2.1. Bioimpedance measurements
For bioimpedance measurements, two outer electrodes are used to inject a small alternating current into the human body and (via two inner electrodes) the voltage drop is measured to calculate the complex impedance. Although a bipolar measurement technique could be used, the tetrapolar technique has the advantage that the electrode impedances do not contribute to the measured voltage. When a frequency spectrum of 5 kHz–1 MHz is used to measure the bioimpedance for each frequency, this method is called ‘bioimpedance spectroscopy’ (BIS). This frequency range (called β-dispersion) is generally the most interesting for diagnostic purposes, since physiological and pathophysiological processes cause changes in body impedance (Grimnes and Martinsen 2000). BIS is commonly used to assess the body composition of humans. If only one frequency of this spectrum is used to continuously measure the bioimpedance on the thorax, this method is called ICG. Since ICG operates at a single frequency between 20–100 kHz, one continuous curve in the β-dispersion range can be obtained by ICG measurements. By measuring the impedance continuously, timedependent hemodynamic parameters can be defined from the measured impedance curve using its temporal derivative. Figure 1 shows an idealized ICG wave with characteristic features. 1453
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Figure 1. ICG wave (−|dZ(t )/dt|) with its characteristic points.
The characteristic points of this derivative are defined as follows (Summers et al 2003). • • • • •
Point A: start of the electromechanical systole. Point B: opening of the aortic valve. Point C: maximal mechanical contraction. Point X: closure of aortic valve. Point O: opening of the mitral valve
The left ventricular ejection time (LVET) is defined as the time between opening and closure of the aortic valve. The standard values for |dZ(t )/dt|max are 1–2 s−1 and for tLVET 200–340 ms (Granerus and Elg et al 1982, Lance and Spodick 1976). The SV (in ml) measured with ICG depends on the underlying model, for which multiple equations exist, as follows (Bernstein and Lemmens 2005): tLVET l 2 dZ · · 2 (Kubicek) (1) SV = σb dt max Z0 tLVET (0.17 · H )3 dZ · · SV = 4.2 dt max Z0 SV = δ ·
tLVET (0.17 · H )3 dZ · · 4.2 dt max Z0
VITBV SV = · ζ2
dZ dt
tLVET · √ Z0 max
(Sramek)
(2)
(Bernstein–Sramek)
(3)
(Bernstein–Osypka).
(4)
All equations are influenced by three values: the LVET tLVET , the static thoracic base impedance Z0 and the maximum of the derivative of the continuous impedance |dZ/dt|max . Equation (1), first introduced by Kubicek, calculates the SV by employing the blood 1454
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conductivity (σb ) and the distance between the measuring electrodes (l). Sramek utilized the patient’s height (H) instead of the electrode distance l (equation (2)). In equation (3), the factor δ is the actual weight divided by the ideal weight; this was introduced by Bernstein (Van De Water et al 2003). The most recent equation (equation (4)) was also developed by Bernstein in 2005 and here factor VITBV = 16 · Weight1.02 is the intra-thoracic blood volume and ζ the index of transthoracic aberrant conduction (Bernstein and Lemmens 2005). His equation assumes the velocity of the blood to be the only contributor to the signal. The first three equations are based on pure volumetric changes. Using one of these equations, CO can be calculated by: l . (5) CO = SV · HR min 2.2. Dynamic physiological sources
Besides the static influence of each tissue on the measured impedance caused by conductivity and permittivity of different tissues and their volume inside the human body, several dynamic sources alter the impedance signal. All volume changes and conductivity changes influence the measured impedance of the thorax. The main contributors to the dynamic impedance are: blood conductivity changes, changes of conductivity due to lung perfusion (blood delivery), and volume changes by heart contraction and by aortic expansion. The conductivity of blood changes during a heartbeat is caused by erythrocytes (red blood cells) only, since hemolyzed blood or blood plasma have no effect on the impedance change. In stationary blood, erythrocytes are oriented arbitrarily due to Brownian motion and, therefore, its resistivity is isotropic (Hoetink et al 2004). This effect can be observed at the end of diastole. The shape of the erythrocytes is biconcave and they will reorientate in a way that minimizes motion shear stress caused by the increase of blood velocity. Thus, with increasing alignment, blood resistivity decreases and becomes anisotropic in the direction of blood flow since the current may flow through a larger area of low-resistance plasma (Visser et al 1976, Kanai et al 1976). This means that the measured bioimpedance is mainly affected by erythrocyte orientation due to blood flow in vessels in the direction of the excitation current flow. This effect is visible during systole, especially in the rapid ejection phase during early systole and is frequency-dependent having a strong influence on ICG measurements around 100 kHz. However, since the current flows through cells for frequencies exceeding the β-dispersion range, the effect of erythrocyte orientation is negligible for frequencies above 1 MHz (Gaw 2010). 2.3. Static tissue parameters
For the non-dynamic electrical behavior of body tissue, conductivity (σ ) and permittivity (r ) values have to be assigned for each tissue type at the selected frequency since these parameters change due to dispersion. It is difficult to obtain reliable electric parameters of tissues since they cannot be acquired in vivo and, after death, these parameters change rapidly. For example, heart muscle tissue changes irreversibly after only 20 min because cells cannot maintain the concentration gradient of electrolytes between extra- and intracellular space without bloody supply. Water enters cells and breaks up the cell membranes so that it is no longer possible to observe the dispersion effect between 5 kHz and 1 MHz (Wieskotten 2008). Several groups aimed to assess these parameters in vivo and in vitro, mainly by examining animals. In a metaanalysis of review studies (Faes et al 1999), the aim was to obtain a consensus between these various studies. A total of 103 resistivities for 21 different tissues were taken into account; 1455
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analysis showed that the resistivity of most tissues do not show a significant deviation (within a 95% confidence interval). Only bone, fat and stratum corneum show significantly higher values. In order to avoid errors introduced by differences in measurement conditions (e.g. inter-rater errors or inter-subject variations) we decided to use data from one study only. The most suitable dataset was provided by Gabriel et al (1996) who examined human tissues 24–48 h after death. That way, a dataset containing all tissues of interest could be created between 10 Hz to 20 GHz at body temperature (Gabriel et al 1996). Since this is the most complete, reliable and up-to-date database (IT’IS Foundation 2012, Carrara 2010) it has been used by various groups and is also used for the present study. 3. Methods Since the geometry of the thorax and its organs is essential for the current distribution during ICG measurements and determines the contribution of various static and dynamic sources to the ICG signal, FEM simulations were chosen to simulate ICG measurements. R from Computer Simulation Technology, Darmstadt, Germany was used to CST EM Studio perform the simulations which were computed on a personal computer with a 64 bit operating R Xeon R 5240 processor with 2 cores and 24 GB RAM. The excitation system, an Intel frequency in the simulations was set to 100 kHz because most ICG devices operate around this frequency. Since this wavelength (λ = 340 m) is much higher than our measuring volume, the human thorax, the low frequency electroquasistatic solver (electroquasistatic Maxwell’s equations) was employed. Using a discretization density of 50 units, each model is composed of 1.5 million tetrahedrons. Besides this global discretization, a finer local discretization was used for organs with altering geometry in order to obtain accurate results for small geometry changes. Figure 13 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) presents these discretizations. 3.1. Simulation model
To ensure a good representation of a human thorax, the basis for the volumes representing each organ is an MRI dataset (known as the Visible Human of the Visible Human Project© dataset) from the National Library of Medicine, USA (National Library of Medicine 1986). Since this dataset contains no information about dynamics, a new model was created based on the geometries of the Visible Human using simplified geometries, such as cylinders, spheres and frustums. The new model in combination with the MRI dataset is shown in figure 12 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia). This abstracted model corresponds well with the volume of major organs, although their shape is not matched perfectly (see lung wings in figure 13). Figure 2 describes geometries and volumes of all tissues of the implemented model. A more detailed description of all volumes can be found in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) (table 1). The model is composed of static volumes from the Visible Human dataset and new dynamic volumes: aorta and heart. The static volumes include the tissues fat, muscle, bone, lung, blood vessels and abdominal organs. Since the impedance change of abdominal organs plays a subordinate role for the ICG signal during a heartbeat, a simplification was made in that the abdominal part of the model was filled with a uniform ‘tissue mixture’. Then, an average permittivity and conductivity of all abdominal organs has been assigned to this tissue. Table 2 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) lists the conductivity σ and permittivity r values for all static tissues, taken from Gabriel et al (1996). 1456
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Carotid artery
Neck 100 mm
Bone
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Fat
50 mm 50 mm 100 mm 70 mm
80 mm
125 mm
x
150 mm
y
z 75 mm
25 mm
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35 mm
z 70 mm
Muscle
90 mm 120 mm
Figure 2. Measures of the model in mediosagittal (left) and mediofrontal view (right).
A sensitivity analysis for these parameters on the model output was made since measured tissue parameters vary among research groups. This influences the variability of models and has an impact on the ICG morphology as well as on extracted parameters from the measured curve. Therefore, mean resistivities (ρmean ) and their 95% confidence intervals were used to calculate conductivity deviations of each tissue (Faes et al 1999). That way, the deviation caused by higher σhigh and lower conductivities σlow was obtained and the tissue conductivity of one tissue was changed to analyze its influence on the impedance and ICG curve. In addition, various organ displacements were simulated in order to take interindividual organ positions as well as organ movements during respiration into account. The diaphragm is a dome-shaped, fibromuscular partition between the thoracic and abdominal cavities which accounts for 75% of the increase in lung volume during quiet inspiration. Deep breathing is characterized by expansion of the abdomen rather than the chest and causes a higher motion and displacement of the diaphragm up to 6 cm on average (Gerscovich et al 2001). This craniocaudal displacement (+z direction) was simulated by moving the abdominal organs by 6 cm. During respiration, the heart changes its position about 3 cm in craniocaudal direction (Wang et al 2005). This was implemented in combination with abdominal organ displacement. In addition, intraindividual differences in heart position were taken into account by simulating displacements in craniocaudal direction (3 cm), 3 cm in caudocranial direction (−z) and 3 cm in dorsoventral direction (+y). For reasons of simplicity, ring electrodes were used in the model at neck and abdomen, although spot electrodes are typically used nowadays for bioimpedance measurements since studies have shown that the highest signal can be obtained by this configuration (Patterson et al 1990). In addition, this configuration for ICG measurements does not affect the measurement results (Sherwood et al 1992). 1457
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39
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Figure 3. Implemented geometry changes of heart (left) and aorta (right). (a) Radius
change of the heart. (b) Diameter change of the aorta.
3.2. Model dynamics
Dynamic sources were implemented by model functions matching typical physiological parameters based on measured data. Coupling of organs and the other physiological dynamic sources were temporally matched. The largest chamber of the human heart is the left ventricle, which is approximately conical in shape (Guyton and Hall 2006). Hence, we focus on using the left ventricle as representation for the single chamber spherical heart since the left ventricle dominates volumetric changes. This is a common approach found in literature to analyze electromechanical properties of the heart (Puwal 2013). The radius of a sphere representing the heart was altered to mimic the heartbeat while assuming a SV of 80 ml. The left ventricular volume change obtained by MRI data was used as physiologic basis for the radius change (Feng et al 2009). This change ranges from 38.5 to 33.8 mm and is shown in figure 3(a). Due to the constraints explained in section 1, the aortic expansion has to be modeled by using simple geometries. That way, the necessary sources can be used to build a model with volume changes creating high temporal resolution ICG curves. PhysioNet aortic blood pressure data from humans were used to model the aortic expansion, since it is proportional to the aortic blood pressure (see equation (6))3
P · R0 · extensibility . (6)
R = 100 Here, R0 is the diastolic radius of the aorta. This pressure–diameter relationship was estimated directly in the ascending aorta of man in ten patients undergoing open-heart surgery. The diameter was measured by means of an electrical strain-gauge caliper sutured to the vessel wall. The intravascular pressure was measured using a gauge needle connected directly to a strain gauge (Greenfield and Patel 1962). The aortic blood pressure has then been scaled to fit the requirement for the maximum aortic expansion of 20% (L¨anne et al 1992). Thus, the diameter of the aorta ranges from 25 to 30 mm (see figure 3(b)). This is of course a simplification, since we use a quasi-stationary approach and neglect the effects of wave propagation along the aorta. Since the lung receives the entire CO, its conductivity change due to lung perfusion will have a high impact on the measured ICG signal. This was implemented by assuming a 3 National Institute of Biomedical Imaging and Bioengineering. Physionet—the research resource for complex physiologic signals.
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0.82
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Figure 4. Implemented conductivity changes. (a) Lung perfusion. (b) Erythrocyte
orientation.
maximum conductivity change of lung tissue of 10% (Brown et al 1992). Based on measured conductivity changes with electrical impedance tomographic spectroscopy, a dataset was created (Zhao et al 1996). The conductivity change due to lung perfusion is shown in figure 4(a). Since blood volume changes in a volume of interest alter the impedance signal, changes in blood resistivity in major blood vessels will have a high impact. Since blood resistivity changes of 15% due to erythrocyte orientation are reported in literature, measured conductivity curves were used as base data. Together with a diastolic conductivity of 0.702 92 S m−1 , this results in a maximum conductivity of 0.808 36 S m−1 during systole (Raaijmakers et al 1996). The resulting curve is shown in figure 4(b). For every point in time of one heartbeat, a new model had to be created since the discretization of the simulated volume has to be recalculated due to the altered thorax geometry; this resulted in 103 models representing a temporal resolution of 125 Hz.
4. Results 4.1. Source identification
For validation purposes, the simulated curves for 100 kHz were compared to real measured TM data. These data were acquired using the Niccomo device (medis, Ilmenau, Germany) measuring a male human (medis GmbH 2012). To compare both curves, Z0 was subtracted. It should be mentioned that simulated Z0 = 58.8 is higher than typically measured values (between 20 and 48 (Critchley 1998)). However, higher values can also be obtained measuring healthy subjects. One reason for the high simulative Z0 value is that the parameter set for each tissue is obtained from the data of Gabriel (see table 2). It can be seen that the morphology of the measured and the simulated signal is very similar (figure 5). In addition, the peak-to-peak impedance of the sum signal (Zmax = 0.215 ), as well as the maximum of its derivative (|dZ/dt|max = 1.736 s−1 ), are in the range of typical ICG signals. Furthermore, the cross-correlation factor is r = 0.89; although the curves do not match perfectly, it is in the range of interpersonal variability. Figure 6 shows the simulation results of the impedance and its temporal derivative for each single source and for the sum signal which is composed of the four single source signals. Note that the impedances and the ICG curves are drawn invertedly, since this is common in literature. 1459
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Figure 5. Measured - - - - and simulated —— impedance signal (Z(t ) − Z0 ).
0.05 0 -0.05 -0.1
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Figure 6. Simulation results of the thoracic bioimpedance comprising: all sources , volumetric changes of the aorta — · —, volumetric changes of the heart ——, conductivity changes due to erythrocyte orientation · · · · · · and conductivity changes due to lung perfusion - - - -. (a) Impedance simulation results with offset correction. (b) ICG curves (temporal derivatives of impedance simulation results).
To quantify the contribution of each source to the impedance and the ICG signal, the point in time at which the curves have their maximum was analyzed. Thus, the absolute contribution of each signal as well as the percentaged values with respect to the sum signal, are obtained; the results are shown in table 3 (supplement available from stacks.iop.org/PM/35/1451/mmedia). It can be stated that the aortic signal seems to be the cause for the shape of the sum signal despite its low maximum impedance of 0.082 . The signal caused by erythrocyte orientation increases the signal strength with a maximum impedance change of 0.11 and a relative contribution of 50.59%. Interestingly, lung perfusion and the signal caused by heart contraction nearly compensate themselves. Hence, the simulation results suggest that erythrocyte orientation together with volumetric changes of the aorta might play a major role in forming the ICG signal. To assess the LVET, B- and the X-point have to be extracted from the ICG curve. Multiple approaches can be found in literature. However, for this work the zero-crossing of the ICG 1460
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Figure 7. Aortic blood flow measured with doppler echocardiography and ICG.
curve before the C-point was used for the B-point extraction and the X-point was assumed to be the local minimum after the C-point (Debski et al 1993). The B-point can be assessed by using the first local minimum of the ICG curve, the minimum of the second derivative, and the maximum of the third derivative occurring before the C-point; however, since the characteristic notch is not present and the local minimum corresponds to an earlier non-characteristic point, the zero-crossing method is the most reasonable one (Debski et al 1993). Figure 7 shows synchronized aortic blood flow assessed by doppler echocardiography with ICG and annotated aortic valve opening and closing by a physician. This figure visualizes that on the one hand, the B-point is not well defined, and on the other hand that the aortic valve closes earlier than indicated by the local minimum after the C-point. This is also reflected by the simulated ICG curve where the isovolumetric relaxation phase occurs before the X-point (see figure 6). Using LVET to calculate SV and CO with the equations shown in chapter 2.1, the following values are used: body height H = 1.78 m, electrode distance l = 420 mm, correction factor δ = 0.987, factor ζ = 1, body weight 69.1 kg and heart rate HR = 70.6 1/ min. The extracted and calculated parameters for the curve comprising all sources are: • • • • •
LVET: 383.7 ms SV calculated with Kubicek equation: 48.3 ml SV calculated with Sramek equation: 73.8 ml SV calculated with Bernstein–Sramek equation: 72.8 ml SV calculated with Bernstein–Osypka equation: 79.3 ml.
Note that the geometrically implemented SV is 80 ml. Table 4 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) lists the variations in LVET and SV when choosing different algorithms for B-point extraction (explained above). The difference in the B-point time ( tB ) obtained by the maximum of the third derivative of the impedance signal shows the lowest deviation and, thus, LVET and SV are close to the calculated values for the total curve. The biggest difference is given by the minimum of the second derivative which leads 1461
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(a)
(b)
Figure 8. Impedance and ICG curves for decreased tissue conductivity: original signal x, muscle · · · · · ·, blood – – –. (a) Impedance curves. (b) ICG curves.
to an overestimation of LVET (+ 99 ms) and of SV (+ 20.5 ml); this means that the chosen algorithm or the maximum of the third derivative should be chosen for the B-point extraction of the signals generated by the simulation model. 4.2. Sensitivity analysis 4.2.1. Conductivity changes. Figure 8 shows impedance and ICG curves plotted during one single simulated heartbeat for tissue conductivity changes towards lower values according to table 2. In both figures, only curves for conductivity changes of muscle tissue and blood are marked because effects of all other simulated tissues drawn in this graph can be neglected. In figure 8(a) offset-corrected impedance curves are plotted and most of these are almost identical with the impedance curve of the unchanged model, only muscle (+0.08 ) and blood conductivity changes (−0.02 ) alter the impedance signal significantly resulting in a maximum deviation of 0.1 . Since muscle tissue with lowered conductivity does not contribute to the dynamic changes of the impedance, this result reflects the fact that more current will flow through well conducting blood-filled areas contributing to signal changes. In figure 8(b) the maximum of the ICG curves is altered with muscle conductivity (+0.72 s−1 ) and blood conductivity changes (−0.28 s−1 ) resulting in a total change of 1 s−1 . In addition, lower muscle conductivity decreases the X-point value by 0.34 s−1 while lower blood conductivity increases this value by 0.13 s−1 . Most importantly, none of the characteristic points are altered in time. Impedance and ICG curves for increased tissue conductivity are depicted in figure 9. Here, lung conductivity changes are also marked, since they alter characteristic points in the ICG signal. Apart from muscle and blood conductivity changes, all curves in figure 9(a) are located in the same range. Muscle conductivity change alteres the maximum of the original curve by −0.097 and blood conductivity change by +0.0486 resulting in a total change of +0.145 . In addition, a temporal shift of the maximum is observed for blood (−17 ms) and lung conductivity changes (+41 ms). In the ICG plot (figure 9(b)), O-, C- and B-point are not affected by conductivity changes whereas the X-point is shifted due to muscle and lung conductivity (+9 ms) as well as blood conductivity changes (−16 ms). As for the ICG maximum related to decreased conductivity changes, only muscle (−0.78 s−1 ) and blood conductivity changes (+0.47 s−1 ) cause significant deviations resulting in a maximum deviation of 1.25 s−1 . 1462
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(a)
(b)
Figure 9. Impedance and ICG curves for increased tissue conductivity: original signal
x, muscle · · · · · ·, blood – – –, lung ♦. (a) Impedance curves. (b) ICG curves.
(a)
(b)
Figure 10. Impedance and ICG curves for organ movements: original signal
x, heart(y+30 mm) · · · · · ·, abdomen and heart(z+30 mm) ♦, abdomen , heart(z − 30 mm) – – –, heart(z + 30 mm) . (a) Impedance curves. (b) ICG curves.
Table 5 summarizes all altered values due to tissue conductivity changes (supplement available from stacks.iop.org/PM/35/1451/mmedia). Figure 10 shows ICG and impedance curves for organ displacements during respiration and due to interindividual organ positions as discussed in section 3.1. The maximal increase in impedance (0.05 ) is due to a displacement of the heart of 30 mm in z-direction, the maximal decrease of 0.02 is due to a displacement of the heart of 30 mm in z-direction. Minor temporal shifts of the maximum can be observed for a displacement of the heart of 30 mm in z-direction (+16 ms), a displacement of the heart of 30 mm in z-direction (−25 ms) and a displacement of the abdominal organs (−17 ms). In addition, all signals have altered morphology. Thus, a temporal change of characteristic points in the ICG is expected. The C-point shows only a neglectable temporal shift of 8 ms for displacements of the heart in z-direction whereas a B-point shift of 16 ms is observed for a displacement of the heart of 30 mm in y-direction 4.2.2. Organ displacements.
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Figure 11. Impedance curves for multiple frequencies, simulated (left) and measured
(right): 5 kHz ——, 20 kHz - - - -, 50 kHz , 100 kHz · · · · · ·. (a) Simulated impedance curves. (b) Measured impedance curves.
and a shift of 8 ms for combined displacement of heart and abdomen. The X-point is shifted by −16 ms for heart displacements of 30 mm in z- and y-direction. For all other geometric displacements, a temporal shift of the X-point of −33 ms is observed. The maximum of the ICG curve deviates for every organ displacement slightly. The highest increase is due to the displacement of abdominal organs (+0.314 s−1 ), whereas the lowest decrease is due to a displacement of the heart in y-direction (−0.175 s−1 ). The results for all displacements for SV calculation are summarized in table 6 (supplement available from stacks.iop.org/PM/35/1451/mmedia). 4.3. Multi-frequency analysis
A multi-frequency analysis was conducted to verify the performance of the FEM model to reflect frequency-dependent changes of the ICG curve. Therefore, continuous impedances were simulated at 4 frequencies: 5 , 20 , 50 and 100 kHz (Ulbrich et al 2011). Impedances were measured at standard ICG positions on the thorax using a AFE4300 from Texas Instruments, TX, USA. Figure 11 visualizes measured and simulated curves for all frequencies. These figures show that the maximum of the impedances decreases with frequency. From 5 to 100 kHz, the simulated impedance decreases by 28% whereas the measured impedance decreases by 50%. Z0 shows the same behavior for increasing frequency. Note that only aortic diameter changes were taken into consideration for the simulations since no data was available for the frequency-dependent behavior of erythrocyte orientation. This explains the higher decrease of the measured impedance for increasing frequencies, most likely caused by erythrocyte orientation. 5. Discussion Four dynamic sources were successfully included in the presented model, simulating the bioimpedance for one heartbeat: aortic expansion, heart contraction, lung perfusion and erythrocyte orientation. Our results suggest that since heart contraction and lung perfusion nearly compensate each other, only aortic expansion and erythrocyte orientation contribute to the dynamic impedance signal. 1464
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The very good correlation of simulated curves with measured curves shows that the morphology of the signal seems to be reasonably well reproduced and thus allows the extraction of all necessary characteristic points to calculate SV. This is an achievement by using FEM simulations with volumetric and conductivity based dynamic changes which was not reported in literature before. The model-inherent left ventricular volume change of 80 ml (see chapter 3.2) was reproduced quite well by all algorithms typically used for SV estimation (2)–(4), except the Kubicek algorithm (1). With the new Bernstein–Osypka equation (4), the SV is estimated almost exactly (79.3 ). It should be noted that physiologic LVET values for healthy subjects range from 200 ms to 330 ms (Lance and Spodick 1976). Here, we assumed a LVET of 300 ms according to the dicrotic notch of the aortic blood pressure. Therefore, based on our model in combination with the classically used characteristic points, overestimated values are obtained. Nevertheless, it is known from literature that classically extracted X-points are the reason for overestimated LVET values reflected by our simulations. Another reason for an overestimated LVET is the lack of a B-point notch in the simulated curves which would be located behind the zero crossing of the ICG curve, which is used for B-point extraction here. It should be noted, that standard definitions of the B-point are also still under debate because they do not necessarily match the opening of the aortic valve (Carvalho et al 2011). In addition, a LVET of 384 ms is not unrealistic since certain pathologies prolong LVET to more than 440 ms (Wigle et al 1967). Based on the given values CO is 5.65 l min−1 , showing that Kubicek’s equation underestimates CO by 2.25 l min−1 , which is supported by measurements comparing CO assessed by thermodilution and ICG (Van De Water et al 2003). A sensitivity analysis was made to analyze the influence of tissue conductivity changes and organ displacements using parameters found in literature and reflecting realistic scenarios. Organ movements do not influence characteristic points significantly. Table 5 shows that only conductivity changes of blood and muscle tissue have a significant influence on characteristic points as well as the simulated impedance. Temporal shifts of multiples of 8.2 ms are due to discretization noise which means that we can assume that there is no difference in estimated LVET due to conductivity changes. Nevertheless, significant impedance changes are observed leading to a maximum SV change of 16% due to increased muscle conductivity. Since increased muscle conductivity reroutes the current paths away from blood vessels and aorta due to its high percentage of the total body volume, it is clear that this lowers the dynamic influence of blood related changes on the impedance signal. Hence, this shows the importance of not mixing tissue property databases in order to avoid e.g. muscle conductivity to have a wrong conductivity related to other tissue conductivities. Furthermore, this result suggests that a calibration is needed for measuring people with an increased muscle conductivity, e.g. due to physical education. In addition, the influence of blood conductivity changes on the impedance signal strengthens the assumption that conductivity changes due to erythrocyte orientation influence SV estimation in the same way. To sum up, conductivity changes of most tissues do not influence the simulation results which makes the model robust to implemented tissue property databases. Organ displacements of heart and abdomen in general influence characteristic points as well as the dynamic impedance. Changes in Z0 and B-point can be neglected but a displacement of the heart of 30 mm in -z-direction causes an underestimation of SV of 12% mainly due to a decrease of the X-point and thus estimated LVET. Since there is no significant change in any other value contributing to the SV and the X-point deviates by −41.3 which is a multiple of 8.2, this is supposed to be a result of high discretization noise. Kubicek assumed that aortic volume changes in the thorax are the main (and the only) source for the dynamic impedance change (Raaijmakers et al 1997) which is partly supported 1465
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by our findings since the aortic diameter change seems to be determining the morphology of the impedance signal and hence the characteristic points. However, erythrocyte orientation as dynamic signal contributes substantially to 50% of the impedance signal, more than the aorta, mainly by amplifying the signal during systole. This result partly agrees with Bernstein’s newest assumption that due to blood acceleration during systole, erythrocyte orientation is the main contributor to the signal (Bernstein and Lemmens 2005). Hence, both approaches probably do not describe the ICG signal comprehensively. Previous related works could not come to the same conclusion, since their approaches have only limited explanatory power because the amount of contribution of different sources vary depending on the point of time, as shown in figure 6.
6. Conclusion The aim of this study was to create a model which is suitable to simulate current paths and voltages during dynamic impedance measurements on the human thorax, to investigate the impact of four dynamic sources on the ICG signal to reproduce experimentally observed signals. Therefore, the complex dynamic impedance should be simulated with a high temporal resolution. First, a simplified model based on human MRI data was successfully created containing two volumetric dynamic sources (heartbeat and aortic expansion) as well as two conductive dynamic sources (lung perfusion and erythrocyte orientation) based on measured physiological data. The results show very good correlation with measured curves produced by a commercially available ICG device which indicates that the model simulates ICG sources reasonably well. Second, it was shown that the ICG signal is mainly composed of the aortic impedance change and the blood conductivity change due to erythrocyte orientation. The morphology of the ICG signal seems to be mainly determined by the aortic impedance, whereas erythrocyte orientation, whose peak impedance derivative occurs simultaneously with the peak acceleration of blood, increases the signal strength. This supports partly Kubicek’s and partly Bernstein’s assumption. Third, standard algorithms to extract characteristic points, and algorithms to calculate SV, could be applied to the data to estimate hemodynamic parameters. The calculated SV with the new Bernstein–Osypka equation matches best with the implemented left ventricular heart volume change of 80 ml, however, LVET is overestimated by the algorithms and the simulated curves. This might indicate that the characteristic points typically mentioned in literature do not match well with the underlying physiological processes. Fourth, results of sensitivity analyses concerning conductivity changes due to differences in empirically assessed databases and concerning physiologic organ displacements show that this model is reliable enough to extract hemodynamic parameters such as LVET and SV from simulated impedance curves. In addition, the results suggest that equations for SV estimation have to be adapted for subjects with an increased muscle conductivity. Fifth, a similar behavior of simulated and measured impedance curves between 5 kHz and 1 MHz support the usage of the proposed model. In summary, a valuable tool to simulate ICG signals was developed which allows to analyze the behavior of different sources and their impact on the signal—including a focus on pathologies in the future. The approach with simplified geometries in combination with adjustable temporal resolution allows fast and inexpensive calculations. Nevertheless, several improvements can be made in the future. Wave propagation on the aorta could be included, and a correct anatomic representation of the aorta and heart would be preferable. Real MRI 1466
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data could be used for the representation of organs and shape of the human body. Pathologies, such as heart failure, should be simulated to identify problems when making measurements in patients suffering from this disease. Acknowledgment This work was funded by ‘HeartCycle’, an EU-project on compliance and effectiveness in Heart Failure and Coronary Heart Disease closed-loop management. References Bernstein D P and Lemmens H J M 2005 Stroke volume equation for impedance cardiography Med. Biol. Eng. Comput. 43 443–50 Brown B H, Sinton A M, Barber D C, Leathard A D and McArdle F J 1992 Simultaneous display of lung ventilation and perfusion on a real-time EIT system Proc. Annu. Int. Conf IEEE Engineering in Medicine and Biology Society vol 5 pp 1710–1 Carrara N 2010 Dielectric Properties of Body Tissues http://niremf.ifac.cnr.it/tissprop Carvalho P, Paiva R P, Henriques J, Antunes M, Quintal I and M¨uhlsteff J 2011 Robust characteristic points for ICG: definition and comparative analysis Biosignals’11: Int. Conf. on Bio-inspired Systems and Signal Processing pp 161–8 Cotter G, Schachner A, Sasson L, Dekel H and Moshkovitz Y 2006 Impedance cardiography revisited Physiol. Meas. 27 817–27 Critchley L A H 1998 Impedance cardiography—the impact of new technology Anaesthesia 53 677–84 Darovic G 2002 Hemodynamic Monitoring: Invasive and Noninvasive Clinical Application (Philadelphia, PA: Saunders) Debski T T, Zhang Y, Jennings J R and Kamarck T W 1993 Stability of cardiac impedance measures: aortic opening (b-point) detection and scoring Biol. Psychol. 36 63–74 Faes T J C, van der Meij H A, de Munck J C and Heethaar R M 1999 The electric resistivity of human tissues (100 Hz–10 MHz): a meta-analysis of review studies Physiol. Meas. 20 R1–R10 Feng W, Nagaraj H, Gupta H, Lloyd S G, Aban I, Perry G J, Calhoun D A, Dell’Italia L J and Denney T S Jr 2009 A dual propagation contours technique for semi-automated assessment of systolic and diastolic cardiac function by CMR J. Cardiovasc. Magn. Reson. 11 30 Gabriel C, Gabriel S and Corthout E 1996 The dielectric properties of biological tissues Phys. Med. Biol. 41 2231–49 Gaw R 2010 The effect of red blood cell orientation on the electrical impedance of pulsatile blood with implications for impedance cardiography PhD Thesis Queensland University of Technology, School of Physical and Chemical Sciences Gerscovich E O, Cronan M, McGahan J P, Jain K, Jones C D and McDonald C 2001 Ultrasonographic evaluation of diaphragmatic motion J. Ultrasound Med. 20 597–604 Granerus G and Elg R 1982 Stroke volume measurement by impedance cardiography using a formula based on the dz waveform Clin. Phys. Physiol. Meas. 3 131–9 Greenfield J C Jr and Patel D J 1962 Relation between pressure and diameter in the ascending aorta of man Circ. Res. 10 778–81 Grimnes S and Martinsen O G 2000 Bioimpedance and Bioelectricity Basics (New York: Academic) Guyton A C and Hall J E 2006 Textbook of Medical Physiology 11th edn (Philadelphia, PA: Saunders) Hoetink A E, Faes T J, Visser K R and Heethaar R M 2004 On the flow dependency of the electrical conductivity of blood IEEE Trans. Biomed. Eng. 51 1251–61 IT’IS Foundation 2012 Documentation Dielectric Properties Database www.itis.ethz.ch/itis-for-health/ tissue-properties/database Kanai H, Sakamoto H and Miki M 1976 Impedance of blood: the effects of red cell orientation Digest of the 11th Int. Conf. on Medical and Biological Engineering vol 11 pp 238–9 Kauppinen P K, Hyttinen J A and Malmivuo J A 1998 Sensitivity distributions of impedance cardiography using band and spot electrodes analyzed by a three-dimensional computer model Ann. Biomed. Eng. 26 694–702 Kim D W, Baker L E, Pearce J A and Kim W K 1988 Origins of the impedance change in impedance cardiography by a three-dimensional finite element model IEEE Trans. Biomed. Eng. 35 993–1000 1467
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Lance V Q and Spodick D H 1976 Heart rate–left ventricular ejection time relations Br. Heart J. 38 1332–8 L¨anne T, Sonesson B, Bergqvist D, Bengtsson H and Gustafsson D 1992 Diameter and compliance in the male human abdominal aorta: influence of age and aortic aneurysm Eur. J. Vasc. Surg. 6 178–84 medis GmbH 2012 Niccomo—Non-Invasive Continuous Cardiac Output Monitor www.medis-de.com/ index.php?option=com_content&task=view&id=24&Itemid=49&lang=en National Library of Medicine 1986 The Visible Human Project www.nlm.nih.gov/research/visible/ visible_human.html Northridge D B, Findlay I N, Wilson J, Henderson E and Dargie H J 1990 Non-invasive determination of cardiac output by doppler echocardiography and electrical bioimpedance Br. Heart J. 63 93–97 Patterson R P, Wang L, Raza B and Wood K 1990 Mapping the cardiogenic impedance signal on the thoracic surface Med. Biol. Eng. Comput. 28 212–6 Puwal S 2013 Two-domain mechanics of a spherical, single chamber heart with applications to specific cardiac pathologies SpringerPlus 2 1–10 Raaijmakers E, Faes Th J C, Goovaerts H G, de Vries P M J M and Heethaar R M 1997 The inaccuracy of Kubicek’s one-cylinder model in thoracic impedance cardiography IEEE Trans. Biomed. Eng. 44 70–76 Raaijmakers E, Faes T J, Scholten R J, Goovaerts H G and Heethaar R M 1999 A meta-analysis of three decades of validating thoracic impedance cardiography Crit. Care Med. 27 1203–13 Raaijmakers E, Marcus J T, Goovaerts H G, de Vries P M J M, Faes Th J C and Heethaar R M 1996 The influence of pulsatile blood flow on blood resistivity in impedance cardiography 18th Int. Conf. IEEE Engineering in Medicine and Biology Society vol 5 pp 1957–8 Sakamoto K, Muto K, Kanai H and Iizuka M 1979 Problems of impedance cardiography Med. Biol. Eng. Comput. 17 697–709 Sherwood A, Royal S A, Hutcheson J S and Turner J R 1992 Comparison of impedance cardiographic measurements using band and spot electrodes Psychophysiology 29 734–41 Summers R L, Shoemaker W C, Peacock W F, Ander D S and Coleman T G 2003 Bench to bedside: electrophysiologic and clinical principles of noninvasive hemodynamic monitoring using impedance cardiography Acad. Emerg. Med. 10 669–80 Ulbrich M, Marleaux B, M¨uhlsteff J, Schoth F, Koos R, Teichmann D and Leonhardt S 2013 High spatial and temporal resolution 4d FEM simulation of the thoracic bioimpedance using MRI scans ICEBI’13: Int. Conf. on Electrical Bioimpedance (Heilbad Heiligenstadt, Germany) (International Society of Electrical Bioimpedance) Ulbrich M, M¨uhlsteff J, Walter M and Leonhardt S 2011 Simulation of continuous spectroscopic bioimpedance measurements for impedance cardiography Lecture Notes on Impedance Spectroscopy: Measurement, Modeling and Applications vol 2 (Boca Raton, FL: CRC Press) pp 139–43 Van De Water J M, Miller T W, Vogel R L, Mount B E and Dalton M L 2003 Impedance cardiography— the next vital sign technology? Chest 123 2028–33 Visser K R, Lamberts R, Korsten H H M and Zijlstra W G 1976 Observations on blood flow related electrical impedance changes in rigid tubes Eur. J. Physiol. 366 289–91 Wang L and Patterson R 1995 Multiple sources of the impedance cardiogram based on 3-D finite difference human thorax models IEEE Trans. Biomed. Eng. 42 141–8 Wang Y, Haynor D R and Kim Y 2002 A finite-element study of the effects of electrode position on the measured impedance change in impedance cardiography IEEE Trans. Biomed. Eng. 48 1390–401 Wang Y, Riederer S J and Ehman R L 2005 Respiratory motion of the heart: kinematics and the implications for the spatial resolution in coronary imaging Magn. Reson. Med. 33 713–9 Wieskotten S 2008 Modellbasiertes Assistenzsystem bei der Diagnose und Therapie von Mangelern¨ahrung PhD Thesis Technische Universit¨at Darmstadt, Germany Wigle E D, Auger P and Marquis Y 1967 Muscular subaortic stenosis—the direct relation between the intraventricular pressure difference and the left ventricular ejection time Circulation 36 36–44 Zhao T X, Brown B H, Nopp P, Wang W, Leathard A D and Lu L Q 1996 Modelling of cardiac-related changes in lung resistivity measured with EITS Physiol. Meas. 17 A227–34
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Influence of physiological sources on the impedance cardiogram analyzed using 4D FEM simulations
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Institute of Physics and Engineering in Medicine Physiol. Meas. 35 (2014) 1451–1468
Physiological Measurement
doi:10.1088/0967-3334/35/7/1451
Influence of physiological sources on the impedance cardiogram analyzed using 4D FEM simulations 2 Mark Ulbrich 1 , Jens Muhlsteff ¨ , Steffen Leonhardt 1 1 and Marian Walter 1
RWTH Aachen University, Philips Chair for Medical Information Technology, Pauwelsstrasse 20, D-52074 Aachen, Germany 2 Philips Research, High Tech Campus 34, 5656 AE Eindhoven, The Netherlands E-mail: [email protected] Received 26 December 2013, revised 25 March 2014 Accepted for publication 13 May 2014 Published 5 June 2014 Abstract
Impedance cardiography is a simple and inexpensive method to acquire data on hemodynamic parameters. This study analyzes the influence of four dynamic physiological sources (aortic expansion, heart contraction, lung perfusion and erythrocyte orientation) on the impedance signal using a model of the human thorax with a high temporal resolution (125 Hz) based on human MRI data. Simulations of electromagnetic fields were conducted using the finite element method. The ICG signal caused by these sources shows very good agreement with the measured signals (r = 0.89). Standard algorithms can be used to extract characteristic points to calculate left ventricular ejection time and stroke volume (SV). In the presented model, the calculated SV equals the implemented left ventricular volume change of the heart. It is shown that impedance changes due to lung perfusion and heart contraction compensate themselves, and that erythrocyte orientation together with the aortic impedance basically form the ICG signal while taking its characteristic morphology from the aortic signal. The model is robust to conductivity changes of tissues and organ displacements. In addition, it reflects the multi-frequency behavior of the thoracic impedance. Keywords: impedance cardiography, ICG, finite element simulations, lung perfusion, erythrocyte orientation, characteristic points, stroke volume
S Online supplementary data available from stacks.iop.org/PM/35/1451/mmedia
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0967-3334/14/071451+18$33.00
© 2014 Institute of Physics and Engineering in Medicine Printed in the UK
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1. Introduction In Europe, the ever-increasing numbers of geriatric patients and associated diseases are leading to increasing costs and burden on medical resources. Therefore, methods to treat elderly persons more (cost-)effectively are needed by improving the diagnostic processes and monitoring those diseases prevalent among the elderly. A common cause of death in western Europe is heart failure. Measures for its severity are hemodynamic parameters, including stroke volume (SV) or cardiac output (CO). Until now, the gold standards to measure these parameters are the thermodilution technique using pulmonary artery catheters and echocardiography using ultrasound imaging. However, the risks associated with estimating CO by means of catheters include infections, sepsis and arrhythmias, as well as increased morbidity and mortality (Darovic 2002). For echocardiography, expensive devices and trained personnel are needed. In addition, this technique bears a higher inter-individual variation for repeated measurements compared to impedance cardiography (ICG) (Northridge et al 1990). At present, ICG is not commonly used as a diagnostic method because it is not considered reliable (Cotter et al 2006, Raaijmakers et al 1999). One reason for this is the controversially discussed accuracy of the technology concerning the calculation of SV, especially in critically ill patients (Critchley 1998). Another reason is that contributions of processes such as certain conductivity changes in the human body to measured impedance changes are largely unknown. One way to analyze where the electrical current paths run, and which tissue or organ makes a significant contribution to the measurement result, is to use computer simulations based on the finite element method. Many research groups have already worked with FEM models to analyze various issues concerning ICG which cannot be analyzed in vivo. Different models were used to analyze effects of electrode positions (Wang et al 2002) and electrode type (Kauppinen et al 1998) as well as contributions of organs to the ICG (Sakamoto et al 1979). The question of preferred electrode type and positions could thus be solved, but contradictory results were discussed concerning the contribution of dynamic sources to the ICG signal. Kim et al (1988) reported a linear relationship between aortic blood volume change and impedance change and the highest impact of ventricular blood volume change. The effect of lung resistivity change and blood resistivity change are supposed to be even smaller (only 40% of the aortic blood volume change) (Kim et al 1988). In contrast, Wang and Patterson identified blood resistivity changes as major contributor to the signal, lung conductivity change as secondary contributor and volume changes as last important influence on the ICG (Wang and Patterson 1995). Another research group (Wang et al 2002) stated that the volume change due to heart contraction is the major contributor to the signal whereas other dynamic sources contribute equally. One possible reason for these inconsistent statements is that only discrete points in the cardiac cycle were analyzed in these studies. The simplest approach is to simulate end-systolic volumes (Kim et al 1988), other works used end-systolic and end-diastolic (Wang et al 2002) or additionally end-inspiratory and end-expiratory volumes (Sakamoto et al 1979). Besides temporal resolution, the aforementioned models differ in geometry and implemented tissue parameters which might be other reasons for opposing results. Earlier works used cylinder models (Raaijmakers et al 1997), simple plumbers models (Sakamoto et al 1979), three-dimensional representations of the thorax using anatomical maps (Kim et al 1988) and static models derived from static MRI scans by segmentation (Wang et al 2002). In general, a model which comprises all possible and known sources for dynamic and static impedances should be used for simulations. The best solution would be of course to use dynamic MRI data to create a model which we tried in an earlier project (Ulbrich et al 1452
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2013). In clinical practice, one can get good dynamic images of the heart but it is not possible to get an ECG gated representation of major blood vessels, such as aorta, since this would include a huge amount of contrast agent to be injected in the subject. In addition, even if it would be possible to get scans of a thorax with a high temporal resolution, these geometries would be far too complex to be solved in a reasonable amount of time. Another limitation is the amount of memory (RAM) of computers for this problem which again suggests the implementation of simplified geometries. To be more precise: an MRI thorax model with 11 million mesh cells consumes 48 GB of RAM and takes weeks to be simulated with only providing a temporal resolution of 10 frames per heart cycle. This is also due to the restriction of the chosen simulation software to use only one core for calculations. As described in section 2.3, only one reliable dataset of human tissue parameters exists in literature. Unfortunately, none of the previous works used this dataset. Mixed parameters of different research groups, often in combination with parameters from varying animal studies (pigs, dogs, cows) were used, making it difficult to interpret and to transfer the simulation result. To sum up, none of the aforementioned models provide the possibility to generate timecontinuous impedance curves with adjustable temporal resolution based on physiological measurements, including reliable human datasets of tissue parameters and reflecting volumetric and conductivity-based dynamic changes in the human thorax, to analyze the ICG by extracting characteristic points with available algorithms used in practice. This aim is realized in this work by simulating the impact of four dynamic sources (aortic expansion, heart contraction, lung perfusion and erythrocyte orientation) on the ICG signal including a sensitivity analysis of the contribution of tissue conductivity and organ movement on the measured signal. By establishing such a model, it will be possible to identify reasons for the inaccuracy of ICG in combination with pathologies and to improve measurement techniques in the future. 2. Background Since the aim of this work is to analyze the impact of specific sources on the impedance cardiogram, we first present some information on bioimpedance measurements and physiological sources for impedance measurements. 2.1. Bioimpedance measurements
For bioimpedance measurements, two outer electrodes are used to inject a small alternating current into the human body and (via two inner electrodes) the voltage drop is measured to calculate the complex impedance. Although a bipolar measurement technique could be used, the tetrapolar technique has the advantage that the electrode impedances do not contribute to the measured voltage. When a frequency spectrum of 5 kHz–1 MHz is used to measure the bioimpedance for each frequency, this method is called ‘bioimpedance spectroscopy’ (BIS). This frequency range (called β-dispersion) is generally the most interesting for diagnostic purposes, since physiological and pathophysiological processes cause changes in body impedance (Grimnes and Martinsen 2000). BIS is commonly used to assess the body composition of humans. If only one frequency of this spectrum is used to continuously measure the bioimpedance on the thorax, this method is called ICG. Since ICG operates at a single frequency between 20–100 kHz, one continuous curve in the β-dispersion range can be obtained by ICG measurements. By measuring the impedance continuously, timedependent hemodynamic parameters can be defined from the measured impedance curve using its temporal derivative. Figure 1 shows an idealized ICG wave with characteristic features. 1453
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Figure 1. ICG wave (−|dZ(t )/dt|) with its characteristic points.
The characteristic points of this derivative are defined as follows (Summers et al 2003). • • • • •
Point A: start of the electromechanical systole. Point B: opening of the aortic valve. Point C: maximal mechanical contraction. Point X: closure of aortic valve. Point O: opening of the mitral valve
The left ventricular ejection time (LVET) is defined as the time between opening and closure of the aortic valve. The standard values for |dZ(t )/dt|max are 1–2 s−1 and for tLVET 200–340 ms (Granerus and Elg et al 1982, Lance and Spodick 1976). The SV (in ml) measured with ICG depends on the underlying model, for which multiple equations exist, as follows (Bernstein and Lemmens 2005): tLVET l 2 dZ · · 2 (Kubicek) (1) SV = σb dt max Z0 tLVET (0.17 · H )3 dZ · · SV = 4.2 dt max Z0 SV = δ ·
tLVET (0.17 · H )3 dZ · · 4.2 dt max Z0
VITBV SV = · ζ2
dZ dt
tLVET · √ Z0 max
(Sramek)
(2)
(Bernstein–Sramek)
(3)
(Bernstein–Osypka).
(4)
All equations are influenced by three values: the LVET tLVET , the static thoracic base impedance Z0 and the maximum of the derivative of the continuous impedance |dZ/dt|max . Equation (1), first introduced by Kubicek, calculates the SV by employing the blood 1454
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conductivity (σb ) and the distance between the measuring electrodes (l). Sramek utilized the patient’s height (H) instead of the electrode distance l (equation (2)). In equation (3), the factor δ is the actual weight divided by the ideal weight; this was introduced by Bernstein (Van De Water et al 2003). The most recent equation (equation (4)) was also developed by Bernstein in 2005 and here factor VITBV = 16 · Weight1.02 is the intra-thoracic blood volume and ζ the index of transthoracic aberrant conduction (Bernstein and Lemmens 2005). His equation assumes the velocity of the blood to be the only contributor to the signal. The first three equations are based on pure volumetric changes. Using one of these equations, CO can be calculated by: l . (5) CO = SV · HR min 2.2. Dynamic physiological sources
Besides the static influence of each tissue on the measured impedance caused by conductivity and permittivity of different tissues and their volume inside the human body, several dynamic sources alter the impedance signal. All volume changes and conductivity changes influence the measured impedance of the thorax. The main contributors to the dynamic impedance are: blood conductivity changes, changes of conductivity due to lung perfusion (blood delivery), and volume changes by heart contraction and by aortic expansion. The conductivity of blood changes during a heartbeat is caused by erythrocytes (red blood cells) only, since hemolyzed blood or blood plasma have no effect on the impedance change. In stationary blood, erythrocytes are oriented arbitrarily due to Brownian motion and, therefore, its resistivity is isotropic (Hoetink et al 2004). This effect can be observed at the end of diastole. The shape of the erythrocytes is biconcave and they will reorientate in a way that minimizes motion shear stress caused by the increase of blood velocity. Thus, with increasing alignment, blood resistivity decreases and becomes anisotropic in the direction of blood flow since the current may flow through a larger area of low-resistance plasma (Visser et al 1976, Kanai et al 1976). This means that the measured bioimpedance is mainly affected by erythrocyte orientation due to blood flow in vessels in the direction of the excitation current flow. This effect is visible during systole, especially in the rapid ejection phase during early systole and is frequency-dependent having a strong influence on ICG measurements around 100 kHz. However, since the current flows through cells for frequencies exceeding the β-dispersion range, the effect of erythrocyte orientation is negligible for frequencies above 1 MHz (Gaw 2010). 2.3. Static tissue parameters
For the non-dynamic electrical behavior of body tissue, conductivity (σ ) and permittivity (r ) values have to be assigned for each tissue type at the selected frequency since these parameters change due to dispersion. It is difficult to obtain reliable electric parameters of tissues since they cannot be acquired in vivo and, after death, these parameters change rapidly. For example, heart muscle tissue changes irreversibly after only 20 min because cells cannot maintain the concentration gradient of electrolytes between extra- and intracellular space without bloody supply. Water enters cells and breaks up the cell membranes so that it is no longer possible to observe the dispersion effect between 5 kHz and 1 MHz (Wieskotten 2008). Several groups aimed to assess these parameters in vivo and in vitro, mainly by examining animals. In a metaanalysis of review studies (Faes et al 1999), the aim was to obtain a consensus between these various studies. A total of 103 resistivities for 21 different tissues were taken into account; 1455
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analysis showed that the resistivity of most tissues do not show a significant deviation (within a 95% confidence interval). Only bone, fat and stratum corneum show significantly higher values. In order to avoid errors introduced by differences in measurement conditions (e.g. inter-rater errors or inter-subject variations) we decided to use data from one study only. The most suitable dataset was provided by Gabriel et al (1996) who examined human tissues 24–48 h after death. That way, a dataset containing all tissues of interest could be created between 10 Hz to 20 GHz at body temperature (Gabriel et al 1996). Since this is the most complete, reliable and up-to-date database (IT’IS Foundation 2012, Carrara 2010) it has been used by various groups and is also used for the present study. 3. Methods Since the geometry of the thorax and its organs is essential for the current distribution during ICG measurements and determines the contribution of various static and dynamic sources to the ICG signal, FEM simulations were chosen to simulate ICG measurements. R from Computer Simulation Technology, Darmstadt, Germany was used to CST EM Studio perform the simulations which were computed on a personal computer with a 64 bit operating R Xeon R 5240 processor with 2 cores and 24 GB RAM. The excitation system, an Intel frequency in the simulations was set to 100 kHz because most ICG devices operate around this frequency. Since this wavelength (λ = 340 m) is much higher than our measuring volume, the human thorax, the low frequency electroquasistatic solver (electroquasistatic Maxwell’s equations) was employed. Using a discretization density of 50 units, each model is composed of 1.5 million tetrahedrons. Besides this global discretization, a finer local discretization was used for organs with altering geometry in order to obtain accurate results for small geometry changes. Figure 13 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) presents these discretizations. 3.1. Simulation model
To ensure a good representation of a human thorax, the basis for the volumes representing each organ is an MRI dataset (known as the Visible Human of the Visible Human Project© dataset) from the National Library of Medicine, USA (National Library of Medicine 1986). Since this dataset contains no information about dynamics, a new model was created based on the geometries of the Visible Human using simplified geometries, such as cylinders, spheres and frustums. The new model in combination with the MRI dataset is shown in figure 12 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia). This abstracted model corresponds well with the volume of major organs, although their shape is not matched perfectly (see lung wings in figure 13). Figure 2 describes geometries and volumes of all tissues of the implemented model. A more detailed description of all volumes can be found in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) (table 1). The model is composed of static volumes from the Visible Human dataset and new dynamic volumes: aorta and heart. The static volumes include the tissues fat, muscle, bone, lung, blood vessels and abdominal organs. Since the impedance change of abdominal organs plays a subordinate role for the ICG signal during a heartbeat, a simplification was made in that the abdominal part of the model was filled with a uniform ‘tissue mixture’. Then, an average permittivity and conductivity of all abdominal organs has been assigned to this tissue. Table 2 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) lists the conductivity σ and permittivity r values for all static tissues, taken from Gabriel et al (1996). 1456
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A sensitivity analysis for these parameters on the model output was made since measured tissue parameters vary among research groups. This influences the variability of models and has an impact on the ICG morphology as well as on extracted parameters from the measured curve. Therefore, mean resistivities (ρmean ) and their 95% confidence intervals were used to calculate conductivity deviations of each tissue (Faes et al 1999). That way, the deviation caused by higher σhigh and lower conductivities σlow was obtained and the tissue conductivity of one tissue was changed to analyze its influence on the impedance and ICG curve. In addition, various organ displacements were simulated in order to take interindividual organ positions as well as organ movements during respiration into account. The diaphragm is a dome-shaped, fibromuscular partition between the thoracic and abdominal cavities which accounts for 75% of the increase in lung volume during quiet inspiration. Deep breathing is characterized by expansion of the abdomen rather than the chest and causes a higher motion and displacement of the diaphragm up to 6 cm on average (Gerscovich et al 2001). This craniocaudal displacement (+z direction) was simulated by moving the abdominal organs by 6 cm. During respiration, the heart changes its position about 3 cm in craniocaudal direction (Wang et al 2005). This was implemented in combination with abdominal organ displacement. In addition, intraindividual differences in heart position were taken into account by simulating displacements in craniocaudal direction (3 cm), 3 cm in caudocranial direction (−z) and 3 cm in dorsoventral direction (+y). For reasons of simplicity, ring electrodes were used in the model at neck and abdomen, although spot electrodes are typically used nowadays for bioimpedance measurements since studies have shown that the highest signal can be obtained by this configuration (Patterson et al 1990). In addition, this configuration for ICG measurements does not affect the measurement results (Sherwood et al 1992). 1457
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3.2. Model dynamics
Dynamic sources were implemented by model functions matching typical physiological parameters based on measured data. Coupling of organs and the other physiological dynamic sources were temporally matched. The largest chamber of the human heart is the left ventricle, which is approximately conical in shape (Guyton and Hall 2006). Hence, we focus on using the left ventricle as representation for the single chamber spherical heart since the left ventricle dominates volumetric changes. This is a common approach found in literature to analyze electromechanical properties of the heart (Puwal 2013). The radius of a sphere representing the heart was altered to mimic the heartbeat while assuming a SV of 80 ml. The left ventricular volume change obtained by MRI data was used as physiologic basis for the radius change (Feng et al 2009). This change ranges from 38.5 to 33.8 mm and is shown in figure 3(a). Due to the constraints explained in section 1, the aortic expansion has to be modeled by using simple geometries. That way, the necessary sources can be used to build a model with volume changes creating high temporal resolution ICG curves. PhysioNet aortic blood pressure data from humans were used to model the aortic expansion, since it is proportional to the aortic blood pressure (see equation (6))3
P · R0 · extensibility . (6)
R = 100 Here, R0 is the diastolic radius of the aorta. This pressure–diameter relationship was estimated directly in the ascending aorta of man in ten patients undergoing open-heart surgery. The diameter was measured by means of an electrical strain-gauge caliper sutured to the vessel wall. The intravascular pressure was measured using a gauge needle connected directly to a strain gauge (Greenfield and Patel 1962). The aortic blood pressure has then been scaled to fit the requirement for the maximum aortic expansion of 20% (L¨anne et al 1992). Thus, the diameter of the aorta ranges from 25 to 30 mm (see figure 3(b)). This is of course a simplification, since we use a quasi-stationary approach and neglect the effects of wave propagation along the aorta. Since the lung receives the entire CO, its conductivity change due to lung perfusion will have a high impact on the measured ICG signal. This was implemented by assuming a 3 National Institute of Biomedical Imaging and Bioengineering. Physionet—the research resource for complex physiologic signals.
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maximum conductivity change of lung tissue of 10% (Brown et al 1992). Based on measured conductivity changes with electrical impedance tomographic spectroscopy, a dataset was created (Zhao et al 1996). The conductivity change due to lung perfusion is shown in figure 4(a). Since blood volume changes in a volume of interest alter the impedance signal, changes in blood resistivity in major blood vessels will have a high impact. Since blood resistivity changes of 15% due to erythrocyte orientation are reported in literature, measured conductivity curves were used as base data. Together with a diastolic conductivity of 0.702 92 S m−1 , this results in a maximum conductivity of 0.808 36 S m−1 during systole (Raaijmakers et al 1996). The resulting curve is shown in figure 4(b). For every point in time of one heartbeat, a new model had to be created since the discretization of the simulated volume has to be recalculated due to the altered thorax geometry; this resulted in 103 models representing a temporal resolution of 125 Hz.
4. Results 4.1. Source identification
For validation purposes, the simulated curves for 100 kHz were compared to real measured TM data. These data were acquired using the Niccomo device (medis, Ilmenau, Germany) measuring a male human (medis GmbH 2012). To compare both curves, Z0 was subtracted. It should be mentioned that simulated Z0 = 58.8 is higher than typically measured values (between 20 and 48 (Critchley 1998)). However, higher values can also be obtained measuring healthy subjects. One reason for the high simulative Z0 value is that the parameter set for each tissue is obtained from the data of Gabriel (see table 2). It can be seen that the morphology of the measured and the simulated signal is very similar (figure 5). In addition, the peak-to-peak impedance of the sum signal (Zmax = 0.215 ), as well as the maximum of its derivative (|dZ/dt|max = 1.736 s−1 ), are in the range of typical ICG signals. Furthermore, the cross-correlation factor is r = 0.89; although the curves do not match perfectly, it is in the range of interpersonal variability. Figure 6 shows the simulation results of the impedance and its temporal derivative for each single source and for the sum signal which is composed of the four single source signals. Note that the impedances and the ICG curves are drawn invertedly, since this is common in literature. 1459
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Figure 5. Measured - - - - and simulated —— impedance signal (Z(t ) − Z0 ).
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To quantify the contribution of each source to the impedance and the ICG signal, the point in time at which the curves have their maximum was analyzed. Thus, the absolute contribution of each signal as well as the percentaged values with respect to the sum signal, are obtained; the results are shown in table 3 (supplement available from stacks.iop.org/PM/35/1451/mmedia). It can be stated that the aortic signal seems to be the cause for the shape of the sum signal despite its low maximum impedance of 0.082 . The signal caused by erythrocyte orientation increases the signal strength with a maximum impedance change of 0.11 and a relative contribution of 50.59%. Interestingly, lung perfusion and the signal caused by heart contraction nearly compensate themselves. Hence, the simulation results suggest that erythrocyte orientation together with volumetric changes of the aorta might play a major role in forming the ICG signal. To assess the LVET, B- and the X-point have to be extracted from the ICG curve. Multiple approaches can be found in literature. However, for this work the zero-crossing of the ICG 1460
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curve before the C-point was used for the B-point extraction and the X-point was assumed to be the local minimum after the C-point (Debski et al 1993). The B-point can be assessed by using the first local minimum of the ICG curve, the minimum of the second derivative, and the maximum of the third derivative occurring before the C-point; however, since the characteristic notch is not present and the local minimum corresponds to an earlier non-characteristic point, the zero-crossing method is the most reasonable one (Debski et al 1993). Figure 7 shows synchronized aortic blood flow assessed by doppler echocardiography with ICG and annotated aortic valve opening and closing by a physician. This figure visualizes that on the one hand, the B-point is not well defined, and on the other hand that the aortic valve closes earlier than indicated by the local minimum after the C-point. This is also reflected by the simulated ICG curve where the isovolumetric relaxation phase occurs before the X-point (see figure 6). Using LVET to calculate SV and CO with the equations shown in chapter 2.1, the following values are used: body height H = 1.78 m, electrode distance l = 420 mm, correction factor δ = 0.987, factor ζ = 1, body weight 69.1 kg and heart rate HR = 70.6 1/ min. The extracted and calculated parameters for the curve comprising all sources are: • • • • •
LVET: 383.7 ms SV calculated with Kubicek equation: 48.3 ml SV calculated with Sramek equation: 73.8 ml SV calculated with Bernstein–Sramek equation: 72.8 ml SV calculated with Bernstein–Osypka equation: 79.3 ml.
Note that the geometrically implemented SV is 80 ml. Table 4 in the supplement (available from stacks.iop.org/PM/35/1451/mmedia) lists the variations in LVET and SV when choosing different algorithms for B-point extraction (explained above). The difference in the B-point time ( tB ) obtained by the maximum of the third derivative of the impedance signal shows the lowest deviation and, thus, LVET and SV are close to the calculated values for the total curve. The biggest difference is given by the minimum of the second derivative which leads 1461
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Figure 8. Impedance and ICG curves for decreased tissue conductivity: original signal x, muscle · · · · · ·, blood – – –. (a) Impedance curves. (b) ICG curves.
to an overestimation of LVET (+ 99 ms) and of SV (+ 20.5 ml); this means that the chosen algorithm or the maximum of the third derivative should be chosen for the B-point extraction of the signals generated by the simulation model. 4.2. Sensitivity analysis 4.2.1. Conductivity changes. Figure 8 shows impedance and ICG curves plotted during one single simulated heartbeat for tissue conductivity changes towards lower values according to table 2. In both figures, only curves for conductivity changes of muscle tissue and blood are marked because effects of all other simulated tissues drawn in this graph can be neglected. In figure 8(a) offset-corrected impedance curves are plotted and most of these are almost identical with the impedance curve of the unchanged model, only muscle (+0.08 ) and blood conductivity changes (−0.02 ) alter the impedance signal significantly resulting in a maximum deviation of 0.1 . Since muscle tissue with lowered conductivity does not contribute to the dynamic changes of the impedance, this result reflects the fact that more current will flow through well conducting blood-filled areas contributing to signal changes. In figure 8(b) the maximum of the ICG curves is altered with muscle conductivity (+0.72 s−1 ) and blood conductivity changes (−0.28 s−1 ) resulting in a total change of 1 s−1 . In addition, lower muscle conductivity decreases the X-point value by 0.34 s−1 while lower blood conductivity increases this value by 0.13 s−1 . Most importantly, none of the characteristic points are altered in time. Impedance and ICG curves for increased tissue conductivity are depicted in figure 9. Here, lung conductivity changes are also marked, since they alter characteristic points in the ICG signal. Apart from muscle and blood conductivity changes, all curves in figure 9(a) are located in the same range. Muscle conductivity change alteres the maximum of the original curve by −0.097 and blood conductivity change by +0.0486 resulting in a total change of +0.145 . In addition, a temporal shift of the maximum is observed for blood (−17 ms) and lung conductivity changes (+41 ms). In the ICG plot (figure 9(b)), O-, C- and B-point are not affected by conductivity changes whereas the X-point is shifted due to muscle and lung conductivity (+9 ms) as well as blood conductivity changes (−16 ms). As for the ICG maximum related to decreased conductivity changes, only muscle (−0.78 s−1 ) and blood conductivity changes (+0.47 s−1 ) cause significant deviations resulting in a maximum deviation of 1.25 s−1 . 1462
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Figure 9. Impedance and ICG curves for increased tissue conductivity: original signal
x, muscle · · · · · ·, blood – – –, lung ♦. (a) Impedance curves. (b) ICG curves.
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x, heart(y+30 mm) · · · · · ·, abdomen and heart(z+30 mm) ♦, abdomen , heart(z − 30 mm) – – –, heart(z + 30 mm) . (a) Impedance curves. (b) ICG curves.
Table 5 summarizes all altered values due to tissue conductivity changes (supplement available from stacks.iop.org/PM/35/1451/mmedia). Figure 10 shows ICG and impedance curves for organ displacements during respiration and due to interindividual organ positions as discussed in section 3.1. The maximal increase in impedance (0.05 ) is due to a displacement of the heart of 30 mm in z-direction, the maximal decrease of 0.02 is due to a displacement of the heart of 30 mm in z-direction. Minor temporal shifts of the maximum can be observed for a displacement of the heart of 30 mm in z-direction (+16 ms), a displacement of the heart of 30 mm in z-direction (−25 ms) and a displacement of the abdominal organs (−17 ms). In addition, all signals have altered morphology. Thus, a temporal change of characteristic points in the ICG is expected. The C-point shows only a neglectable temporal shift of 8 ms for displacements of the heart in z-direction whereas a B-point shift of 16 ms is observed for a displacement of the heart of 30 mm in y-direction 4.2.2. Organ displacements.
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and a shift of 8 ms for combined displacement of heart and abdomen. The X-point is shifted by −16 ms for heart displacements of 30 mm in z- and y-direction. For all other geometric displacements, a temporal shift of the X-point of −33 ms is observed. The maximum of the ICG curve deviates for every organ displacement slightly. The highest increase is due to the displacement of abdominal organs (+0.314 s−1 ), whereas the lowest decrease is due to a displacement of the heart in y-direction (−0.175 s−1 ). The results for all displacements for SV calculation are summarized in table 6 (supplement available from stacks.iop.org/PM/35/1451/mmedia). 4.3. Multi-frequency analysis
A multi-frequency analysis was conducted to verify the performance of the FEM model to reflect frequency-dependent changes of the ICG curve. Therefore, continuous impedances were simulated at 4 frequencies: 5 , 20 , 50 and 100 kHz (Ulbrich et al 2011). Impedances were measured at standard ICG positions on the thorax using a AFE4300 from Texas Instruments, TX, USA. Figure 11 visualizes measured and simulated curves for all frequencies. These figures show that the maximum of the impedances decreases with frequency. From 5 to 100 kHz, the simulated impedance decreases by 28% whereas the measured impedance decreases by 50%. Z0 shows the same behavior for increasing frequency. Note that only aortic diameter changes were taken into consideration for the simulations since no data was available for the frequency-dependent behavior of erythrocyte orientation. This explains the higher decrease of the measured impedance for increasing frequencies, most likely caused by erythrocyte orientation. 5. Discussion Four dynamic sources were successfully included in the presented model, simulating the bioimpedance for one heartbeat: aortic expansion, heart contraction, lung perfusion and erythrocyte orientation. Our results suggest that since heart contraction and lung perfusion nearly compensate each other, only aortic expansion and erythrocyte orientation contribute to the dynamic impedance signal. 1464
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The very good correlation of simulated curves with measured curves shows that the morphology of the signal seems to be reasonably well reproduced and thus allows the extraction of all necessary characteristic points to calculate SV. This is an achievement by using FEM simulations with volumetric and conductivity based dynamic changes which was not reported in literature before. The model-inherent left ventricular volume change of 80 ml (see chapter 3.2) was reproduced quite well by all algorithms typically used for SV estimation (2)–(4), except the Kubicek algorithm (1). With the new Bernstein–Osypka equation (4), the SV is estimated almost exactly (79.3 ). It should be noted that physiologic LVET values for healthy subjects range from 200 ms to 330 ms (Lance and Spodick 1976). Here, we assumed a LVET of 300 ms according to the dicrotic notch of the aortic blood pressure. Therefore, based on our model in combination with the classically used characteristic points, overestimated values are obtained. Nevertheless, it is known from literature that classically extracted X-points are the reason for overestimated LVET values reflected by our simulations. Another reason for an overestimated LVET is the lack of a B-point notch in the simulated curves which would be located behind the zero crossing of the ICG curve, which is used for B-point extraction here. It should be noted, that standard definitions of the B-point are also still under debate because they do not necessarily match the opening of the aortic valve (Carvalho et al 2011). In addition, a LVET of 384 ms is not unrealistic since certain pathologies prolong LVET to more than 440 ms (Wigle et al 1967). Based on the given values CO is 5.65 l min−1 , showing that Kubicek’s equation underestimates CO by 2.25 l min−1 , which is supported by measurements comparing CO assessed by thermodilution and ICG (Van De Water et al 2003). A sensitivity analysis was made to analyze the influence of tissue conductivity changes and organ displacements using parameters found in literature and reflecting realistic scenarios. Organ movements do not influence characteristic points significantly. Table 5 shows that only conductivity changes of blood and muscle tissue have a significant influence on characteristic points as well as the simulated impedance. Temporal shifts of multiples of 8.2 ms are due to discretization noise which means that we can assume that there is no difference in estimated LVET due to conductivity changes. Nevertheless, significant impedance changes are observed leading to a maximum SV change of 16% due to increased muscle conductivity. Since increased muscle conductivity reroutes the current paths away from blood vessels and aorta due to its high percentage of the total body volume, it is clear that this lowers the dynamic influence of blood related changes on the impedance signal. Hence, this shows the importance of not mixing tissue property databases in order to avoid e.g. muscle conductivity to have a wrong conductivity related to other tissue conductivities. Furthermore, this result suggests that a calibration is needed for measuring people with an increased muscle conductivity, e.g. due to physical education. In addition, the influence of blood conductivity changes on the impedance signal strengthens the assumption that conductivity changes due to erythrocyte orientation influence SV estimation in the same way. To sum up, conductivity changes of most tissues do not influence the simulation results which makes the model robust to implemented tissue property databases. Organ displacements of heart and abdomen in general influence characteristic points as well as the dynamic impedance. Changes in Z0 and B-point can be neglected but a displacement of the heart of 30 mm in -z-direction causes an underestimation of SV of 12% mainly due to a decrease of the X-point and thus estimated LVET. Since there is no significant change in any other value contributing to the SV and the X-point deviates by −41.3 which is a multiple of 8.2, this is supposed to be a result of high discretization noise. Kubicek assumed that aortic volume changes in the thorax are the main (and the only) source for the dynamic impedance change (Raaijmakers et al 1997) which is partly supported 1465
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by our findings since the aortic diameter change seems to be determining the morphology of the impedance signal and hence the characteristic points. However, erythrocyte orientation as dynamic signal contributes substantially to 50% of the impedance signal, more than the aorta, mainly by amplifying the signal during systole. This result partly agrees with Bernstein’s newest assumption that due to blood acceleration during systole, erythrocyte orientation is the main contributor to the signal (Bernstein and Lemmens 2005). Hence, both approaches probably do not describe the ICG signal comprehensively. Previous related works could not come to the same conclusion, since their approaches have only limited explanatory power because the amount of contribution of different sources vary depending on the point of time, as shown in figure 6.
6. Conclusion The aim of this study was to create a model which is suitable to simulate current paths and voltages during dynamic impedance measurements on the human thorax, to investigate the impact of four dynamic sources on the ICG signal to reproduce experimentally observed signals. Therefore, the complex dynamic impedance should be simulated with a high temporal resolution. First, a simplified model based on human MRI data was successfully created containing two volumetric dynamic sources (heartbeat and aortic expansion) as well as two conductive dynamic sources (lung perfusion and erythrocyte orientation) based on measured physiological data. The results show very good correlation with measured curves produced by a commercially available ICG device which indicates that the model simulates ICG sources reasonably well. Second, it was shown that the ICG signal is mainly composed of the aortic impedance change and the blood conductivity change due to erythrocyte orientation. The morphology of the ICG signal seems to be mainly determined by the aortic impedance, whereas erythrocyte orientation, whose peak impedance derivative occurs simultaneously with the peak acceleration of blood, increases the signal strength. This supports partly Kubicek’s and partly Bernstein’s assumption. Third, standard algorithms to extract characteristic points, and algorithms to calculate SV, could be applied to the data to estimate hemodynamic parameters. The calculated SV with the new Bernstein–Osypka equation matches best with the implemented left ventricular heart volume change of 80 ml, however, LVET is overestimated by the algorithms and the simulated curves. This might indicate that the characteristic points typically mentioned in literature do not match well with the underlying physiological processes. Fourth, results of sensitivity analyses concerning conductivity changes due to differences in empirically assessed databases and concerning physiologic organ displacements show that this model is reliable enough to extract hemodynamic parameters such as LVET and SV from simulated impedance curves. In addition, the results suggest that equations for SV estimation have to be adapted for subjects with an increased muscle conductivity. Fifth, a similar behavior of simulated and measured impedance curves between 5 kHz and 1 MHz support the usage of the proposed model. In summary, a valuable tool to simulate ICG signals was developed which allows to analyze the behavior of different sources and their impact on the signal—including a focus on pathologies in the future. The approach with simplified geometries in combination with adjustable temporal resolution allows fast and inexpensive calculations. Nevertheless, several improvements can be made in the future. Wave propagation on the aorta could be included, and a correct anatomic representation of the aorta and heart would be preferable. Real MRI 1466
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