Bioelectromagnetics 35:547^558 (2014)
Evaluation of Electric Field Distribution in Electromagnetic Stimulation of Human Femoral Head Yukun Su,1* Robert Souffrant,1 Daniel Kluess,1 Martin Ellenrieder,1 Wolfram Mittelmeier,1 Ursula van Rienen,2 and Rainer Bader1 1
Department of Orthopaedics, University Medicine Rostock, Rostock, Germany Institute of General Electrical Engineering, University of Rostock, Rostock, Germany
2
Electromagnetic stimulation is a common therapy used to support bone healing in the case of avascular necrosis of the femoral head. In the present study, we investigated a bipolar induction screw system with an integrated coil. The aim was to analyse the influence of the screw parameters on the electric field distribution in the human femoral head. In addition, three kinds of design parameters (the shape of the screw tip, position of the screw in the femoral head, and size of the screw insulation) were varied. The electric field distribution in the bone was calculated using the finite element software Comsol Multiphysics. Moreover, a validation experiment was set up for an identical bone specimen with an implanted screw. The electric potential of points inside and on the surface of the bone were measured and compared to numerical data. The electric field distribution within the bone was clearly changed by the different implant parameters. Repositioning the screw by a maximum of 10 mm and changing the insulation length by a maximum of 4 mm resulted in electric field volume changes of 16% and 7%, respectively. By comparing the results of numerical simulation with the data of the validation experiment, on average, the electric potential difference of 19% and 24% occurred when the measuring points were at a depth of approximately 5 mm within the femoral bone and directly on the surface of the femoral bone, respectively. The results of the numerical simulations underline that the electro-stimulation treatment of bone in clinical applications can be influenced by the implant parameters. Bioelectromagnetics 35:547–558, 2014. © 2014 Wiley Periodicals, Inc. Key words: finite element method; avascular necrosis; electromagnetic stimulation; electric field distribution
INTRODUCTION Electromagnetic stimulation of bone fractures and other bone diseases, such as avascular necrosis of the femoral head, has been studied for more than half a century. Many research groups have presented the underlying biological mechanism. Fukada and Yasuda [1957] revealed that bone has piezoelectric properties; that is, stress-generated potentials could be created by the shear forces of collagen. Friedenberg and Brighton [1966] reported that a bioelectric potential can be generated by healthy bones. Bassett [1982] found that the behaviour of bone cells could be influenced by externally applied electric energy and showed that biological systems have the capability to transform electric energy to mechanical energy. Recently, Soda et al. [2008] showed that applying low frequency electromagnetic fields on the bone could increase collagen synthesis in osteoblasts. In clinical studies, three technologies are used widely when applying electrical stimulation to aid in bone healing. Direct current (DC) is the most easily 2014 Wiley Periodicals, Inc.
applied technology [Brighton et al., 1981], but it also entails the most faults. This type of invasive stimulator of bone growth is implanted at the time of surgery. An energy source is connected directly to stimulation electrodes and the cathode is placed in the bone area that needs to be healed. The second technology is capacitive coupling (CC) [Goodwin et al., 1999], which uses extracorporeal electrodes to stimulate the bone in the healing area. The third technology is pulsed electromagnetic field (PEMF), which was Grant sponsor: Deutsche Forschungsgemeinschaft (DFG) (German Research Foundation), Research Training Group 1505/2 “Welisa”. *Correspondence to: Yukun Su, Department of Orthopaedics, University Medicine Rostock, Doberaner Strasse 142, Rostock, Germany. E-mail: [email protected] Received for review 18 December 2013; Accepted 3 August 2014 DOI: 10.1002/bem.21879 Published online 23 September 2014 in Wiley Online Library (wileyonlinelibrary.com).
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implemented by Kraus’s application [1984]. The process of this system is based on the interplay of two coils and two electrodes. The primary coil is placed outside the body where the two electrodes are implanted and is used to generate a sinusoidal oscillating magnetic field in the range of 12–20 Hz. The second coil is an implanted transducer coil used to receive an induced current from an external alternating magnetic field; it is connected to two screw electrodes. One electrode is placed in the bone to be healed, and another is placed in the immediate proximity. Based on the approach by Kraus [1984], Mittelmeier et al. [2004] proposed a bipolar induction screw system (BISS) for treatment of avascular head necrosis; an Asnis III s-series screw (Stryker Trauma, Kiel, Germany) has an integrated coil and two electrodes. In this system, the transducer coil is embedded into the screw, and no extra wires need to be implanted. This reduces the failure risk of electro stimulation due to wire disconnection and it is much easier to insert the implant and to remove it 3 months after treatment. After implantation, the patient is asked to wear an extracorporeal coil around the body. An external sinusoidal oscillating magnetic field, which is generated from an extracorporeal coil, induces voltage to the embedded coils. This results in a current flow in the adjacent bone tissue between the two electrodes. In this activated area, the electric field should stimulate new bone growth. Ellenrieder et al. [2013] performed a retrospective clinical observation of 53 patients (59 hips) with an Asnis III s-series screw. In this study, none of the patients had undergone an intertrochanteric osteotomy in the past, or had an avascular necrosis state higher than stage III according to the Steinberg classification [Steinberg and Steinberg, 2004]. The preliminary results of the study showed that 86% of the patients had significantly improved medical condition. Since the bipolar induction screw system is already commonly used for internal electrical stimulation of the bone healing process, it is necessary to analyse the impact of screw parameters on the electric field distribution in the femoral head. Moreover, using numerical simulation to analyse the electric field in biological tissues is a convenient approach. For instance, Isaacson et al. [2011] used the finite element method to calculate the electric fields in the limb caused by a transcutaneous bone implant. Prodanovic et al. [2013] studied the energy distribution in biological tissues during electrical stimulation using the finite element method. Since the position of the electric implant in the femoral bone is not uniform, patients may have different electric field distributions and outcomes postoperatively. For instance, when tibia Bioelectromagnetics
fractures were treated with electrical stimulation, one patient refused to continue treatment because of heat and pain in the affected limb [Jorgensen, 1977]. Hence, the aim of our present study was to investigate the dependence of the electric field distribution in the femoral head on the position and design of an electrostimulating implant. MATERIALS AND METHODS Model Generation A femoral head from a patient undergoing total hip replacement was used. The geometrical structure of the human femoral head (Fig. 1) was based on the highresolution computed tomography (CT scans) according to the procedure described by Kluess et al. [2009]. Cortical and cancellous bone, two layers of bone structure of the human femoral head, were segmented manually from CT scans using the Amira 5.4 software (Mercury Systems, Chelmsford, MA) and converted to stereolithography (STL) files in American Standard Code for Information Interchange (ASCII) format. The STL of the human femoral head was transferred to the reverse engineering Geomagic (Raindrop Geomagic, Morrisville, NC) and the surface of the femoral head bone structure was refined and generated in a nonuniform rational B-spline (NURBS) computer-aided design (CAD) model for import into Comsol Multiphysics (Version 4.3; Comsol, Göttingen, Germany), In order to keep the coordinate system in both the numerical simulation and validation experiment consistent, the human femoral head was fixed on a frame made of perpendicular plates and placed in the CT scanner. The data of the coordinate system in numerical simulation were reconstructed from the CT scans of the perpendicular plates using the same procedure as the reconstruction of the CAD model of the femoral head. The screw model for the numerical simulation was based on CAD datasets. In order to reduce computational and mesh generation complexity, the
Fig.1. (a) X-ray of the Asnis III s-series screw, (b) the real Asnis IIIs-seriesscrew.Thetipandshaft aretwo electrodes; inbetween isoneinsulator.One coilisintegratedintothescrew.
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thread of the implant was not taken into account in the numerical simulation. Since the surrounding tissues of the femoral head have a high complexity and are of minor interest for the electric field distribution inside the femoral bone, the surrounding tissue was first substituted by blood in the present simulation. The surrounding blood cylinder had a radius of 100 mm and a length of 100 mm. The human femoral head was located in the middle axis of the cylinder. However, to better understand how the electric field in the femoral head was influenced by tissue around the bone, the surrounding tissues in the simulations were also represented by muscle tissue only, muscle tissue in combination with fat, and muscle tissue in combination with both fat and dry skin. In the case of surrounding muscle tissue only, the blood cylinder around the femoral head was replaced by muscle. In the cases of surrounding muscle tissue in combination with fat and muscle tissue in combination with both fat and dry skin, the thicknesses of the fat and the skin above the muscles were 4 and 1 mm, respectively. A designed sphere-shaped lesion was located in the femoral head as a model. Based on the surgical procedure, the numerical simulations with lesions were categorised into two cases: lesion as fat and lesion as blood. Finite Element Simulation The numerical simulation of the human femoral head was performed using Comsol Multiphysics (Comsol) which has an implementation of the finite element method. In Comsol, the AC/DC model was used to compute the electric potentials within the volume conductor model, specifically the module for electric currents in the frequency domain. An iterative solver with the generalised minimal residual method (GMRES) was used to solve the resulting system of equations. Iteration was stopped when the 2-norm of the residual was below 106. The bipolar induction screw system was made of titanium alloy Ti6A14V (Stryker Trauma). The insulation layer is based on epoxy resin. All the human tissues in the present simulation, for example, cancellous bone, cortical bone in the femoral head, blood, muscle, fat, and skin, were all simplified to be homogenous and isotropic. To our knowledge, the dielectric properties of bone at 20 Hz have not been widely studied. To simulate the electric field distribution in biological tissue, the electric properties derived from Gabriel et al. [1996a,b] were often used [Prodanovic et al., 2013]. The dielectric properties of human trabecular bone at 50 Hz were also investigated by Sierpowska et al. [2003]. Their results are comparable to those of Gabriel et al. [1996a,b]. Therefore the
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TABLE 1. Electric Properties of Materials Used for Simulation According to Gabriel et al. [1996a,b] Material Cortical bone Cancellous bone Muscle Fat Skin (dry) Blood
Conductivity,
s (S/m)
Relative permittivity, er
0.020045 0.078902 0.20742 0.015477 0.0002 0.7
25119 4020200 24306000 5032800 1136 2560
conductivity and permittivity of the tissues in Table 1 were taken from Gabriel et al. [1996a,b]. The free tetrahedral mesh was implemented in all models and adjusted manually. In order to ensure sufficient computational accuracy, the triangular element size on the surface of the electrode was based on a parametric study of the triangular element length. The screw implant surface was meshed using triangular elements with a maximum element length of 0.5 mm. Due to the limitation on computational resources, the human femoral head was meshed using free tetrahedral elements with a maximum element length of 0.8 mm. The resulting model for each implant parameter variation consisted of three million mesh elements. The model was discretised with four million degrees of freedom (DoF). The screw was located in the centre axis of the human femoral head. Three kinds of parameters were considered: screw tip design, screw insulation length, and screw positioning. Besides the original tip, a round and a flat tip were also simulated. To analyse the influence of screw position on the electric field distribution, the screw was positioned, one step at a time, further into the femoral head dome or out of the femoral head in the simulation model. The screw insulation length was varied in both the screw tip and the shaft direction in order to keep the screw tip and shaft length proportionately the same. Furthermore, three cases of surrounding tissues were also considered to investigate how the tissues surrounding the bone influenced the electric field in the femoral head: muscle tissue only, muscle tissue with fat, and muscle tissue with fat and dry skin. To take into account the real clinical conditions, one designed lesion in the sphere shape was located in the femoral head. The tissues surrounding the bone in the lesion cases were considered as muscle tissue with fat and dry skin. During surgery, when weak bone tissue is removed from the bone, blood fills up the open space; therefore, lesion materials of fat and blood were respectively used in the simulation. Bioelectromagnetics
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Electric Field Computation The potential inside the femoral head was solved by assuming that the outer boundaries of blood were isolated and a zero Neumann condition existed at these boundaries. The frequency (20 Hz) and electric potential on the surface of the screw (maximum secondary root mean square (RMS) voltage 700 mV) used in the numerical simulation were taken from the manual of the Stryker Asnis III s-series (Stryker Trauma; Fig. 2). The induced eddy currents in the femoral head were neglected since with 20 Hz stimulation frequency and the relatively low conductivity of the cancellous bone the induced eddy currents are several orders of magnitude smaller than the currents generated by the coils that are integrated in the screw implant. Therefore, under these conditions, the Maxwell equations can be considered as the time harmonic electro-quasistatic equation
computational accuracy and computational time consumption. In order to quantify the VTA changes according to different screw parameters, the volume fraction was calculated by volume fraction ¼
VTA 100% Volumefemoral head
r½ðs þ ive0 er Þrf ¼ 0
To reduce the computational complexity, the influence of the permittivity of the cortical and cancellous bone at a frequency of 20 Hz could be neglected theoretically, since the conduction current in the femoral head is several orders of magnitude higher than the displacement current. With the same stimulation parameters (electric voltage 700 mV and frequency 20 Hz) as the clinical situation, the numerical simulations were solved in the frequency domain. The influence of surrounding tissue on the electric field distribution in the femoral head was investigated by three different layers (muscle, fat, and skin) in the simulation.
in which f is the electric potential, s is the conductivity, er is the relative permittivity, and e0 8.854 1012 As/V m is the electric field constant. Although the influence of permittivity of cortical and cancellous bone at this frequency is relatively small, in order to keep the same conditions as in the clinical study, it was not neglected in our numerical simulation. The interval of the electric field, which activates the tissue in the femoral head, was 5–70 V/m [Kraus, 1984]. The volume of tissue activated (VTA) was calculated in Comsol with Matlab Version R2011b (Mathworks, Ismaning, Germany) using the grid method. The 2norm of the electric field on each grid node was interpolated from the nearest point in Matlab. The grid size was chosen to be 2 mm in all screw parameter variations to maintain the balance between
Validation Experiment Validating is utilised to determine if the numerical model is an accurate representation of the real system. Therefore, we set up a validation experiment with the same human femoral head and screw implant. To verify the numerical data, the electric potential was determined experimentally using a bone specimen. The validation experiment (Fig. 3) was set up according to the clinical application in order to prove the numerical simulation accuracy. Due to the lack of sources of fresh femoral heads from patients with early stage avascular head necrosis, the human femoral head used for the experimental validation and numerical simulation was retrieved from an osteoarthritic patient undergoing total hip replacement. Since the cartilage lesion of the femoral
Fig. 2. (a) CTscan of the femoral head with reference frame; (b) simulation model of the femoral head and reference coordinate system. Bioelectromagnetics
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Fig. 3. (a) Validation experiment set up, bipolar induction screw system generator, (b) primary hip coil, and (c) measuring arm (MicroScribe G2x).
head is relatively small, this should not result in relevant discrepancies between numerical simulation and experimental measurement. The electric properties of the bone tissue can be influenced by many factors, such as time of exposure or moisture [Saha et al., 1984]. The bone specimen used in our study was refrigerated at 20 8C from post-surgery until the experiment. Freezing is recognised as a common method of preserving bone samples for electrical measurements [Saha and Williams, 1989]; however the influence on the electric bone properties is not known. To avoid drying of the thawed specimen, the femoral bone was moistened using NaCl solution during experimental measurements. Before setting up the validation experiment, a CT scan of the bone specimen with a reference frame had to be carried out first to reconstruct the CAD model of the bone for numerical simulation. A threedimensional (3D) coordinate measuring arm, MicroScribe G2x (Solution Technologies, Oella, MD) was used to determine the coordinates of the measuring points, which should be kept consistent in the numerical simulation. The primary coil generated an oscillating (20 Hz) magnetic flux density of 5 mT. The bipolar
induction screw system was implanted into the centre of the bone. Before the screw was implanted into the bone, the RMS voltage on the surface of the screw was measured at 500 mV. This electric potential was also used in the numerical simulation to compare the results to the experimental ones. The RMS voltage on the surface of the bone and approximately 5 mm into the bone (Fig. 4) was measured in the validation experiment and the results were compared with those of numerical simulation. To keep the position of the screw in both the numerical simulation and validation experiment consistent, X-ray scans of the bone specimen were taken after the validation experiment and the position of the screw in the simulation was refined accordingly. RESULTS The activated tissue electric field distributions in the human femoral head under different screw parameter variations are shown in Figures 5–7. To give an insight into the activated tissue electric field distribution, contour lines of the field for a two-dimensional (2D) cutting plane of the human femoral head are Bioelectromagnetics
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Fig. 4. Measuring points in validation experiment (left), and in numerical simulation model (right).
presented. Figure 5 shows that by keeping the screw in the same position, the original tip and the round tip designs have similar electric field distributions. After changing the screw to the flat tip design, the electric field showed a minor difference around the screw tip. In Figure 8, the volume fraction shows an electric field change in the human femoral head of only 0.2% between the original tip and the round tip designs. This difference rises to 1.4% when the tip design is changed to flat. The linear regression function for simulation of tip designs is f(x) ¼ 0.698x þ 25.161 and R2 is 0.876. The screw insulation length was varied under the condition of keeping the screw position constant and using the original screw tip design. Figure 6a shows
the insulation length variation in the case of the same screw shaft electrode. The tissue area activated by the electric field increased when the screw insulation length decreased. Figure 9a shows that each 1 mm change in the insulation length resulted in a volume fraction difference in the femoral head of approximately 1.8%. The linear regression function is f(x) ¼ 1.738x þ 31.063 and R2 is 0.997. In Figure 6b, the length of the insulation varied, while the screw tip was kept the same. The results show that the larger the screw insulation length is in this variation, the larger the activated tissue electric field distribution area. The volume fraction increased by approximately 1% when the insulation length was increased by 1 mm (see Fig. 9b). The linear regression function for the
Fig. 5. Numerical simulation of electric field distribution testing of three screw tip designs. The electric field in light and black areas provides regions of 70 V/m, whereas the mid-grey areasare optimalactivatedregionsforbonetissuegrowth. Bioelectromagnetics
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Fig. 6. Numerical simulation of electric field distribution testing of different screw insulation lengths, where (a) thelengthofscrewshaftelectrodestaysthesameand (b) thelengthofthescrew tip electrode stays the same.The electric field in light and black areas provides regions of 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
Fig. 7. Numerical simulation of electric field distribution testing: (a) screw backward positioning and (b) forward positioning.The electric field in light and black areas provides regions of 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
simulation of this kind of insulation variation is f (x) ¼ 0.973x þ 23.029 and R2 is 0.996. Figure 7 shows the electric field distribution of the backward and forward screw positions under the condition of using the original screw design. The electric field distribution area is larger when the screw is moved backwards and smaller when the screw is moved to the dome of the femoral head. Figure 10 shows that each 1 mm change in the screw position results in an approximately 1.5% change in the volume
fraction in the femoral head. The linear regression function for the simulation of the screw positioning parameter is f(x) ¼ 1.517x þ 26.575 and R2 is 0.989. The volume fraction for these four parameter variations shows that the screw tip design has the least effect on the electric field distribution, while the insulation length and position variations have similar effects. Figure 11 shows the electric field distribution in the femoral head of the different tissues surrounding Bioelectromagnetics
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Fig. 8. Numerical simulation of screw tip design: results of volume fraction. The line with the star is the volume fraction for each screw positioning parameter, and the dashed line without a star is the best fitting linear regression function of the numerical simulation.
the bone but keeping the screw position and design the same. Tests under these conditions revealed that the activated tissue electric field area increased when the surrounding tissue changed from blood to muscle. But in the other two cases (muscle tissue with fat and muscle tissue with fat and skin), the electric field area of the activated tissue remained almost the same as in the case of muscle only. In Figure 12, these three scenarios are demonstrated by the volume fraction of the electric field in the femoral bone. Compared with the case of blood, 4% volume fraction is gained in the case of muscle tissue surrounded. But a further change in the volume fraction cannot be found in the cases of muscle tissue and fat, or muscle tissue with fat and skin. Figure 13 shows the electric field distribution of the different lesion materials under the condition of keeping the tissues surrounding the bone as muscle tissue with fat and skin. The screw position and design
Fig. 10. Numerical simulation of screw positioning: results of volume fraction. The line with the star is the volume fraction for each screw positioning parameter, and the dashed line without a star is the best fitting linear regression function of the numerical simulation.
were kept the same. The activated tissue electric field in the femoral head significantly increased when the tissues are changed from fat to blood. Figure 14 shows that when the lesion is fat, the volume fraction is 46% higher than when the lesion is blood. Figure 15 reveals that the results of the validation experiment are close to those of the numerical simulation when the measuring points are at 5 mm depth in the femoral head and on the surface of the bone. On average, RMS voltages show a 24% difference when the measuring points are on the surface of the bone. When the measuring points are at 5 mm depth in the bone, this percentage decreases to 19%. DISCUSSION Our present study was the first to investigate the influence of different parameters of an electro-stimu-
Fig.9. Numericalsimulationof screwinsulationlength, where (a) thelengthofthescrewshaftelectrodesstaysthe sameand (b) thelengthofthe screw tip electrodestaysthe same: volume fraction. The line with the star is the volume fraction foreach screw positioning parameter, and the dashed linewithout a staristhebest fittinglinearregressionfunctionofthenumericalsimulation. Bioelectromagnetics
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Fig. 13. Numerical simulation of electric field distribution testing of different lesions, where the designed sphere-shaped lesion in thebone is considered as (a) fat and (b) blood.The electric fieldin light andblackareasprovidesregionsof 70 V/m, whereas the mid-grey areas are optimal activated regions for bone tissuegrowth.
lating implant on the electric field distribution in the human femoral head. We experimentally validated the numerical simulation model of a femoral head and demonstrated that the position of the implant in the femoral head and length of the implant insulation have a significant influence on the volume of tissue activated in the femoral head compared to the effect from the implant tip design. Comparing the numerical data to the experimental results, the electric potential differences at all the measuring points were in an acceptable range (average
20%). Subsequently, a series of evaluations on the effect of different screw parameters on the electric field were carried out using the numerical model. Nevertheless, the electric properties of the human femoral head in the model were not calibrated according to the experimental validation. Although only 20% difference was tested by using the electric properties from Gabriel et al. [1996a,b], the real electric properties of the specific human femoral head need to be calibrated and used in the evaluation of electric field distribution in the femoral head. This could be achieved by an automatic optimisation process. The goal of the optimisation could be the minimum difference of numerical data to experimental results. In Kraus [1984], the electric stimulating implant was located in the weak bone to stimulate new bone growth, but the sensitivity of the electric field in the bone to the implant was not investigated. Our results show that in the current human femoral head, the insulation
Fig.12. Numericalsimulationoftissue surroundingthebone: volumefraction.
Fig. 14. Numerical simulation of lesion in the bone: volume fraction.
Fig. 11. Numerical simulation of electric field distribution testing of different tissues surrounding the bone, where the surrounding tissueis (a) blood, (b) muscle, (c) muscle with fat, and (d) muscle with fat andskin.The electric fieldinlight andblackareasprovides regionsof 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
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Fig.15. Results of validation experiment, where the measuring points are (a) approximately 5 mm depthinthefemoralheadand (b) onthesurfaceofthefemoralhead: whitebarsarethe RMSvoltages inthevalidationexperiment; andgreybarsarethe RMSvoltagesinthenumericalsimulation.
length of the screw had a linear relation to the change in the activated tissue electric volume in the femoral head. To achieve large VTA in the femoral head by changing the length of the insulation, two methods are possible: Increasing the screw insulation length while keeping the screw tip electrode length the same or decreasing screw insulation length while keeping the screw shaft electrode length the same. The influence of a 1 mm screw insulation length change on the VTA in the screw shaft case is approximately double as high in comparison to the screw tip case (1.8% and 1.0%, respectively). Moreover, the relevant low influence on VTA was found from the screw tip designs (0.2% in round tip and 1.4% in flat tip). This demonstrates that the shape of the screw tip design does not influence the VTA in the femoral head. However, the effect of VTA in the femoral head from the radius of the screw implant was not included in our present study because the size of the screw radius is based on the patient’s femoral head size. Therefore, to design a patient’s specific screw implant, the number of the screw implant and the radius for each implant should be taken from the relevant surgery process and evaluated. In our present work, the mechanical stability of the bipolar induction screw system with different tip designs and insulation lengths was not tested. Although in Mittelmeier et al. [2004], the stability of the original Asnis III s-series screw was tested and the result showed that the BISS screw (which was later named the Asnis III s-series screw) had significantly higher mechanical values due to a reinforcing effect by the attached electrode (in order to produce a customised screw for specific patients, our results and the mechanical stability should be considered). In a previous study by Su et al. [2013], the insulation length was examined with only one implant parameter. In the present study, screw positioning, Bioelectromagnetics
screw tip design, and screw insulation length were analysed. Among these parameters, the screw positioning in particular was relevant and important because it could be changed during the implantation process. Our numerical data showed that each 1 mm tiny screw positioning could bring 1.5% VTA change in the femoral head. It revealed an approximated negative linear relation between the screw positioning and VTA in the femoral head. This can give guidance for intraoperative application considering the effect of the screw position on the electric field in the bone (for instance, by moving the screw implant outside of the femoral head to get a larger VTA). The screw position revealed the largest effect on the electric field distribution in the femoral head. The screw position was only investigated without considering a necrotic lesion; as they are usually removed and filled with fresh autologous bone during surgery [Ellenrieder et al., 2013]. In the future, the optimum screw position in the femoral head could be calculated pre-operatively using a patient-specific model reconstructed from the patient’s data. Future approaches could integrate numerical optimisation algorithms to find optimum screw parameters for each individual patient. The present electric field distribution evaluation was based on various assumptions and simplifications. The electrical properties of cancellous bone and cortical bone for the human femoral head were set to both isotropic and homogeneous conductivity and permittivity. Since bone density varied between patients, the electrical properties of the femoral bone could also differ, especially for osteoporosis patients. Williams and Saha [1996] found that the specific capacity of wet human cortical and cancellous bone depended on bone density. Sierpowska et al. [2006] found that the electrical and dielectric parameters of human trabecular
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bone, especially the relative permittivity and the dissipation factor, were significantly and specifically related to the trabecular microstructure. Therefore, to achieve patient-specific stimulation modelling, the relationship between bone density and dielectric properties should be taken into account in future studies. Electric fields varying from 5 to 70 V/m were considered to find the optimum effect on bone growth [Kraus, 1984]. Kuzyk and Schemitsch [2009] explored electrical stimulation techniques leading to bone cell proliferation and attempted to elucidate the intracellular processes for cell proliferation. The biological effects of PEMF on bone growth have been recently studied. Chang et al. [2004] investigated the effect of PEMF stimulation on osteoblast cell activities and found that the effect of PEMF on bone tissue formation was most likely associated with an increase in the number of cells but without enhancement of the osteoblast differentiation. A low frequency of 7.5 Hz has been found to play a modulating role in human mesenchymal stem cell (hMSC) osteogenesis [Tsai et al., 2009]. The most significant effect of PEMF stimulation on hMSC differentiation was observed at 50 Hz [Luo et al., 2012]. However, the limit of the electric field that can damage bone growth is still an open question. Moreover, in our study, the bipolar induction screw system was used for stimulating the weak bone in the femoral head in the case of avascular necrosis. However, the necrotic lesion within the femoral head has not been taken into account in the evaluation of implant parameters until now. Although the size of the surrounding tissue of the human femoral head in the simulation model was comparable to reality, it was simplified by using blood due to the geometric complexity of model reconstruction and lack of knowledge of the electric properties of the soft tissue at a frequency of 20 Hz. This model simplification is acceptable because the attached tissue surrounding the bone has the greatest influence on the electric field distribution in the numerical simulation. But the necrotic lesion in the femoral head cannot be neglected when using numerical simulation to guide a surgical approach. For future patient-specific modelling, the position and size of the necrotic lesion within the numerical model of the femoral head considering the attached surrounding tissues may be acquired from the patient’s MRI data. CONCLUSION Numerical simulations can give insight into the electric field distribution in bones. Our study demonstrated that the electromagnetic stimulation of bone was sensitive to the given implant parameters. The calculated data are relevant for the optimisation of
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implant design and the clinical application. Thereby, both the positioning of the screw and the length and position of the insulator in the screw have a significant effect on the electric field distribution in the femoral head. For a patient-customised screw, the position and the insulation length of the screw, rather than the tip shape, dominate the activated tissue electric field in the femoral head. Repositioning the screw by a maximum of 10 mm and changing the insulation length by a maximum of 4 mm resulted in changes in the electric field volume of 16% and 7%, respectively. Our results also demonstrate that the attached tissue surrounding the bone had the most influence on the numerical simulation. Therefore, it was reasonable to simplify the tissue surrounding the bone in the numerical simulation. Comparing the results of numerical simulation to the experimental data, an average difference in the electric potential of 20% occurs. In future applications, different screw parameters could be calculated pre-operatively in order to find optimal patient-adapted solutions for the treatment of avascular necrosis and bone defects. ACKNOWLEDGMENTS The authors would like to thank the Institute of Radiology, University Medicine Rostock, for providing the CT data and Catherine Ebner for her technical support. REFERENCES Bassett CA. 1982. Pulsing electromagnetic fields: A new method to modify cell behaviour in calcified and noncalcified tissues. Calcif Tissue Int 34:1–8. Brighton CT, Black J, Friedenberg ZB, Esterhai JL, Day LJ, Connolly JF. 1981. A multicenter study of the treatment of non-union with constant direct current. J Bone Joint Surg Am 63:2–13. Chang WH-S, Cheng L-T, Sun J-S, Lin F-H. 2004. Effect of pulseburst electromagnetic field stimulation on osteoblast cell activities. Bioelectromagnetics 25:457–465. Ellenrieder M, Tischer T, Kreuz PC, Fröhlich S, Fritsche A, Mittelmeier W. 2013. Arthroscopically assisted therapy of avascular necrosis of the femoral head. Oper Orthop Traumatol 25:85–94. Friedenberg ZB, Brighton CT. 1966. Bioelectric potentials in bone. J Bone Joint Surg Am 48:915–923. Fukada E, Yasuda I. 1957. On the piezoelectric effect of bone. Phys Soc Jpn 12:1158–1162. Gabriel S, Lau RW, Gabriel C. 1996a. The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 41:2251–2269. Gabriel S, Lau RW, Gabriel C. 1996b. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41:2271– 2293. Bioelectromagnetics
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Goodwin CB, Brighton CT, Guyer RD, Johnson JR, Light KI, Yuan HA. 1999. A double-blind study of capacitively coupled electrical stimulation as an adjunct to lumbar spinal fusions. Spine (Phila Pa 1976) 24:1349–1356. Isaacson BM, Stinstra JG, Bloebaum RD, Pasquina PF, MacLeod RS. 2011. Establishing multiscale models for simulating whole limb estimates of electric fields for osseointegrated implants. IEEE Trans Biomed Eng 58:2991–2994. Jorgensen TE. 1977. Electrical stimulation of human fracture healing by means of a slow pulsating, asymmetrical direct current. Clin Orthop Relat Res 124–127. Kluess D, Souffrant R, Mittelmeier W, Wree A, Schmitz KP, Bader R. 2009. A convenient approach for finite-elementanalyses of orthopaedic implants in bone contact: Modelling and experimental validation. Comput Methods Programs Biomed 95:23–30. Kraus W. 1984. Magnetic field therapy and magnetically induced electrostimulation in orthopaedics. Orthopäde 13:78–92 (in German). Kuzyk PR, Schemitsch EH. 2009. The science of electrical stimulation therapy for fracture healing. Indian J Orthop 43: 127–131. Luo F, Huo T, Zhang Z, Xie Z, Wu X, Xu J. 2012. Effects of pulsed electromagnetic field frequencies on the osteogenic differentiation of human mesenchymal stem cells. Orthopedics 35:526–531. Mittelmeier W, Lehner S, Kraus W, Matter HP, Gerdesmeyer L, Steinhauser E. 2004. BISS: Concept and biomechanical investigations of a new screw system for electromagnetically induced internal osteostimulation. Arch Orthop Trauma Surg 124:86–91. Prodanovic M, Malesevic J, Filipovic M, Jevtic T, Bijelic G, Malesevic N. 2013. Numerical simulation of the energy distribution biological tissues during electrical stimulation. Serbian J Electr Eng 10:165–173.
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Saha S, Williams PA. 1989. Electric and dielectric properties of wet human cancellous bone as a function of frequency. Ann Biomed Eng 17:143–158. Saha S, Reddy GN, Albright JA. 1984. Factors affecting the measurement of bone impedance. Med Biol Eng Comput 22:123–129. Sierpowska J, Töyräs J, Hakulinen MA, Saarakkala S, Jurvelin JS, Lappalainen R. 2003. Electrical and dielectric properties of bovine trabecular bone—Relationship with mechanical properties and mineral density. Phys Med Biol 48:775– 786. Sierpowska J, Hakulinen MA, Töyräs J, Day JS, Weinans H, Kiviranta I, Jurvelin JS, Lappalainen R. 2006. Interrelationships between electrical properties and microstructure of human trabecular bone. Phys Med Biol 51:5289–5303. Soda A, Ikehara T, Kinouchi Y, Yoshizaki K. 2008. Effect of exposure to an extremely low frequency-electromagnetic field on the cellular collagen with respect to signaling pathways in osteoblast-list cells. J Med Invest 55:267–278. Steinberg ME, Steinberg DR. 2004. Classification systems for osteonecrosis: An overview. Orthop Clin North Am 35: 273–283. Su Y, Souffrant R, Kluess D, Ellenrieder M, van Rienen U, Mittelmeier W, Bader R. 2013. Changes of the electric field distribution in the femoral head due to position and design of an electro-stimulating implant. Biomed Tech(Berl). pii: /j/ bmte.2013.58.issue-s1-N/bmt-2013-4346/bmt-2013-4346. xml. doi: 10.1515/bmt-2013-4346. [Epub ahead of print] Tsai MT, Li WJ, Tuan RS, Chang WH. 2009. Modulation of osteogenesis in human mesenchymal stem cells by specific pulsed electromagnetic field stimulation. J Orthop Res 27:1169–1174. Williams PA, Saha S. 1996. The electrical and dielectric properties of human bone tissue and their relationship with density and bone mineral content. Ann Biomed Eng 24:222–233.
Evaluation of Electric Field Distribution in Electromagnetic Stimulation of Human Femoral Head Yukun Su,1* Robert Souffrant,1 Daniel Kluess,1 Martin Ellenrieder,1 Wolfram Mittelmeier,1 Ursula van Rienen,2 and Rainer Bader1 1
Department of Orthopaedics, University Medicine Rostock, Rostock, Germany Institute of General Electrical Engineering, University of Rostock, Rostock, Germany
2
Electromagnetic stimulation is a common therapy used to support bone healing in the case of avascular necrosis of the femoral head. In the present study, we investigated a bipolar induction screw system with an integrated coil. The aim was to analyse the influence of the screw parameters on the electric field distribution in the human femoral head. In addition, three kinds of design parameters (the shape of the screw tip, position of the screw in the femoral head, and size of the screw insulation) were varied. The electric field distribution in the bone was calculated using the finite element software Comsol Multiphysics. Moreover, a validation experiment was set up for an identical bone specimen with an implanted screw. The electric potential of points inside and on the surface of the bone were measured and compared to numerical data. The electric field distribution within the bone was clearly changed by the different implant parameters. Repositioning the screw by a maximum of 10 mm and changing the insulation length by a maximum of 4 mm resulted in electric field volume changes of 16% and 7%, respectively. By comparing the results of numerical simulation with the data of the validation experiment, on average, the electric potential difference of 19% and 24% occurred when the measuring points were at a depth of approximately 5 mm within the femoral bone and directly on the surface of the femoral bone, respectively. The results of the numerical simulations underline that the electro-stimulation treatment of bone in clinical applications can be influenced by the implant parameters. Bioelectromagnetics 35:547–558, 2014. © 2014 Wiley Periodicals, Inc. Key words: finite element method; avascular necrosis; electromagnetic stimulation; electric field distribution
INTRODUCTION Electromagnetic stimulation of bone fractures and other bone diseases, such as avascular necrosis of the femoral head, has been studied for more than half a century. Many research groups have presented the underlying biological mechanism. Fukada and Yasuda [1957] revealed that bone has piezoelectric properties; that is, stress-generated potentials could be created by the shear forces of collagen. Friedenberg and Brighton [1966] reported that a bioelectric potential can be generated by healthy bones. Bassett [1982] found that the behaviour of bone cells could be influenced by externally applied electric energy and showed that biological systems have the capability to transform electric energy to mechanical energy. Recently, Soda et al. [2008] showed that applying low frequency electromagnetic fields on the bone could increase collagen synthesis in osteoblasts. In clinical studies, three technologies are used widely when applying electrical stimulation to aid in bone healing. Direct current (DC) is the most easily 2014 Wiley Periodicals, Inc.
applied technology [Brighton et al., 1981], but it also entails the most faults. This type of invasive stimulator of bone growth is implanted at the time of surgery. An energy source is connected directly to stimulation electrodes and the cathode is placed in the bone area that needs to be healed. The second technology is capacitive coupling (CC) [Goodwin et al., 1999], which uses extracorporeal electrodes to stimulate the bone in the healing area. The third technology is pulsed electromagnetic field (PEMF), which was Grant sponsor: Deutsche Forschungsgemeinschaft (DFG) (German Research Foundation), Research Training Group 1505/2 “Welisa”. *Correspondence to: Yukun Su, Department of Orthopaedics, University Medicine Rostock, Doberaner Strasse 142, Rostock, Germany. E-mail: [email protected] Received for review 18 December 2013; Accepted 3 August 2014 DOI: 10.1002/bem.21879 Published online 23 September 2014 in Wiley Online Library (wileyonlinelibrary.com).
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implemented by Kraus’s application [1984]. The process of this system is based on the interplay of two coils and two electrodes. The primary coil is placed outside the body where the two electrodes are implanted and is used to generate a sinusoidal oscillating magnetic field in the range of 12–20 Hz. The second coil is an implanted transducer coil used to receive an induced current from an external alternating magnetic field; it is connected to two screw electrodes. One electrode is placed in the bone to be healed, and another is placed in the immediate proximity. Based on the approach by Kraus [1984], Mittelmeier et al. [2004] proposed a bipolar induction screw system (BISS) for treatment of avascular head necrosis; an Asnis III s-series screw (Stryker Trauma, Kiel, Germany) has an integrated coil and two electrodes. In this system, the transducer coil is embedded into the screw, and no extra wires need to be implanted. This reduces the failure risk of electro stimulation due to wire disconnection and it is much easier to insert the implant and to remove it 3 months after treatment. After implantation, the patient is asked to wear an extracorporeal coil around the body. An external sinusoidal oscillating magnetic field, which is generated from an extracorporeal coil, induces voltage to the embedded coils. This results in a current flow in the adjacent bone tissue between the two electrodes. In this activated area, the electric field should stimulate new bone growth. Ellenrieder et al. [2013] performed a retrospective clinical observation of 53 patients (59 hips) with an Asnis III s-series screw. In this study, none of the patients had undergone an intertrochanteric osteotomy in the past, or had an avascular necrosis state higher than stage III according to the Steinberg classification [Steinberg and Steinberg, 2004]. The preliminary results of the study showed that 86% of the patients had significantly improved medical condition. Since the bipolar induction screw system is already commonly used for internal electrical stimulation of the bone healing process, it is necessary to analyse the impact of screw parameters on the electric field distribution in the femoral head. Moreover, using numerical simulation to analyse the electric field in biological tissues is a convenient approach. For instance, Isaacson et al. [2011] used the finite element method to calculate the electric fields in the limb caused by a transcutaneous bone implant. Prodanovic et al. [2013] studied the energy distribution in biological tissues during electrical stimulation using the finite element method. Since the position of the electric implant in the femoral bone is not uniform, patients may have different electric field distributions and outcomes postoperatively. For instance, when tibia Bioelectromagnetics
fractures were treated with electrical stimulation, one patient refused to continue treatment because of heat and pain in the affected limb [Jorgensen, 1977]. Hence, the aim of our present study was to investigate the dependence of the electric field distribution in the femoral head on the position and design of an electrostimulating implant. MATERIALS AND METHODS Model Generation A femoral head from a patient undergoing total hip replacement was used. The geometrical structure of the human femoral head (Fig. 1) was based on the highresolution computed tomography (CT scans) according to the procedure described by Kluess et al. [2009]. Cortical and cancellous bone, two layers of bone structure of the human femoral head, were segmented manually from CT scans using the Amira 5.4 software (Mercury Systems, Chelmsford, MA) and converted to stereolithography (STL) files in American Standard Code for Information Interchange (ASCII) format. The STL of the human femoral head was transferred to the reverse engineering Geomagic (Raindrop Geomagic, Morrisville, NC) and the surface of the femoral head bone structure was refined and generated in a nonuniform rational B-spline (NURBS) computer-aided design (CAD) model for import into Comsol Multiphysics (Version 4.3; Comsol, Göttingen, Germany), In order to keep the coordinate system in both the numerical simulation and validation experiment consistent, the human femoral head was fixed on a frame made of perpendicular plates and placed in the CT scanner. The data of the coordinate system in numerical simulation were reconstructed from the CT scans of the perpendicular plates using the same procedure as the reconstruction of the CAD model of the femoral head. The screw model for the numerical simulation was based on CAD datasets. In order to reduce computational and mesh generation complexity, the
Fig.1. (a) X-ray of the Asnis III s-series screw, (b) the real Asnis IIIs-seriesscrew.Thetipandshaft aretwo electrodes; inbetween isoneinsulator.One coilisintegratedintothescrew.
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thread of the implant was not taken into account in the numerical simulation. Since the surrounding tissues of the femoral head have a high complexity and are of minor interest for the electric field distribution inside the femoral bone, the surrounding tissue was first substituted by blood in the present simulation. The surrounding blood cylinder had a radius of 100 mm and a length of 100 mm. The human femoral head was located in the middle axis of the cylinder. However, to better understand how the electric field in the femoral head was influenced by tissue around the bone, the surrounding tissues in the simulations were also represented by muscle tissue only, muscle tissue in combination with fat, and muscle tissue in combination with both fat and dry skin. In the case of surrounding muscle tissue only, the blood cylinder around the femoral head was replaced by muscle. In the cases of surrounding muscle tissue in combination with fat and muscle tissue in combination with both fat and dry skin, the thicknesses of the fat and the skin above the muscles were 4 and 1 mm, respectively. A designed sphere-shaped lesion was located in the femoral head as a model. Based on the surgical procedure, the numerical simulations with lesions were categorised into two cases: lesion as fat and lesion as blood. Finite Element Simulation The numerical simulation of the human femoral head was performed using Comsol Multiphysics (Comsol) which has an implementation of the finite element method. In Comsol, the AC/DC model was used to compute the electric potentials within the volume conductor model, specifically the module for electric currents in the frequency domain. An iterative solver with the generalised minimal residual method (GMRES) was used to solve the resulting system of equations. Iteration was stopped when the 2-norm of the residual was below 106. The bipolar induction screw system was made of titanium alloy Ti6A14V (Stryker Trauma). The insulation layer is based on epoxy resin. All the human tissues in the present simulation, for example, cancellous bone, cortical bone in the femoral head, blood, muscle, fat, and skin, were all simplified to be homogenous and isotropic. To our knowledge, the dielectric properties of bone at 20 Hz have not been widely studied. To simulate the electric field distribution in biological tissue, the electric properties derived from Gabriel et al. [1996a,b] were often used [Prodanovic et al., 2013]. The dielectric properties of human trabecular bone at 50 Hz were also investigated by Sierpowska et al. [2003]. Their results are comparable to those of Gabriel et al. [1996a,b]. Therefore the
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TABLE 1. Electric Properties of Materials Used for Simulation According to Gabriel et al. [1996a,b] Material Cortical bone Cancellous bone Muscle Fat Skin (dry) Blood
Conductivity,
s (S/m)
Relative permittivity, er
0.020045 0.078902 0.20742 0.015477 0.0002 0.7
25119 4020200 24306000 5032800 1136 2560
conductivity and permittivity of the tissues in Table 1 were taken from Gabriel et al. [1996a,b]. The free tetrahedral mesh was implemented in all models and adjusted manually. In order to ensure sufficient computational accuracy, the triangular element size on the surface of the electrode was based on a parametric study of the triangular element length. The screw implant surface was meshed using triangular elements with a maximum element length of 0.5 mm. Due to the limitation on computational resources, the human femoral head was meshed using free tetrahedral elements with a maximum element length of 0.8 mm. The resulting model for each implant parameter variation consisted of three million mesh elements. The model was discretised with four million degrees of freedom (DoF). The screw was located in the centre axis of the human femoral head. Three kinds of parameters were considered: screw tip design, screw insulation length, and screw positioning. Besides the original tip, a round and a flat tip were also simulated. To analyse the influence of screw position on the electric field distribution, the screw was positioned, one step at a time, further into the femoral head dome or out of the femoral head in the simulation model. The screw insulation length was varied in both the screw tip and the shaft direction in order to keep the screw tip and shaft length proportionately the same. Furthermore, three cases of surrounding tissues were also considered to investigate how the tissues surrounding the bone influenced the electric field in the femoral head: muscle tissue only, muscle tissue with fat, and muscle tissue with fat and dry skin. To take into account the real clinical conditions, one designed lesion in the sphere shape was located in the femoral head. The tissues surrounding the bone in the lesion cases were considered as muscle tissue with fat and dry skin. During surgery, when weak bone tissue is removed from the bone, blood fills up the open space; therefore, lesion materials of fat and blood were respectively used in the simulation. Bioelectromagnetics
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Electric Field Computation The potential inside the femoral head was solved by assuming that the outer boundaries of blood were isolated and a zero Neumann condition existed at these boundaries. The frequency (20 Hz) and electric potential on the surface of the screw (maximum secondary root mean square (RMS) voltage 700 mV) used in the numerical simulation were taken from the manual of the Stryker Asnis III s-series (Stryker Trauma; Fig. 2). The induced eddy currents in the femoral head were neglected since with 20 Hz stimulation frequency and the relatively low conductivity of the cancellous bone the induced eddy currents are several orders of magnitude smaller than the currents generated by the coils that are integrated in the screw implant. Therefore, under these conditions, the Maxwell equations can be considered as the time harmonic electro-quasistatic equation
computational accuracy and computational time consumption. In order to quantify the VTA changes according to different screw parameters, the volume fraction was calculated by volume fraction ¼
VTA 100% Volumefemoral head
r½ðs þ ive0 er Þrf ¼ 0
To reduce the computational complexity, the influence of the permittivity of the cortical and cancellous bone at a frequency of 20 Hz could be neglected theoretically, since the conduction current in the femoral head is several orders of magnitude higher than the displacement current. With the same stimulation parameters (electric voltage 700 mV and frequency 20 Hz) as the clinical situation, the numerical simulations were solved in the frequency domain. The influence of surrounding tissue on the electric field distribution in the femoral head was investigated by three different layers (muscle, fat, and skin) in the simulation.
in which f is the electric potential, s is the conductivity, er is the relative permittivity, and e0 8.854 1012 As/V m is the electric field constant. Although the influence of permittivity of cortical and cancellous bone at this frequency is relatively small, in order to keep the same conditions as in the clinical study, it was not neglected in our numerical simulation. The interval of the electric field, which activates the tissue in the femoral head, was 5–70 V/m [Kraus, 1984]. The volume of tissue activated (VTA) was calculated in Comsol with Matlab Version R2011b (Mathworks, Ismaning, Germany) using the grid method. The 2norm of the electric field on each grid node was interpolated from the nearest point in Matlab. The grid size was chosen to be 2 mm in all screw parameter variations to maintain the balance between
Validation Experiment Validating is utilised to determine if the numerical model is an accurate representation of the real system. Therefore, we set up a validation experiment with the same human femoral head and screw implant. To verify the numerical data, the electric potential was determined experimentally using a bone specimen. The validation experiment (Fig. 3) was set up according to the clinical application in order to prove the numerical simulation accuracy. Due to the lack of sources of fresh femoral heads from patients with early stage avascular head necrosis, the human femoral head used for the experimental validation and numerical simulation was retrieved from an osteoarthritic patient undergoing total hip replacement. Since the cartilage lesion of the femoral
Fig. 2. (a) CTscan of the femoral head with reference frame; (b) simulation model of the femoral head and reference coordinate system. Bioelectromagnetics
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Fig. 3. (a) Validation experiment set up, bipolar induction screw system generator, (b) primary hip coil, and (c) measuring arm (MicroScribe G2x).
head is relatively small, this should not result in relevant discrepancies between numerical simulation and experimental measurement. The electric properties of the bone tissue can be influenced by many factors, such as time of exposure or moisture [Saha et al., 1984]. The bone specimen used in our study was refrigerated at 20 8C from post-surgery until the experiment. Freezing is recognised as a common method of preserving bone samples for electrical measurements [Saha and Williams, 1989]; however the influence on the electric bone properties is not known. To avoid drying of the thawed specimen, the femoral bone was moistened using NaCl solution during experimental measurements. Before setting up the validation experiment, a CT scan of the bone specimen with a reference frame had to be carried out first to reconstruct the CAD model of the bone for numerical simulation. A threedimensional (3D) coordinate measuring arm, MicroScribe G2x (Solution Technologies, Oella, MD) was used to determine the coordinates of the measuring points, which should be kept consistent in the numerical simulation. The primary coil generated an oscillating (20 Hz) magnetic flux density of 5 mT. The bipolar
induction screw system was implanted into the centre of the bone. Before the screw was implanted into the bone, the RMS voltage on the surface of the screw was measured at 500 mV. This electric potential was also used in the numerical simulation to compare the results to the experimental ones. The RMS voltage on the surface of the bone and approximately 5 mm into the bone (Fig. 4) was measured in the validation experiment and the results were compared with those of numerical simulation. To keep the position of the screw in both the numerical simulation and validation experiment consistent, X-ray scans of the bone specimen were taken after the validation experiment and the position of the screw in the simulation was refined accordingly. RESULTS The activated tissue electric field distributions in the human femoral head under different screw parameter variations are shown in Figures 5–7. To give an insight into the activated tissue electric field distribution, contour lines of the field for a two-dimensional (2D) cutting plane of the human femoral head are Bioelectromagnetics
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Fig. 4. Measuring points in validation experiment (left), and in numerical simulation model (right).
presented. Figure 5 shows that by keeping the screw in the same position, the original tip and the round tip designs have similar electric field distributions. After changing the screw to the flat tip design, the electric field showed a minor difference around the screw tip. In Figure 8, the volume fraction shows an electric field change in the human femoral head of only 0.2% between the original tip and the round tip designs. This difference rises to 1.4% when the tip design is changed to flat. The linear regression function for simulation of tip designs is f(x) ¼ 0.698x þ 25.161 and R2 is 0.876. The screw insulation length was varied under the condition of keeping the screw position constant and using the original screw tip design. Figure 6a shows
the insulation length variation in the case of the same screw shaft electrode. The tissue area activated by the electric field increased when the screw insulation length decreased. Figure 9a shows that each 1 mm change in the insulation length resulted in a volume fraction difference in the femoral head of approximately 1.8%. The linear regression function is f(x) ¼ 1.738x þ 31.063 and R2 is 0.997. In Figure 6b, the length of the insulation varied, while the screw tip was kept the same. The results show that the larger the screw insulation length is in this variation, the larger the activated tissue electric field distribution area. The volume fraction increased by approximately 1% when the insulation length was increased by 1 mm (see Fig. 9b). The linear regression function for the
Fig. 5. Numerical simulation of electric field distribution testing of three screw tip designs. The electric field in light and black areas provides regions of 70 V/m, whereas the mid-grey areasare optimalactivatedregionsforbonetissuegrowth. Bioelectromagnetics
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Fig. 6. Numerical simulation of electric field distribution testing of different screw insulation lengths, where (a) thelengthofscrewshaftelectrodestaysthesameand (b) thelengthofthescrew tip electrode stays the same.The electric field in light and black areas provides regions of 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
Fig. 7. Numerical simulation of electric field distribution testing: (a) screw backward positioning and (b) forward positioning.The electric field in light and black areas provides regions of 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
simulation of this kind of insulation variation is f (x) ¼ 0.973x þ 23.029 and R2 is 0.996. Figure 7 shows the electric field distribution of the backward and forward screw positions under the condition of using the original screw design. The electric field distribution area is larger when the screw is moved backwards and smaller when the screw is moved to the dome of the femoral head. Figure 10 shows that each 1 mm change in the screw position results in an approximately 1.5% change in the volume
fraction in the femoral head. The linear regression function for the simulation of the screw positioning parameter is f(x) ¼ 1.517x þ 26.575 and R2 is 0.989. The volume fraction for these four parameter variations shows that the screw tip design has the least effect on the electric field distribution, while the insulation length and position variations have similar effects. Figure 11 shows the electric field distribution in the femoral head of the different tissues surrounding Bioelectromagnetics
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Fig. 8. Numerical simulation of screw tip design: results of volume fraction. The line with the star is the volume fraction for each screw positioning parameter, and the dashed line without a star is the best fitting linear regression function of the numerical simulation.
the bone but keeping the screw position and design the same. Tests under these conditions revealed that the activated tissue electric field area increased when the surrounding tissue changed from blood to muscle. But in the other two cases (muscle tissue with fat and muscle tissue with fat and skin), the electric field area of the activated tissue remained almost the same as in the case of muscle only. In Figure 12, these three scenarios are demonstrated by the volume fraction of the electric field in the femoral bone. Compared with the case of blood, 4% volume fraction is gained in the case of muscle tissue surrounded. But a further change in the volume fraction cannot be found in the cases of muscle tissue and fat, or muscle tissue with fat and skin. Figure 13 shows the electric field distribution of the different lesion materials under the condition of keeping the tissues surrounding the bone as muscle tissue with fat and skin. The screw position and design
Fig. 10. Numerical simulation of screw positioning: results of volume fraction. The line with the star is the volume fraction for each screw positioning parameter, and the dashed line without a star is the best fitting linear regression function of the numerical simulation.
were kept the same. The activated tissue electric field in the femoral head significantly increased when the tissues are changed from fat to blood. Figure 14 shows that when the lesion is fat, the volume fraction is 46% higher than when the lesion is blood. Figure 15 reveals that the results of the validation experiment are close to those of the numerical simulation when the measuring points are at 5 mm depth in the femoral head and on the surface of the bone. On average, RMS voltages show a 24% difference when the measuring points are on the surface of the bone. When the measuring points are at 5 mm depth in the bone, this percentage decreases to 19%. DISCUSSION Our present study was the first to investigate the influence of different parameters of an electro-stimu-
Fig.9. Numericalsimulationof screwinsulationlength, where (a) thelengthofthescrewshaftelectrodesstaysthe sameand (b) thelengthofthe screw tip electrodestaysthe same: volume fraction. The line with the star is the volume fraction foreach screw positioning parameter, and the dashed linewithout a staristhebest fittinglinearregressionfunctionofthenumericalsimulation. Bioelectromagnetics
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Fig. 13. Numerical simulation of electric field distribution testing of different lesions, where the designed sphere-shaped lesion in thebone is considered as (a) fat and (b) blood.The electric fieldin light andblackareasprovidesregionsof 70 V/m, whereas the mid-grey areas are optimal activated regions for bone tissuegrowth.
lating implant on the electric field distribution in the human femoral head. We experimentally validated the numerical simulation model of a femoral head and demonstrated that the position of the implant in the femoral head and length of the implant insulation have a significant influence on the volume of tissue activated in the femoral head compared to the effect from the implant tip design. Comparing the numerical data to the experimental results, the electric potential differences at all the measuring points were in an acceptable range (average
20%). Subsequently, a series of evaluations on the effect of different screw parameters on the electric field were carried out using the numerical model. Nevertheless, the electric properties of the human femoral head in the model were not calibrated according to the experimental validation. Although only 20% difference was tested by using the electric properties from Gabriel et al. [1996a,b], the real electric properties of the specific human femoral head need to be calibrated and used in the evaluation of electric field distribution in the femoral head. This could be achieved by an automatic optimisation process. The goal of the optimisation could be the minimum difference of numerical data to experimental results. In Kraus [1984], the electric stimulating implant was located in the weak bone to stimulate new bone growth, but the sensitivity of the electric field in the bone to the implant was not investigated. Our results show that in the current human femoral head, the insulation
Fig.12. Numericalsimulationoftissue surroundingthebone: volumefraction.
Fig. 14. Numerical simulation of lesion in the bone: volume fraction.
Fig. 11. Numerical simulation of electric field distribution testing of different tissues surrounding the bone, where the surrounding tissueis (a) blood, (b) muscle, (c) muscle with fat, and (d) muscle with fat andskin.The electric fieldinlight andblackareasprovides regionsof 70 V/m, whereasthemid-greyareasare optimalactivatedregionsforbonetissuegrowth.
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Fig.15. Results of validation experiment, where the measuring points are (a) approximately 5 mm depthinthefemoralheadand (b) onthesurfaceofthefemoralhead: whitebarsarethe RMSvoltages inthevalidationexperiment; andgreybarsarethe RMSvoltagesinthenumericalsimulation.
length of the screw had a linear relation to the change in the activated tissue electric volume in the femoral head. To achieve large VTA in the femoral head by changing the length of the insulation, two methods are possible: Increasing the screw insulation length while keeping the screw tip electrode length the same or decreasing screw insulation length while keeping the screw shaft electrode length the same. The influence of a 1 mm screw insulation length change on the VTA in the screw shaft case is approximately double as high in comparison to the screw tip case (1.8% and 1.0%, respectively). Moreover, the relevant low influence on VTA was found from the screw tip designs (0.2% in round tip and 1.4% in flat tip). This demonstrates that the shape of the screw tip design does not influence the VTA in the femoral head. However, the effect of VTA in the femoral head from the radius of the screw implant was not included in our present study because the size of the screw radius is based on the patient’s femoral head size. Therefore, to design a patient’s specific screw implant, the number of the screw implant and the radius for each implant should be taken from the relevant surgery process and evaluated. In our present work, the mechanical stability of the bipolar induction screw system with different tip designs and insulation lengths was not tested. Although in Mittelmeier et al. [2004], the stability of the original Asnis III s-series screw was tested and the result showed that the BISS screw (which was later named the Asnis III s-series screw) had significantly higher mechanical values due to a reinforcing effect by the attached electrode (in order to produce a customised screw for specific patients, our results and the mechanical stability should be considered). In a previous study by Su et al. [2013], the insulation length was examined with only one implant parameter. In the present study, screw positioning, Bioelectromagnetics
screw tip design, and screw insulation length were analysed. Among these parameters, the screw positioning in particular was relevant and important because it could be changed during the implantation process. Our numerical data showed that each 1 mm tiny screw positioning could bring 1.5% VTA change in the femoral head. It revealed an approximated negative linear relation between the screw positioning and VTA in the femoral head. This can give guidance for intraoperative application considering the effect of the screw position on the electric field in the bone (for instance, by moving the screw implant outside of the femoral head to get a larger VTA). The screw position revealed the largest effect on the electric field distribution in the femoral head. The screw position was only investigated without considering a necrotic lesion; as they are usually removed and filled with fresh autologous bone during surgery [Ellenrieder et al., 2013]. In the future, the optimum screw position in the femoral head could be calculated pre-operatively using a patient-specific model reconstructed from the patient’s data. Future approaches could integrate numerical optimisation algorithms to find optimum screw parameters for each individual patient. The present electric field distribution evaluation was based on various assumptions and simplifications. The electrical properties of cancellous bone and cortical bone for the human femoral head were set to both isotropic and homogeneous conductivity and permittivity. Since bone density varied between patients, the electrical properties of the femoral bone could also differ, especially for osteoporosis patients. Williams and Saha [1996] found that the specific capacity of wet human cortical and cancellous bone depended on bone density. Sierpowska et al. [2006] found that the electrical and dielectric parameters of human trabecular
Electric Field in Human Femoral Head
bone, especially the relative permittivity and the dissipation factor, were significantly and specifically related to the trabecular microstructure. Therefore, to achieve patient-specific stimulation modelling, the relationship between bone density and dielectric properties should be taken into account in future studies. Electric fields varying from 5 to 70 V/m were considered to find the optimum effect on bone growth [Kraus, 1984]. Kuzyk and Schemitsch [2009] explored electrical stimulation techniques leading to bone cell proliferation and attempted to elucidate the intracellular processes for cell proliferation. The biological effects of PEMF on bone growth have been recently studied. Chang et al. [2004] investigated the effect of PEMF stimulation on osteoblast cell activities and found that the effect of PEMF on bone tissue formation was most likely associated with an increase in the number of cells but without enhancement of the osteoblast differentiation. A low frequency of 7.5 Hz has been found to play a modulating role in human mesenchymal stem cell (hMSC) osteogenesis [Tsai et al., 2009]. The most significant effect of PEMF stimulation on hMSC differentiation was observed at 50 Hz [Luo et al., 2012]. However, the limit of the electric field that can damage bone growth is still an open question. Moreover, in our study, the bipolar induction screw system was used for stimulating the weak bone in the femoral head in the case of avascular necrosis. However, the necrotic lesion within the femoral head has not been taken into account in the evaluation of implant parameters until now. Although the size of the surrounding tissue of the human femoral head in the simulation model was comparable to reality, it was simplified by using blood due to the geometric complexity of model reconstruction and lack of knowledge of the electric properties of the soft tissue at a frequency of 20 Hz. This model simplification is acceptable because the attached tissue surrounding the bone has the greatest influence on the electric field distribution in the numerical simulation. But the necrotic lesion in the femoral head cannot be neglected when using numerical simulation to guide a surgical approach. For future patient-specific modelling, the position and size of the necrotic lesion within the numerical model of the femoral head considering the attached surrounding tissues may be acquired from the patient’s MRI data. CONCLUSION Numerical simulations can give insight into the electric field distribution in bones. Our study demonstrated that the electromagnetic stimulation of bone was sensitive to the given implant parameters. The calculated data are relevant for the optimisation of
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implant design and the clinical application. Thereby, both the positioning of the screw and the length and position of the insulator in the screw have a significant effect on the electric field distribution in the femoral head. For a patient-customised screw, the position and the insulation length of the screw, rather than the tip shape, dominate the activated tissue electric field in the femoral head. Repositioning the screw by a maximum of 10 mm and changing the insulation length by a maximum of 4 mm resulted in changes in the electric field volume of 16% and 7%, respectively. Our results also demonstrate that the attached tissue surrounding the bone had the most influence on the numerical simulation. Therefore, it was reasonable to simplify the tissue surrounding the bone in the numerical simulation. Comparing the results of numerical simulation to the experimental data, an average difference in the electric potential of 20% occurs. In future applications, different screw parameters could be calculated pre-operatively in order to find optimal patient-adapted solutions for the treatment of avascular necrosis and bone defects. ACKNOWLEDGMENTS The authors would like to thank the Institute of Radiology, University Medicine Rostock, for providing the CT data and Catherine Ebner for her technical support. REFERENCES Bassett CA. 1982. Pulsing electromagnetic fields: A new method to modify cell behaviour in calcified and noncalcified tissues. Calcif Tissue Int 34:1–8. Brighton CT, Black J, Friedenberg ZB, Esterhai JL, Day LJ, Connolly JF. 1981. A multicenter study of the treatment of non-union with constant direct current. J Bone Joint Surg Am 63:2–13. Chang WH-S, Cheng L-T, Sun J-S, Lin F-H. 2004. Effect of pulseburst electromagnetic field stimulation on osteoblast cell activities. Bioelectromagnetics 25:457–465. Ellenrieder M, Tischer T, Kreuz PC, Fröhlich S, Fritsche A, Mittelmeier W. 2013. Arthroscopically assisted therapy of avascular necrosis of the femoral head. Oper Orthop Traumatol 25:85–94. Friedenberg ZB, Brighton CT. 1966. Bioelectric potentials in bone. J Bone Joint Surg Am 48:915–923. Fukada E, Yasuda I. 1957. On the piezoelectric effect of bone. Phys Soc Jpn 12:1158–1162. Gabriel S, Lau RW, Gabriel C. 1996a. The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 41:2251–2269. Gabriel S, Lau RW, Gabriel C. 1996b. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41:2271– 2293. Bioelectromagnetics
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