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Reconstruction of optical scanned images of inhomogeneities in biological tissues by monte Carlo simulation J.B. Jeeva, Megha Singh
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Received date: 28 October 2014 Accepted date: 16 February 2015 Cite this article as: J.B. Jeeva, Megha Singh, Reconstruction of optical scanned images of inhomogeneities in biological tissues by monte Carlo simulation, Computers in Biology and Medicine, http://dx.doi.org/10.1016/j.compbiomed.2015.02.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Reconstruction of optical scanned images of inhomogeneities in biological tissues by Monte Carlo simulation
J.B. Jeeva and Megha Singh1* Biomedical Engineering Division School of Biosciences and Biotechnology V.I.T. University, Vellore-632014, India
1
Center for Biomedical Engineering
S.G.N. Educational Foundation #12, III Street, Park Avenue Velachery, Chennai – 600042, India
Total number of words: 6411 The number words of the abstract: 270 The number of figures: 10 The number of tables: 3
* Corresponding author Email: [email protected]
1
Abstract The optical imaging of inhomogeneities located in phantoms of biological tissues, prepared from goat’s isolated heart as control tissue and embedded with spleen and adipose tissues representing tumors, by Monte Carlo simulation, is carried out. The proposed scanning probe consists of nine units. Each unit is equipped with one photon injection port and three ports arranged in a straight line to collect backscattered photons emerging from various depths, and one port, placed coaxially to the source on the opposite side of the phantom, to collect the transmitted component. At each position of the grid, superposed on the tissue phantom, photons are introduced through source port into the phantoms and backscattered and transmitted photons are collected by respective ports. Based on the data collected from the entire grid surface the respective gray-level images are reconstructed. The inhomogeneity located at certain depth (2,4,6mm) is visualized in three images formed by the backscattered data collected by three ports. Increase or decrease in normalized backscattered intensity (NBI) observed in their scans corresponds to that of high scattering (adipose) or absorbing (spleen) inhomogeneity compared to that of control tissue and also their location as determined by NBI variation as received at various ports. The images constructed from the transmitted data are associated with decrease in intensity. The scans of these images through their centers show that normalized transmitted intensity (NTI) attains its maximum value when the inhomogeneities are at depth 6mm. These scans are of higher amplitude for spleen compared to that of adipose tissues. Thus the data received by backscattering and transmission complement each other in identifying the location and type of inhomogeneities. Index Terms— Monte Carlo simulation, photons backscattering and transillumination, biological phantoms, inhomogeneities/tumor
1. Introduction The interaction of laser radiations with biological tissues is a complex process due to involvement of several mechanisms. These include backscattering, transmission and absorption. The backscattering and transmission processes are further associated with collimated and multiple scattered photons, respectively [1, 2]. Each process involves the interaction of radiations with structural components of tissues, which depend on their optical parameters, absorption and scattering coefficients and anisotropy parameter. Other parameters which influence this process are refractive index of the medium and wavelength of the light source [3, 4]. The tissue
2
parameters vary depending on their composition and functional properties between disease and control. Based on the characteristics of laser radiation, various techniques for clinical applications have been developed. An important application of this is to detect tumor in biological tissues. At present the most prominent screening tool for cancer detection is x-ray mammography, which exposes the patient to ionizing radiation, thus causing risk of cancer induction. The techniques such as positron emission tomography, MRI, ultrasound, and thermography have also contributed significantly in diagnostic medicine. Ultrasound data, based on variation of acoustic impedance, show the presence of tumor at fairly advanced stage after extensive application of computer algorithms. Other techniques require injection of contrast agent and are expensive. In contrast, the optical imaging emerges as an alternative tool in detection of inhomogeneity hidden in soft biological tissues [5, 6]. The prominent optical techniques are based on frequency-resolved [6, 7], time-resolved [8] and continuous wave procedures, employing different geometries [9, 10]. During the past three decades, red and near-infrared spectroscopy and imaging, based on backscattering and transmission of radiation have emerged as powerful research and diagnostics tools for both laboratory studies and clinical trials. Some of the applications include imaging of human tissues, measurements of oxygen consumption of muscle, detection of tumor in breast tissues, functional brain mapping and localization of internal organs in thorax region [11, 12]. Through his pioneering work on transillumination, Cutler viewed the changes in human breast [13], leading to development of the frequency domain optical mammography, carried out by placing the sandwiched human breast between laser source and set of detectors [14-15]. Recently the transillumination of biological tissues, a time dependent procedure, is carried out by placing the source and detectors on the same surface [16, 17]. 3
There are various types of tumors such as carcinoma, subcutaneous fat with melanoma, squamous cell carcinoma, adenocarcinoma, fibrosarcoma with their distinct optical properties [18,19]. The development of tumor may not be confined to single layer of tissues below the surface. The imaging of these, either by application of a single probe directly [20] or indirectly by parameter derived from tissue reflectance, is carried out [21]. The optical coherence tomography (OCT) [22] has extensively been used for imaging of biological tissues to a depth limited to around 1.5mm. Other techniques include mapping of tissue optical properties using modulated imaging [23], time-resolved diffuse reflectance with null source-detector separation [24] and log-slope analysis [25]. As these are single beam techniques, the backscattered data are confined to single layer of tissues under one measurement condition. In contrast to single trans-illumination probe, the image reconstructed by optical tomography provides the cross-sectional details of a single layer which could further be extended to multiple images of respective slices [26] for their 3D image reconstruction [27]. But for routine multilayer imaging of biological tissues, an inexpensive spatially resolved optical system, based on backscattering and transmission of radiation, is required.
The analysis of radiation interaction with multilayer inhomogeneous tissues requires not only the optical parameters of individual tissues but also their refractive indices [28]. Experimentally this has been shown that the backscattered photons emerging closer to beam entry point originates from the tissue layers close to surface, whereas, photons received at farther distances emerge from the deeper layers [29]. The surface profile constructed from these backscattered signals is a unique feature of biological tissues and by best-fit of this profile with that as obtained by Monte Carlo simulation, the optical parameters of various tissues are also determined [30-31]. In contrast to this the transmitted signal emerging out on opposite surface carries information on 4
overall composition of tissue structure, which may be valuable for parametric analysis and reconstruction of respective images. For this purpose a detailed analysis photons interaction in tissue phantoms, with and without inhomogeneties is required. Monte Carlo simulation (MCS), which provides data on scattered photons even close to beam entry point on individual histories, is ideal for this purpose [32]. Thus the objective of the present work, based on the MCS, is to develop an imaging system, which establishes relationship between various optical and tissue phantom related parameters to detect the inhomogeneities in various layers, which are either highly backscattering or absorbing compared to that of control tissues.
2. Materials and Methods 2.1 Simulated multi-layer system Fig 1(a) shows the schematic of the system to measure backscattering and transmission components of radiation after multiple scattering from the control tissue phantom of infinite length and width and thickness 10mm. For imaging purpose a grid of size 30x9mm was superposed on the phantom. The origin of the coordinates system of phantom coincided with the center of the grid. The resolution of the grid was 1mm2, the same as size of injection and collection ports. The scanning head, consisting of nine units to inject and receive backscattered and transmitted photons, was initially placed at the left side of the grid. Each unit contained one input port for injection of infinitely narrow beam of photons and three receiving ports located at distance 2, 4 and 6mm from the input port to collect backscattered radiations, placed at the corresponding grid element. Our preliminary studies had shown that the separation between photons injection and collection ports placed in the probe is sensitive to the corresponding depth
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of tissue layers. Accordingly the nearest receiving port at 2mm received maximum number of backscattered photons from tissue layer located at depth 2mm approximately, whereas, the ports at 4 and 6mm collected photons from deeper layers. The transmitted component in each unit was received by an exit port of area 1mm2, placed coaxially with input port of the phantom. Initially ten million photons of wavelength 632.8nm were injected at each input port, which after interaction with medium emerged as backscattered and transmitted components. The outline of the ports is shown in Fig. 1(b). The center to center separation between any pair of ports was 2mm. After collection of data at first grid line, the scanning head was moved 1mm away along xaxis. By this process the data from the entire grid of size 30x9mm were collected with final position of photon entry port at 24mm.
From the number of backscattered photons collected within 1mm2 the normalized backscattered intensity (NBI) was calculated by
NBI (%) =
Ni , j N0
X 100
N0 – total number of incident photons Ni,j - total number of photons collected at any port The NBI values as obtained at various locations of grid, along with their positions (i,j), were stored in the computer for further processing [33]. Similarly the number of transmitted photons collected within 1mm2 grid (i,j) was represented as the normalized transmitted intensity, given by
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NTI % =
Ti , j N0
X 100
N0 – total number of incident photons Ti,j – total number of transmitted photons collected by the port The NTI values were stored in the computer along with their positions for further processing.
2.2 Monte Carlo Simulation Monte Carlo simulation (MCS), due to its stochastic features, can be applied to any random event in nature. For this study it was used to simulate the light transport by injecting photons or photon packets on a random walk through biological tissues. The photon was treated as a neutral particle and its movement was governed by the mean free path, scattering and absorption coefficients, and anisotropy parameter of the medium [34]. The photons after multiple interactions within the medium, emerged as backscattered and transmitted components on the entry and exit surfaces of the phantom, respectively. The code for MCS is written in C++ language and time taken by 10 million photons at one grid location is 12min on a computer with quad-core processor of speed 3GHz and 2GB RAM. Total time taken for one operation over the grid surface was 12x9x24 min = 44hr. The photons were introduced perpendicular to the surface for maximizing their entry and minimizing the surface reflection. Each photon, out of ten million, was initialized with a weight of unity. The step-size‘s’ of the photon was calculated by a generated random variable, ς , given by
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s=
− ln ς
µt
, and µ t = µ a + µ s
(1)
where µ t , µ a , µ s were total attenuation, absorption and scattering coefficients of the medium, respectively. The value of the random number ς was between 0 and 1. The deflection angle θ was calculated by
(1 − g 2 ) 1 cosθ = 1 + g 2 − 2g (1 − g + 2 gς )
cosθ = 2ς − 1
2
for g≠0
(2)
for g =0
(3)
where g is the anisotropy parameter of the medium. The azimuthal angle ψ was given by
ψ = 2πγ
(4)
where γ is a random variable between 0 and 1. The path length of first interaction of photon was found, and thereafter this was moved. If the photon has left the tissue, the possibility of its presence at one of the receiving ports was checked. If detected, a counter was incremented to count the photon received by the corresponding port. If the photon was internally reflected, then the photon location was updated and the program continues. With each step the photon weight was reduced due to absorption by the tissue. The amount of weight lost, ∆Q in absorption was given by
∆Q = W
µa µt
(5)
where W was the total weight of the photon. The photon weight and direction, after scattering in tissues of matched and mismatched refractive indices, were updated. The new position of the photon (x’,y’,z’) from the previous position (x,y,z) was given by
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x ' x sin θ cosψ y ' = y + s sin θ sinψ ' z z cos θ
(6)
If the photon weight falls below a minimum threshold (Wc = 0.001), then it was subjected to roulette condition to eliminate this. Further details of this simulation are given elsewhere [34].
2.3 Tissue phantoms In order to test the optical probe, digital tissue phantoms were made. For this purpose the goat tissues heart, adipose and spleen were chosen, which was based on the optical properties of tumor removed from cancer patients [35]. Heart tissue was used as the control, and adipose and spleen as inhomogeneities, representing abnormal conditions. The optical properties of the tissues are given in table 1. The refractive indices of heart, adipose and spleen were 1.40, 1.455 and 1.4, respectively [33].
Table 1 Optical parameters of adipose, spleen and heart tissues
Organ/tissue
Scattering coefficient (cm-1)
Absorption coefficient (cm-1)
Anisotropy parameter
Heart
100.03
1.27
0.990
Spleen
109.86
4.00
0.995
Adipose
419.92
1.50
0.994
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Adipose or spleen tissue of size 2mm diameter was located below the center (0,0,0) of the control tissue phantom. For first simulation adipose was embedded at depth (0, 0,2mm), followed by its placement at (0, 0,4mm) and (0, 0,6mm). For each position the MCS was performed. Similarly, spleen tissue was also embedded in control phantoms at locations (0, 0,2mm), (0, 0,4mm) and (0, 0,6mm) and their MCS carried out. By same procedure the distribution of the transmitted and backscattered photons in the control tissue, to be used for image subtraction purpose, was also performed. Tissues considered for this work are prepared under in vitro conditions. Hence there is no movement of sub-cellular component, in contrast to proteins molecular dynamics in tissues [36]. Hence the tissues are considered under equilibrium conditions with fixed values of the optical parameters.
2.4 Data acquisition The optical probe was implemented by performing the MCS of light photon propagation in tissues. The photons out of 10 million that reach the output ports were counted and converted into respective NTI and NBI values. By shifting of scanning head by 1mm in x-axis direction on to next grid line, the MCS for photon transport was repeated. This process was repeated till source port reaches at position x=24mm. Entire data were stored in four files, one for transmission port and three for the backscattering ports.
2.5 Data processing The data acquired were processed separately to obtain transmission and backscattered images by MATLAB.
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2.5.1 Transmission data processing
The data acquired by the transmission port was filtered by 5x5 low pass Gaussian filter. The filter function of this in frequency domain is given by
H (u , v) = e − D
2
( u , v ) / 2 D02
(7)
where D0 is the cutoff frequency and D(u,v) is the distance from the center of the frequency rectangle [37]. This filter reduces noise and produces a smoothed image. The background data, as obtained from control tissue, was subtracted to increase the contrast of the image.
2.5.2 Backscattered data processing To reduce the variability, averaging was performed on the acquired data. For an N x N data the averaged value u(x,y) of NBI, by averaging the predefined neighborhood of f(x,y), was obtained [38]. This is performed by the formula
u ( x, y ) =
1 M
∑ f ( n, m )
(8)
n , m∈ S
For x,y=0,1….N-1, S is the set of coordinates in the neighborhood of (x,y), M is the total number of neighboring points (=9) taken. This operation forms an averaged image. The background data was subtracted to increase the contrast of the image. The resultant image was median (3x3) filtered to reduce the statistical noise and the noise associated with averaging procedure. In this filtering process, a predefined window consisting of the neighborhood of the data point (x,y) was chosen and the median of the data points within the window was found out. This was repeated for all data points in the image. Thereafter gray level transformation was applied on the resultant image for localization of the embedded tissue. Further details of the 11
image processing procedures are given in [38]. The sequence of various operations applied for image processing is given in Fig. 2.
2.6 Testing of simulation procedure Monte Carlo methods follow a pattern when they are implemented without error. To test the developed code a circle inscribed inside a square was considered. The ratio of the area of the circle and square is pi/4. Here the %NBI data obtained for heart tissue, measured by the probe at 2mm, were used. A point p(x,y) is chosen on the xy-plane of the raw image where the reflectance data are present. With p as center and R as radius a circle is drawn and the number of photons reflected within this region is counted. Thereafter with p as center and 2R as length of each side a square is drawn and the number of photons present in this region is counted. The ratio of the number of photons within the circle to that of square region was calculated for each simulation with input of 1000 to 10million, were calculated. The ratio varies from 0.798 to 0.7853, with minimum deviation from the actual value, 0.785(pi/4) with an input of 10 Million photons.
2.6.1 Convergence of Monte Carlo method The convergence of the Monte Carlo code was determined by calculating the 95% confidence interval (CI) of the %NBI with respect to the number of photons using the expression [39],
95%CI = [ mean − 1.96 X
σ m
, mean + 1.96 X
σ m
(9)
where m (=16) is the number of simulations and σ is the standard deviation of %NBI. Fig. 3 shows the confidence interval calculated for heart tissue for photon numbers ranging from 1000
12
to million. This shows that the CI converges with increase in the number of photons as used for this simulation.
The mean statistical error was calculated using the equation,
MSE =
σ
(10)
m
and the results obtained show (Fig. 4) that the error is reduced with increase in number of photons, indicating the convergence of the NBI. Tissues are assumed to be of homogeneous nature. This was further verified by plotting of the surface profiles of heart, adipose and spleen tissues, represented as variation of normalized backscattered intensity with distance along x-axis (Fig. 5). The profiles obtained by this procedure, as shown on the left and right sides, match each other. The analyses carried out in other directions also show similar results, thus confirming the homogeneous nature of tissues.
3. Results Based on data of backscattered photons received at three ports located at various distances from beam entry port the images are constructed. Fig. 6 shows these images of adipose tissue of size 2mm placed at various depths. Fig. 6(i) shows the spatial distribution of NBI obtained on the surface of the control with adipose tissue located at (0,0,2mm), as collected by three ports shown as a, b and c, respectively. For determination of the NBI distribution these images are scanned through their centers. The maximum intensity is observed at port ‘a’, whereas, this is reduced at ports ‘b’ and with further reduction at ‘c’, attributed to the increased multiple scattering of
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photons in the tissues. With the placement of inhomogeneity at depth (0,0,4mm) the photons received at port ‘b’ are comparatively increased, whereas, their number at ports ‘a’ and ‘c’ is reduced (Fig.6(ii)). Accordingly the NBI is reduced. A further change is observed by placing the adipose tissue at (0,0,6mm) (Fig. 6(iii)). The NBI at port ‘c’ is more than that as measured at ports ‘a’ and ‘b’. Due to increased scattering of adipose tissues compared to that of control tissue the net change is positive. In contrast to adipose, the spleen is highly absorbing. Fig. 7 (i-iii) shows the images of the NBI as received at three ports (a-c). Fig. 7(i) shows the NBI images after placing the spleen tissue at (0,0,2mm). Due to image subtraction procedure the photons collected at port ‘a’ are less than that collected at ports ‘b’ and ‘c’. This aspect is further highlighted by the horizontal scan taken at the center of the images. By placing the inhomogeneity at depth (0,0,4mm) all the NBI values are reduced with minimum occurring at port 4mm away from input port (Fig. 7(ii)). With the increase of depth of placement (0,0,6mm) the multiple scattering is further increased, leading to decrease in NBI with its minimum value at 6.0mm away from beam entry point (Fig. 7(iii)). These finding further support that even for highly absorbing tissues the number of photons received at various ports depends on the depth of location of inhomogeneity.
The peak NBI (PIB) and the full width at 75% of maximum (FW75%MB) obtained from the images constructed using the data collected by the three backscattered ports are given in Table 2. We observe that the peak value decreases with the depth of placement of tissue increases. The |PI| value is more for adipose compared to that of spleen. The FW75%W values obtained for adipose tissue show slight increase with depth whereas for spleen it remains around the same value.
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Table 2 Peak NBI (PIB) and full width at 75% of maximum (FW75%MB) from the images constructed by data collected at the backscattered port Depth (mm)
FW75%MB (mm)
PIB Spleen
Adipose
Spleen
Adipose
2
0.00386
0.11784
3.24
3.24
4
0.00206
0.00335
3
3.36
6
0.00054
0.00171
3.18
3.48
Fig. 8 shows the surface profiles, as plotted by the NBI values, measured at different ports with inhomogeneity placed at location (0,0,2mm). The NBI values at all collection ports are higher for adipose compared to that of spleen tissues, which are attributed to their optical characteristics.
The reconstructed images from the transmission data, after background subtraction, when adipose and spleen are embedded at different depths are shown in Fig. 9(i) and Fig. 9(ii), respectively. The influence of scattering on the image depends on the location of the inhomogeneity. The placement at (0,0,2mm) is associated with high scattering, which leads to noisy image after passing through adipose or spleen tissues (Fig.9a). The effect of noise is reduced when the inhomogeneity is placed at (0,0,4mm) (Fig.9b). The noise is minimized when this is placed at depth (0,0,6mm) as shown by its NTI profile (Fig.9c). This further shows the minimal effect of the overlying tissues.
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The peak NTI (PIT) and full width at 75% of maximum (FW75%MT) are calculated from the scans of reconstructed transmission images. The magnitude of peak intensity |PI| increases as the depth of placement of the tissue increases and the FW75%M decreases, as shown in Table 3. The |PI| is more for adipose compared to that of spleen tissue when these are embedded at (0,0,6) but an opposite pattern is observed for the FW75%M. This is taken as representation of size of inhomogeneity, which shows deviation from actual size due to occurrence of multiple scattering, depending on location within the tissue.
Table 3. Peak NTI (PIT) and full width at 75% of maximum (FW75%MT) from the images constructed by the transmission data. Depth (mm)
PIT
FW75%MT (mm)
Spleen
Adipose
Spleen
Adipose
2
0.0000904
0.00014
4.7
2.875
4
0.00016
0.00017
3.25
2.5
6
0.00033
0.00023
2.25
2.127
The depth distribution of photons within the control phantom with adipose and spleen tissues embedded at 6mm is shown in Fig 10. The distribution varies in the neighborhood of the embedded tissue. It is associated with high scattering and absorption for adipose and spleen inhomogeneities, respectively. This also explains the occurrence of higher PIT due to high scattering of photons by adipose tissues and high absorption in spleen tissues leading to lower PIT.
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4. Discussion The laser scattering and absorption processes in biological tissues depend on their optical parameters. The collimated transmission, associated with less scattered photons, carries the information about the medium but the signal intensity is low. In contrast the collection of collimated and less scattered photons over a comparatively longer time duration form high intensity signals leading to diffuse imaging of the objects hidden in tissues [1,10]. On the other hand, the backscattered component carries the multiple scattered photons, collected at various distances from the beam entry point. The processing of these provides useful information on clinical status of tissues as demonstrated by the success of NIRS [16]. In the present study the contribution of specular reflection, due to normal incidence of the photons, is minimized [3]. The present study is based on the diffuse backscattering and transmission. To obtain the net change due to inhomogeneity in backscattering the output received from each port is background subtracted. After averaging the data are median filtered [37]. The recent results show that the placement of adipose inhomogeneity at a depth 2mm is not only detected by port located at 2mm but also by ports located at 4 and 6mm. This is attributed to migration of photons through the additional path-length of tissues after undergoing multiple scattering [17]. With the placement of inhomogeneity at deeper locations, the NBI attains maximum at respective ports associated with very low values of NBI at other ports. This pattern of reduced backscattering within the tissue medium is attributed to high value of anisotropic parameter [3]. In contrast to this, spleen is an absorber leading to reduced NBI values at every port due to its optical parameters. Due to this the pattern of variation in the NBI images is reversed. The migration of photons in spleen also contributes to form images, similar to that of adipose, observed at various ports [17].
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The diffuse reflectance directly [1,35,40] and a feature parameter derived from diffuse reflectance indirectly [21] have been applied to differentiate benign and malignant tissues. In contrast to this the surface diffuse reflectance profile possesses unique features as it provides information on the tissue compositional variation within multi-layers, observed at various ports. Due to this the experimentally measured profiles of various in vivo tissues are used to determine their optical parameters by matching these with profiles as obtained by Monte Carlo simulation [41,42]. The present studies show that by placing an inhomogeneity at depth 2mm a distinct surface reflectance profile is obtained but this could not be achieved with its placement at deeper locations due to shift in scattering pattern. This is valid for different type of inhomogeneities. In transillumination, the photons are interacting with the entire medium and overall changes in the NTI are observed at the exit end. By image subtraction the net change due to placement of abnormality is determined. When the inhomogeneity is placed at depth 2mm a broadening of the scan is observed, attributed to multiple scattering of photons. The broadening, represented as the FWHM is reduced and pulse height is increased when inhomogeneity is placed at depth 6mm, which means the photons are less scattered prior to exiting from the surface. The presence of spleen shows enhanced absorption, leading to better visualization compared to its placement near the entry surface. These findings are in contrast to results obtained by Boas et al [43], who have shown that the placement of the inhomogeneity in the middle of tissue phantom could be better visualized than that at other positions. The transillumination presents image of the 3D system in 2D, as in optical mammography [7], and due to this the location of inhomogeneity could not be well elaborated. But in the present study this information is provided by backscattered signal which is associated with location of the inhomogeneities within the tissues [44]. Similar to optical tomography [26,27] this technique also 18
provides the cross-sectional images of tissue structure. The multi-port system thus provides multi-slices images for further analysis of tumor development in tissues. The image enhancement agents are not required for this analysis, which is in contrast to as determined by log-slope method [45] and can detect the object of 2mm diameter even placed at depth 6mm. To minimize the effect of blurring due to multiple scattering [46,47] the parameter full width at half maximum is calculated as full width at 75% of the maximum intensity. By this procedure the size of the inhomogeneity as calculated from intensity plots from backscattering data is 60-80% larger than actual ones. In contrast, in transmission mode the calculated size, when inhomogeneity is placed near the exit surface is comparable and at depths 2 and 4mm are 25-45% larger than actual size. In conclusion, this simulation present the details which are applicable in both backscattering and transillumination conditions. The variability in images and their scans show that in the presence of inclusions placed at a depth affects their contrast due to multiple scattering [47]. This simulation is for non-invasive and contact conditions, in which the photons source is kept in touch with tissues surface. This procedure is even capable of detecting 10% change in optical parameters of tissues, a condition close to onset of cancer in tissues [48], thus providing the possibility of identifying the tumor (highly absorbing) and cyst (highly scattering) in biological tissues. Further simulation, similar to non-invasive and non-contact technique [49] may overcome the changes induced by movement of the tissue surface.
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23
[49]
Mazurenka M, Jelzow A, Wabnitz H, Contini D, Spinelli L, Pifferi A, Cubeddu R, Dalla Mora A, Tosi A, Zappa F, Macdonald R, Non-contact time-resolved diffuse reflectance imaging at null source-detector separation. Optics Express 2012; 20: 283-290.
24
Figures
Fig.1. (a) Schematic of the optical scanning system for measurement of backscattered and transmitted photons after interacting with tissues. (b) Each unit is consisting of five ports, one for photon injection and three to collect backscattered photons at various distances from beam entry port, and one to collect transmitted photons located coaxial to the input port.
25
Fig. 2. Sequence of operations for image construction
26
Fig. 3. 95% Confidence interval of the %NBI with increase in number of photons.
27
Fig. 4. Reduction of MSE with increase in photon numbers used for simulation
28
Fig. 5. NBI profiles of individual tissues along the horizontal direction with source at (0,0,0).
29
Fig.6. The reconstructed images and scans of the of normalized backscattered intensity (NBI) (%) of photons received by the first (a), second (b) and third (c) collection ports when adipose tissue is embedded in control at (i) 0,0,2mm (ii) 0,0,4mm and (iii) 0,0,6mm, respectively.
30
Fig. 7. The reconstructed images of backscattered photons and their scans (NBI(%)), as received by the first (a), second (b) and third (c) collection ports with spleen tissue embedded in control at (i) (0,0,2), (ii) (0,0,4) and (iii) (0,0,6)mm, respectively.
31
Fig. 8. The NBI profiles of control with adipose (h+a) and with spleen (h+s) phantoms with placement of inhomogeneity at (0,0,2mm).
32
(i)
(ii)
Fig. 9. Reconstructed Images, (after background subtraction) obtained from the data collected at the transmission port located coaxial to the input port with placement of adipose (i) and spleen (ii) tissues embedded inside the control tissue at (0,0,2mm) (a), (0,0,4mm) (b) and (0,0,6mm) (c).
33
Fig. 10. Depth distribution profiles when adipose (a) and spleen (b) are embedded at depth 6mm.
34
Table 1 Optical parameters of adipose, spleen and heart tissues
Organ/tissue
Scattering coefficient (cm-1)
Absorption coefficient (cm-1)
Anisotropy parameter
Heart
100.03
1.27
0.990
Spleen
109.86
4.00
0.995
Adipose
419.92
1.50
0.994
35
Table 2 Peak NBI (PIB) and full width at 75% of maximum (FW75%MB) from the images constructed by data collected at the backscattered port Depth (mm)
PIB
FW75%MB (mm)
Spleen
Adipose
Spleen
Adipose
2
0.00386
0.11784
3.24
3.24
4
0.00206
0.00335
3
3.36
6
0.00054
0.00171
3.18
3.48
36
Table 3. Peak NTI (PIT) and full width at 75% of maximum (FW75%MT) from the images constructed by the transmission data. Depth (mm)
FW75%MT (mm)
PIT Spleen
Adipose
Spleen
Adipose
2
0.0000904
0.00014
4.7
2.875
4
0.00016
0.00017
3.25
2.5
6
0.00033
0.00023
2.25
2.127
Conflict of interest
This research is supported by VIT University, Vellore, India.
There is no conflict of interest
37
Highlights • • •
Simulation of multiport optical scanning system Capable of differentiating the embedded inhomogeneities Characterization of their optical properties
38
Graphical Abstract Monte Carlo simulation is applied to imaging of photons backscattered and transmitted through a tissue phantom, made of heart tissues implanted with adipose or spleen tissues as inhomogeneities. The proposed optical scanning probe is consisting of nine units. Each unit has one photon injection port and three ports arranged in a straight line at 2, 4 and 6mm to collect backscattered photons emerging from various depths, and one port to collect the transmitted component placed coaxially to the source on the opposite side of the phantom. Figure 1 shows one unit of the optical scanning probe. The backscattered data are collected by first port located at 2mm from the input port. The path-length of photons emerging out of first port is shorter compared to that of photons received by other ports. By collections of scanned signals on the tissue surface the tissues images located at various depths are constructed. By scanning of these images the normalized backscattered intensity (NBI) signals are obtained. By comparison of NBI signals the type of inhomogeneities and their locations are determined. Such data could be helpful in development of scanning devices for early detection of tumor in tissues.
39
Reconstruction of optical scanned images of inhomogeneities in biological tissues by monte Carlo simulation J.B. Jeeva, Megha Singh
www.elsevier.com/locate/cbm
PII: DOI: Reference:
S0010-4825(15)00063-3 http://dx.doi.org/10.1016/j.compbiomed.2015.02.014 CBM2052
To appear in:
Computers in Biology and Medicine
Received date: 28 October 2014 Accepted date: 16 February 2015 Cite this article as: J.B. Jeeva, Megha Singh, Reconstruction of optical scanned images of inhomogeneities in biological tissues by monte Carlo simulation, Computers in Biology and Medicine, http://dx.doi.org/10.1016/j.compbiomed.2015.02.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Reconstruction of optical scanned images of inhomogeneities in biological tissues by Monte Carlo simulation
J.B. Jeeva and Megha Singh1* Biomedical Engineering Division School of Biosciences and Biotechnology V.I.T. University, Vellore-632014, India
1
Center for Biomedical Engineering
S.G.N. Educational Foundation #12, III Street, Park Avenue Velachery, Chennai – 600042, India
Total number of words: 6411 The number words of the abstract: 270 The number of figures: 10 The number of tables: 3
* Corresponding author Email: [email protected]
1
Abstract The optical imaging of inhomogeneities located in phantoms of biological tissues, prepared from goat’s isolated heart as control tissue and embedded with spleen and adipose tissues representing tumors, by Monte Carlo simulation, is carried out. The proposed scanning probe consists of nine units. Each unit is equipped with one photon injection port and three ports arranged in a straight line to collect backscattered photons emerging from various depths, and one port, placed coaxially to the source on the opposite side of the phantom, to collect the transmitted component. At each position of the grid, superposed on the tissue phantom, photons are introduced through source port into the phantoms and backscattered and transmitted photons are collected by respective ports. Based on the data collected from the entire grid surface the respective gray-level images are reconstructed. The inhomogeneity located at certain depth (2,4,6mm) is visualized in three images formed by the backscattered data collected by three ports. Increase or decrease in normalized backscattered intensity (NBI) observed in their scans corresponds to that of high scattering (adipose) or absorbing (spleen) inhomogeneity compared to that of control tissue and also their location as determined by NBI variation as received at various ports. The images constructed from the transmitted data are associated with decrease in intensity. The scans of these images through their centers show that normalized transmitted intensity (NTI) attains its maximum value when the inhomogeneities are at depth 6mm. These scans are of higher amplitude for spleen compared to that of adipose tissues. Thus the data received by backscattering and transmission complement each other in identifying the location and type of inhomogeneities. Index Terms— Monte Carlo simulation, photons backscattering and transillumination, biological phantoms, inhomogeneities/tumor
1. Introduction The interaction of laser radiations with biological tissues is a complex process due to involvement of several mechanisms. These include backscattering, transmission and absorption. The backscattering and transmission processes are further associated with collimated and multiple scattered photons, respectively [1, 2]. Each process involves the interaction of radiations with structural components of tissues, which depend on their optical parameters, absorption and scattering coefficients and anisotropy parameter. Other parameters which influence this process are refractive index of the medium and wavelength of the light source [3, 4]. The tissue
2
parameters vary depending on their composition and functional properties between disease and control. Based on the characteristics of laser radiation, various techniques for clinical applications have been developed. An important application of this is to detect tumor in biological tissues. At present the most prominent screening tool for cancer detection is x-ray mammography, which exposes the patient to ionizing radiation, thus causing risk of cancer induction. The techniques such as positron emission tomography, MRI, ultrasound, and thermography have also contributed significantly in diagnostic medicine. Ultrasound data, based on variation of acoustic impedance, show the presence of tumor at fairly advanced stage after extensive application of computer algorithms. Other techniques require injection of contrast agent and are expensive. In contrast, the optical imaging emerges as an alternative tool in detection of inhomogeneity hidden in soft biological tissues [5, 6]. The prominent optical techniques are based on frequency-resolved [6, 7], time-resolved [8] and continuous wave procedures, employing different geometries [9, 10]. During the past three decades, red and near-infrared spectroscopy and imaging, based on backscattering and transmission of radiation have emerged as powerful research and diagnostics tools for both laboratory studies and clinical trials. Some of the applications include imaging of human tissues, measurements of oxygen consumption of muscle, detection of tumor in breast tissues, functional brain mapping and localization of internal organs in thorax region [11, 12]. Through his pioneering work on transillumination, Cutler viewed the changes in human breast [13], leading to development of the frequency domain optical mammography, carried out by placing the sandwiched human breast between laser source and set of detectors [14-15]. Recently the transillumination of biological tissues, a time dependent procedure, is carried out by placing the source and detectors on the same surface [16, 17]. 3
There are various types of tumors such as carcinoma, subcutaneous fat with melanoma, squamous cell carcinoma, adenocarcinoma, fibrosarcoma with their distinct optical properties [18,19]. The development of tumor may not be confined to single layer of tissues below the surface. The imaging of these, either by application of a single probe directly [20] or indirectly by parameter derived from tissue reflectance, is carried out [21]. The optical coherence tomography (OCT) [22] has extensively been used for imaging of biological tissues to a depth limited to around 1.5mm. Other techniques include mapping of tissue optical properties using modulated imaging [23], time-resolved diffuse reflectance with null source-detector separation [24] and log-slope analysis [25]. As these are single beam techniques, the backscattered data are confined to single layer of tissues under one measurement condition. In contrast to single trans-illumination probe, the image reconstructed by optical tomography provides the cross-sectional details of a single layer which could further be extended to multiple images of respective slices [26] for their 3D image reconstruction [27]. But for routine multilayer imaging of biological tissues, an inexpensive spatially resolved optical system, based on backscattering and transmission of radiation, is required.
The analysis of radiation interaction with multilayer inhomogeneous tissues requires not only the optical parameters of individual tissues but also their refractive indices [28]. Experimentally this has been shown that the backscattered photons emerging closer to beam entry point originates from the tissue layers close to surface, whereas, photons received at farther distances emerge from the deeper layers [29]. The surface profile constructed from these backscattered signals is a unique feature of biological tissues and by best-fit of this profile with that as obtained by Monte Carlo simulation, the optical parameters of various tissues are also determined [30-31]. In contrast to this the transmitted signal emerging out on opposite surface carries information on 4
overall composition of tissue structure, which may be valuable for parametric analysis and reconstruction of respective images. For this purpose a detailed analysis photons interaction in tissue phantoms, with and without inhomogeneties is required. Monte Carlo simulation (MCS), which provides data on scattered photons even close to beam entry point on individual histories, is ideal for this purpose [32]. Thus the objective of the present work, based on the MCS, is to develop an imaging system, which establishes relationship between various optical and tissue phantom related parameters to detect the inhomogeneities in various layers, which are either highly backscattering or absorbing compared to that of control tissues.
2. Materials and Methods 2.1 Simulated multi-layer system Fig 1(a) shows the schematic of the system to measure backscattering and transmission components of radiation after multiple scattering from the control tissue phantom of infinite length and width and thickness 10mm. For imaging purpose a grid of size 30x9mm was superposed on the phantom. The origin of the coordinates system of phantom coincided with the center of the grid. The resolution of the grid was 1mm2, the same as size of injection and collection ports. The scanning head, consisting of nine units to inject and receive backscattered and transmitted photons, was initially placed at the left side of the grid. Each unit contained one input port for injection of infinitely narrow beam of photons and three receiving ports located at distance 2, 4 and 6mm from the input port to collect backscattered radiations, placed at the corresponding grid element. Our preliminary studies had shown that the separation between photons injection and collection ports placed in the probe is sensitive to the corresponding depth
5
of tissue layers. Accordingly the nearest receiving port at 2mm received maximum number of backscattered photons from tissue layer located at depth 2mm approximately, whereas, the ports at 4 and 6mm collected photons from deeper layers. The transmitted component in each unit was received by an exit port of area 1mm2, placed coaxially with input port of the phantom. Initially ten million photons of wavelength 632.8nm were injected at each input port, which after interaction with medium emerged as backscattered and transmitted components. The outline of the ports is shown in Fig. 1(b). The center to center separation between any pair of ports was 2mm. After collection of data at first grid line, the scanning head was moved 1mm away along xaxis. By this process the data from the entire grid of size 30x9mm were collected with final position of photon entry port at 24mm.
From the number of backscattered photons collected within 1mm2 the normalized backscattered intensity (NBI) was calculated by
NBI (%) =
Ni , j N0
X 100
N0 – total number of incident photons Ni,j - total number of photons collected at any port The NBI values as obtained at various locations of grid, along with their positions (i,j), were stored in the computer for further processing [33]. Similarly the number of transmitted photons collected within 1mm2 grid (i,j) was represented as the normalized transmitted intensity, given by
6
NTI % =
Ti , j N0
X 100
N0 – total number of incident photons Ti,j – total number of transmitted photons collected by the port The NTI values were stored in the computer along with their positions for further processing.
2.2 Monte Carlo Simulation Monte Carlo simulation (MCS), due to its stochastic features, can be applied to any random event in nature. For this study it was used to simulate the light transport by injecting photons or photon packets on a random walk through biological tissues. The photon was treated as a neutral particle and its movement was governed by the mean free path, scattering and absorption coefficients, and anisotropy parameter of the medium [34]. The photons after multiple interactions within the medium, emerged as backscattered and transmitted components on the entry and exit surfaces of the phantom, respectively. The code for MCS is written in C++ language and time taken by 10 million photons at one grid location is 12min on a computer with quad-core processor of speed 3GHz and 2GB RAM. Total time taken for one operation over the grid surface was 12x9x24 min = 44hr. The photons were introduced perpendicular to the surface for maximizing their entry and minimizing the surface reflection. Each photon, out of ten million, was initialized with a weight of unity. The step-size‘s’ of the photon was calculated by a generated random variable, ς , given by
7
s=
− ln ς
µt
, and µ t = µ a + µ s
(1)
where µ t , µ a , µ s were total attenuation, absorption and scattering coefficients of the medium, respectively. The value of the random number ς was between 0 and 1. The deflection angle θ was calculated by
(1 − g 2 ) 1 cosθ = 1 + g 2 − 2g (1 − g + 2 gς )
cosθ = 2ς − 1
2
for g≠0
(2)
for g =0
(3)
where g is the anisotropy parameter of the medium. The azimuthal angle ψ was given by
ψ = 2πγ
(4)
where γ is a random variable between 0 and 1. The path length of first interaction of photon was found, and thereafter this was moved. If the photon has left the tissue, the possibility of its presence at one of the receiving ports was checked. If detected, a counter was incremented to count the photon received by the corresponding port. If the photon was internally reflected, then the photon location was updated and the program continues. With each step the photon weight was reduced due to absorption by the tissue. The amount of weight lost, ∆Q in absorption was given by
∆Q = W
µa µt
(5)
where W was the total weight of the photon. The photon weight and direction, after scattering in tissues of matched and mismatched refractive indices, were updated. The new position of the photon (x’,y’,z’) from the previous position (x,y,z) was given by
8
x ' x sin θ cosψ y ' = y + s sin θ sinψ ' z z cos θ
(6)
If the photon weight falls below a minimum threshold (Wc = 0.001), then it was subjected to roulette condition to eliminate this. Further details of this simulation are given elsewhere [34].
2.3 Tissue phantoms In order to test the optical probe, digital tissue phantoms were made. For this purpose the goat tissues heart, adipose and spleen were chosen, which was based on the optical properties of tumor removed from cancer patients [35]. Heart tissue was used as the control, and adipose and spleen as inhomogeneities, representing abnormal conditions. The optical properties of the tissues are given in table 1. The refractive indices of heart, adipose and spleen were 1.40, 1.455 and 1.4, respectively [33].
Table 1 Optical parameters of adipose, spleen and heart tissues
Organ/tissue
Scattering coefficient (cm-1)
Absorption coefficient (cm-1)
Anisotropy parameter
Heart
100.03
1.27
0.990
Spleen
109.86
4.00
0.995
Adipose
419.92
1.50
0.994
9
Adipose or spleen tissue of size 2mm diameter was located below the center (0,0,0) of the control tissue phantom. For first simulation adipose was embedded at depth (0, 0,2mm), followed by its placement at (0, 0,4mm) and (0, 0,6mm). For each position the MCS was performed. Similarly, spleen tissue was also embedded in control phantoms at locations (0, 0,2mm), (0, 0,4mm) and (0, 0,6mm) and their MCS carried out. By same procedure the distribution of the transmitted and backscattered photons in the control tissue, to be used for image subtraction purpose, was also performed. Tissues considered for this work are prepared under in vitro conditions. Hence there is no movement of sub-cellular component, in contrast to proteins molecular dynamics in tissues [36]. Hence the tissues are considered under equilibrium conditions with fixed values of the optical parameters.
2.4 Data acquisition The optical probe was implemented by performing the MCS of light photon propagation in tissues. The photons out of 10 million that reach the output ports were counted and converted into respective NTI and NBI values. By shifting of scanning head by 1mm in x-axis direction on to next grid line, the MCS for photon transport was repeated. This process was repeated till source port reaches at position x=24mm. Entire data were stored in four files, one for transmission port and three for the backscattering ports.
2.5 Data processing The data acquired were processed separately to obtain transmission and backscattered images by MATLAB.
10
2.5.1 Transmission data processing
The data acquired by the transmission port was filtered by 5x5 low pass Gaussian filter. The filter function of this in frequency domain is given by
H (u , v) = e − D
2
( u , v ) / 2 D02
(7)
where D0 is the cutoff frequency and D(u,v) is the distance from the center of the frequency rectangle [37]. This filter reduces noise and produces a smoothed image. The background data, as obtained from control tissue, was subtracted to increase the contrast of the image.
2.5.2 Backscattered data processing To reduce the variability, averaging was performed on the acquired data. For an N x N data the averaged value u(x,y) of NBI, by averaging the predefined neighborhood of f(x,y), was obtained [38]. This is performed by the formula
u ( x, y ) =
1 M
∑ f ( n, m )
(8)
n , m∈ S
For x,y=0,1….N-1, S is the set of coordinates in the neighborhood of (x,y), M is the total number of neighboring points (=9) taken. This operation forms an averaged image. The background data was subtracted to increase the contrast of the image. The resultant image was median (3x3) filtered to reduce the statistical noise and the noise associated with averaging procedure. In this filtering process, a predefined window consisting of the neighborhood of the data point (x,y) was chosen and the median of the data points within the window was found out. This was repeated for all data points in the image. Thereafter gray level transformation was applied on the resultant image for localization of the embedded tissue. Further details of the 11
image processing procedures are given in [38]. The sequence of various operations applied for image processing is given in Fig. 2.
2.6 Testing of simulation procedure Monte Carlo methods follow a pattern when they are implemented without error. To test the developed code a circle inscribed inside a square was considered. The ratio of the area of the circle and square is pi/4. Here the %NBI data obtained for heart tissue, measured by the probe at 2mm, were used. A point p(x,y) is chosen on the xy-plane of the raw image where the reflectance data are present. With p as center and R as radius a circle is drawn and the number of photons reflected within this region is counted. Thereafter with p as center and 2R as length of each side a square is drawn and the number of photons present in this region is counted. The ratio of the number of photons within the circle to that of square region was calculated for each simulation with input of 1000 to 10million, were calculated. The ratio varies from 0.798 to 0.7853, with minimum deviation from the actual value, 0.785(pi/4) with an input of 10 Million photons.
2.6.1 Convergence of Monte Carlo method The convergence of the Monte Carlo code was determined by calculating the 95% confidence interval (CI) of the %NBI with respect to the number of photons using the expression [39],
95%CI = [ mean − 1.96 X
σ m
, mean + 1.96 X
σ m
(9)
where m (=16) is the number of simulations and σ is the standard deviation of %NBI. Fig. 3 shows the confidence interval calculated for heart tissue for photon numbers ranging from 1000
12
to million. This shows that the CI converges with increase in the number of photons as used for this simulation.
The mean statistical error was calculated using the equation,
MSE =
σ
(10)
m
and the results obtained show (Fig. 4) that the error is reduced with increase in number of photons, indicating the convergence of the NBI. Tissues are assumed to be of homogeneous nature. This was further verified by plotting of the surface profiles of heart, adipose and spleen tissues, represented as variation of normalized backscattered intensity with distance along x-axis (Fig. 5). The profiles obtained by this procedure, as shown on the left and right sides, match each other. The analyses carried out in other directions also show similar results, thus confirming the homogeneous nature of tissues.
3. Results Based on data of backscattered photons received at three ports located at various distances from beam entry port the images are constructed. Fig. 6 shows these images of adipose tissue of size 2mm placed at various depths. Fig. 6(i) shows the spatial distribution of NBI obtained on the surface of the control with adipose tissue located at (0,0,2mm), as collected by three ports shown as a, b and c, respectively. For determination of the NBI distribution these images are scanned through their centers. The maximum intensity is observed at port ‘a’, whereas, this is reduced at ports ‘b’ and with further reduction at ‘c’, attributed to the increased multiple scattering of
13
photons in the tissues. With the placement of inhomogeneity at depth (0,0,4mm) the photons received at port ‘b’ are comparatively increased, whereas, their number at ports ‘a’ and ‘c’ is reduced (Fig.6(ii)). Accordingly the NBI is reduced. A further change is observed by placing the adipose tissue at (0,0,6mm) (Fig. 6(iii)). The NBI at port ‘c’ is more than that as measured at ports ‘a’ and ‘b’. Due to increased scattering of adipose tissues compared to that of control tissue the net change is positive. In contrast to adipose, the spleen is highly absorbing. Fig. 7 (i-iii) shows the images of the NBI as received at three ports (a-c). Fig. 7(i) shows the NBI images after placing the spleen tissue at (0,0,2mm). Due to image subtraction procedure the photons collected at port ‘a’ are less than that collected at ports ‘b’ and ‘c’. This aspect is further highlighted by the horizontal scan taken at the center of the images. By placing the inhomogeneity at depth (0,0,4mm) all the NBI values are reduced with minimum occurring at port 4mm away from input port (Fig. 7(ii)). With the increase of depth of placement (0,0,6mm) the multiple scattering is further increased, leading to decrease in NBI with its minimum value at 6.0mm away from beam entry point (Fig. 7(iii)). These finding further support that even for highly absorbing tissues the number of photons received at various ports depends on the depth of location of inhomogeneity.
The peak NBI (PIB) and the full width at 75% of maximum (FW75%MB) obtained from the images constructed using the data collected by the three backscattered ports are given in Table 2. We observe that the peak value decreases with the depth of placement of tissue increases. The |PI| value is more for adipose compared to that of spleen. The FW75%W values obtained for adipose tissue show slight increase with depth whereas for spleen it remains around the same value.
14
Table 2 Peak NBI (PIB) and full width at 75% of maximum (FW75%MB) from the images constructed by data collected at the backscattered port Depth (mm)
FW75%MB (mm)
PIB Spleen
Adipose
Spleen
Adipose
2
0.00386
0.11784
3.24
3.24
4
0.00206
0.00335
3
3.36
6
0.00054
0.00171
3.18
3.48
Fig. 8 shows the surface profiles, as plotted by the NBI values, measured at different ports with inhomogeneity placed at location (0,0,2mm). The NBI values at all collection ports are higher for adipose compared to that of spleen tissues, which are attributed to their optical characteristics.
The reconstructed images from the transmission data, after background subtraction, when adipose and spleen are embedded at different depths are shown in Fig. 9(i) and Fig. 9(ii), respectively. The influence of scattering on the image depends on the location of the inhomogeneity. The placement at (0,0,2mm) is associated with high scattering, which leads to noisy image after passing through adipose or spleen tissues (Fig.9a). The effect of noise is reduced when the inhomogeneity is placed at (0,0,4mm) (Fig.9b). The noise is minimized when this is placed at depth (0,0,6mm) as shown by its NTI profile (Fig.9c). This further shows the minimal effect of the overlying tissues.
15
The peak NTI (PIT) and full width at 75% of maximum (FW75%MT) are calculated from the scans of reconstructed transmission images. The magnitude of peak intensity |PI| increases as the depth of placement of the tissue increases and the FW75%M decreases, as shown in Table 3. The |PI| is more for adipose compared to that of spleen tissue when these are embedded at (0,0,6) but an opposite pattern is observed for the FW75%M. This is taken as representation of size of inhomogeneity, which shows deviation from actual size due to occurrence of multiple scattering, depending on location within the tissue.
Table 3. Peak NTI (PIT) and full width at 75% of maximum (FW75%MT) from the images constructed by the transmission data. Depth (mm)
PIT
FW75%MT (mm)
Spleen
Adipose
Spleen
Adipose
2
0.0000904
0.00014
4.7
2.875
4
0.00016
0.00017
3.25
2.5
6
0.00033
0.00023
2.25
2.127
The depth distribution of photons within the control phantom with adipose and spleen tissues embedded at 6mm is shown in Fig 10. The distribution varies in the neighborhood of the embedded tissue. It is associated with high scattering and absorption for adipose and spleen inhomogeneities, respectively. This also explains the occurrence of higher PIT due to high scattering of photons by adipose tissues and high absorption in spleen tissues leading to lower PIT.
16
4. Discussion The laser scattering and absorption processes in biological tissues depend on their optical parameters. The collimated transmission, associated with less scattered photons, carries the information about the medium but the signal intensity is low. In contrast the collection of collimated and less scattered photons over a comparatively longer time duration form high intensity signals leading to diffuse imaging of the objects hidden in tissues [1,10]. On the other hand, the backscattered component carries the multiple scattered photons, collected at various distances from the beam entry point. The processing of these provides useful information on clinical status of tissues as demonstrated by the success of NIRS [16]. In the present study the contribution of specular reflection, due to normal incidence of the photons, is minimized [3]. The present study is based on the diffuse backscattering and transmission. To obtain the net change due to inhomogeneity in backscattering the output received from each port is background subtracted. After averaging the data are median filtered [37]. The recent results show that the placement of adipose inhomogeneity at a depth 2mm is not only detected by port located at 2mm but also by ports located at 4 and 6mm. This is attributed to migration of photons through the additional path-length of tissues after undergoing multiple scattering [17]. With the placement of inhomogeneity at deeper locations, the NBI attains maximum at respective ports associated with very low values of NBI at other ports. This pattern of reduced backscattering within the tissue medium is attributed to high value of anisotropic parameter [3]. In contrast to this, spleen is an absorber leading to reduced NBI values at every port due to its optical parameters. Due to this the pattern of variation in the NBI images is reversed. The migration of photons in spleen also contributes to form images, similar to that of adipose, observed at various ports [17].
17
The diffuse reflectance directly [1,35,40] and a feature parameter derived from diffuse reflectance indirectly [21] have been applied to differentiate benign and malignant tissues. In contrast to this the surface diffuse reflectance profile possesses unique features as it provides information on the tissue compositional variation within multi-layers, observed at various ports. Due to this the experimentally measured profiles of various in vivo tissues are used to determine their optical parameters by matching these with profiles as obtained by Monte Carlo simulation [41,42]. The present studies show that by placing an inhomogeneity at depth 2mm a distinct surface reflectance profile is obtained but this could not be achieved with its placement at deeper locations due to shift in scattering pattern. This is valid for different type of inhomogeneities. In transillumination, the photons are interacting with the entire medium and overall changes in the NTI are observed at the exit end. By image subtraction the net change due to placement of abnormality is determined. When the inhomogeneity is placed at depth 2mm a broadening of the scan is observed, attributed to multiple scattering of photons. The broadening, represented as the FWHM is reduced and pulse height is increased when inhomogeneity is placed at depth 6mm, which means the photons are less scattered prior to exiting from the surface. The presence of spleen shows enhanced absorption, leading to better visualization compared to its placement near the entry surface. These findings are in contrast to results obtained by Boas et al [43], who have shown that the placement of the inhomogeneity in the middle of tissue phantom could be better visualized than that at other positions. The transillumination presents image of the 3D system in 2D, as in optical mammography [7], and due to this the location of inhomogeneity could not be well elaborated. But in the present study this information is provided by backscattered signal which is associated with location of the inhomogeneities within the tissues [44]. Similar to optical tomography [26,27] this technique also 18
provides the cross-sectional images of tissue structure. The multi-port system thus provides multi-slices images for further analysis of tumor development in tissues. The image enhancement agents are not required for this analysis, which is in contrast to as determined by log-slope method [45] and can detect the object of 2mm diameter even placed at depth 6mm. To minimize the effect of blurring due to multiple scattering [46,47] the parameter full width at half maximum is calculated as full width at 75% of the maximum intensity. By this procedure the size of the inhomogeneity as calculated from intensity plots from backscattering data is 60-80% larger than actual ones. In contrast, in transmission mode the calculated size, when inhomogeneity is placed near the exit surface is comparable and at depths 2 and 4mm are 25-45% larger than actual size. In conclusion, this simulation present the details which are applicable in both backscattering and transillumination conditions. The variability in images and their scans show that in the presence of inclusions placed at a depth affects their contrast due to multiple scattering [47]. This simulation is for non-invasive and contact conditions, in which the photons source is kept in touch with tissues surface. This procedure is even capable of detecting 10% change in optical parameters of tissues, a condition close to onset of cancer in tissues [48], thus providing the possibility of identifying the tumor (highly absorbing) and cyst (highly scattering) in biological tissues. Further simulation, similar to non-invasive and non-contact technique [49] may overcome the changes induced by movement of the tissue surface.
19
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Figures
Fig.1. (a) Schematic of the optical scanning system for measurement of backscattered and transmitted photons after interacting with tissues. (b) Each unit is consisting of five ports, one for photon injection and three to collect backscattered photons at various distances from beam entry port, and one to collect transmitted photons located coaxial to the input port.
25
Fig. 2. Sequence of operations for image construction
26
Fig. 3. 95% Confidence interval of the %NBI with increase in number of photons.
27
Fig. 4. Reduction of MSE with increase in photon numbers used for simulation
28
Fig. 5. NBI profiles of individual tissues along the horizontal direction with source at (0,0,0).
29
Fig.6. The reconstructed images and scans of the of normalized backscattered intensity (NBI) (%) of photons received by the first (a), second (b) and third (c) collection ports when adipose tissue is embedded in control at (i) 0,0,2mm (ii) 0,0,4mm and (iii) 0,0,6mm, respectively.
30
Fig. 7. The reconstructed images of backscattered photons and their scans (NBI(%)), as received by the first (a), second (b) and third (c) collection ports with spleen tissue embedded in control at (i) (0,0,2), (ii) (0,0,4) and (iii) (0,0,6)mm, respectively.
31
Fig. 8. The NBI profiles of control with adipose (h+a) and with spleen (h+s) phantoms with placement of inhomogeneity at (0,0,2mm).
32
(i)
(ii)
Fig. 9. Reconstructed Images, (after background subtraction) obtained from the data collected at the transmission port located coaxial to the input port with placement of adipose (i) and spleen (ii) tissues embedded inside the control tissue at (0,0,2mm) (a), (0,0,4mm) (b) and (0,0,6mm) (c).
33
Fig. 10. Depth distribution profiles when adipose (a) and spleen (b) are embedded at depth 6mm.
34
Table 1 Optical parameters of adipose, spleen and heart tissues
Organ/tissue
Scattering coefficient (cm-1)
Absorption coefficient (cm-1)
Anisotropy parameter
Heart
100.03
1.27
0.990
Spleen
109.86
4.00
0.995
Adipose
419.92
1.50
0.994
35
Table 2 Peak NBI (PIB) and full width at 75% of maximum (FW75%MB) from the images constructed by data collected at the backscattered port Depth (mm)
PIB
FW75%MB (mm)
Spleen
Adipose
Spleen
Adipose
2
0.00386
0.11784
3.24
3.24
4
0.00206
0.00335
3
3.36
6
0.00054
0.00171
3.18
3.48
36
Table 3. Peak NTI (PIT) and full width at 75% of maximum (FW75%MT) from the images constructed by the transmission data. Depth (mm)
FW75%MT (mm)
PIT Spleen
Adipose
Spleen
Adipose
2
0.0000904
0.00014
4.7
2.875
4
0.00016
0.00017
3.25
2.5
6
0.00033
0.00023
2.25
2.127
Conflict of interest
This research is supported by VIT University, Vellore, India.
There is no conflict of interest
37
Highlights • • •
Simulation of multiport optical scanning system Capable of differentiating the embedded inhomogeneities Characterization of their optical properties
38
Graphical Abstract Monte Carlo simulation is applied to imaging of photons backscattered and transmitted through a tissue phantom, made of heart tissues implanted with adipose or spleen tissues as inhomogeneities. The proposed optical scanning probe is consisting of nine units. Each unit has one photon injection port and three ports arranged in a straight line at 2, 4 and 6mm to collect backscattered photons emerging from various depths, and one port to collect the transmitted component placed coaxially to the source on the opposite side of the phantom. Figure 1 shows one unit of the optical scanning probe. The backscattered data are collected by first port located at 2mm from the input port. The path-length of photons emerging out of first port is shorter compared to that of photons received by other ports. By collections of scanned signals on the tissue surface the tissues images located at various depths are constructed. By scanning of these images the normalized backscattered intensity (NBI) signals are obtained. By comparison of NBI signals the type of inhomogeneities and their locations are determined. Such data could be helpful in development of scanning devices for early detection of tumor in tissues.
39
