JOURNAL OF INTENSE PULSED LASERS AND APPLICATIONS IN ADVANCED PHYSICS Vol. 3, No. 4, p. 4-45 Modelling of the ner infr-red rdition pulse propgtion in biologicl tissues for medicl imging ppliction A. SAOULI *, K. MANSOUR Lbortory of Electronic Mterils Study for Medicl Applictions (LEMEAMED) Cmpus Ahmed Hmni, Route Ain El Bey, 25000 Constntine, Algeri Diffusive Opticl Tomogrphy (DOT) is rpidly developing imging technology for medicl dignoses nd biomedicl reserch. The dvntges of the opticl techniques in dignostic modlities re significnt nd include the complete noninvsiveness, the use of hrmless, non-ionising rdition nd the prospects for reveling chemicl contrst, which cn represent vluble physiologicl informtion. Indeed, the DOT is bsed on detection of ner InFr-Red Pulse (NIRP) clled Time Pulse Spred Function (TPSF) on surfce of the tissue sending by n opticl source nd simultion of propgtion of this pulse source in our object. The combintion between mesured TPSF nd simulted TPSF cn be reconstructed n opticl mp of the opticl proprieties of the study object. This opticl mp presents the imge in DOT. Therefore, in this work we present the simultion of NIRP propgtion in biologicl tissue nd the influence of source frequency. This simultion is bsed on element finite method (FEM) progrmmed in COMSOL Multiphysics Softwre. (Received July 6, 203; Accepted October 2, 203) Keywords: Diffusive opticl tomogrphy, Ner infr-red pulse, Element finite method, Source frequency. Introduction Soft-field imging methods, such s Opticl Tomogrphy (OT) nd Electricl Impednce Tomogrphy (EIT) hve significnt potentil for medicl imging s they re non-invsive, portble nd inexpensive []. Brest cncer detection, brin function study, infnt nd fetus monitoring nd rthritis dignosis re mong the numerous pplictions of DOT [2]. The tomogrphy imging is n extension of the spectroscopy nd the instrumenttion used is common to both fields. Indeed, in Ner-InFrred Spectroscopy (NIRS) of tissue, light ttenution is due to the bsorption from chromophores of fixed concentrtion, the bsorption from chromophores of vrible concentrtion, nd the light sctters [3]. The (OT) bsed on three technologies depends nture of the source, the (DOT) is one of this lst when the source present (NIRP). The signl detected is clled (TPSF), contins the optic informtion of study object which is biologicl tissue, thus the resolution of inverse problem or reconstruction of imge is bsed on combintion between simulted nd mesured TPSF to reconstruct the opticl proprieties of study object. The simultion of signl propgtion in study object nd clcultion of TPSF bsed on resolution of the diffusion pproximtion of rditive trnsfer eqution is clled forwrd problem. Thus, in homogeneous mediums exists nlyticl solution of more complex geometries, such s circles, semi-infinite spheres or mediums were developed nd detiled in [4]. Although, there is not generl solution for heterogeneous mediums, which is the cse of biologicl tissues, nlyticl expressions were derived for homogeneous medium contining perturbtion. Indeed, model on Finite Element Method (FEM) to solve the diffusion eqution numericlly offers dvntges in speed nd flexibility in comprison with other models [5]. In this pper, we bsed on (FEM) progrmmed in COMSOL Multiphysics Softwre to solve forwrd problem in heterogeneous mediums of circle cut of cylinder form contin three inclusions present tumour in tissue. Generlly, the reconstruction of opticl prmeter do not use the form complete of TPSF clculted becuse it tkes lot of computing time, so there re some prmeters clculted from TPSF to simplify this time such s Mximum intensity, men vlue nd men time of TPSF. Thus, the opticl source hs significnt role in reconstruction of the opticl imge [6]; in this work we study the influence frequency source in this prmeters nd the stbility of propgtion of NIRP in our study object. 2. Implementtion of photon trnsport model in Comsol Multiphysics softwre The propgtion of light in biologicl tissue is governed by the diffusion pproximtion of rditive trnsfer eqution: 3 s r, t r, t S r, t 0 r, t c t Where: c is the light speed in vcuum, Coefficient, s () the bsorption the diffusion reduced Coefficient, S 0 r0, t
42 A. Souli, K. Mnsour the locle Source of photon nd r,t the photons intensity. The forwrd model in DOT is bsed on numericl solution of diffusion pproximtion eqution (DAE) by the finite element method in biologicl tissue. Using Comsol Multiphysics softwre cn solve prtil derivtive eqution in given geometry by FEM who is the cse of diffusion pproximtion eqution. Thus in prtil derivtive eqution mode (PDE) of this softwre the governed eqution presents the form of eqution (2): 2 u e 2 t. u r, t ur, t d t r, t ur, t f 2 Cu. r, t ur, t To build (DAE) we tke the vribles nd coefficients of eqution (2) with following conditions: u r, t r, t, f S0r, t, e 0, d, c C, 0, 0, 0,. 2 3 s This work is bsed on two dimension cut of cylinder form of phntom contin three inclusions with different optic proprieties (figure). We use Dirichlet nd Robin (2) boundry conditions presented in equtions (3) (DBC) nd equtions (4) (RBC) respectively [7]. r, t 0 (3) R r, t r, t 2 0 3 (4) s R n Where, n is the norml vector nd ( R 0) the reflection prmeter. The simultion bsed on three sources of ner InFr- Red Pulse in temporl nd spectrl profile presented in (figure 2), the spectrl profile present two peks in the figure, where the pek on the right is mirror of the ones to the left. This mirror effect is due to the smpling of the impulse signls, which lwys crete mirror spectrum round the smpling frequency. Thus ech source hs their frequency nd wvelength, Source: (f =4*0 9 [Hz], λ =0.024 [m]), Source2: (f 2 =5*0 9 [Hz], λ 2 =0.06 [m]), Source3: (f 3 =0.5*0 9 [Hz], λ 3 =0.6 [m]), but ll sources hve the sme intensity. The mesh of our structure is presented in figure 3, we use free mesh prmeters with: (Mximum element size scling fctor=, Element growth rte=.3, Mesh curvture fctor= 0.3, Mesh curvture cutoff= 0.00, resolution of nrrow region= ), in this cses we hve 3755 elements. (NIRP) Source Detectors y [m] Principl phntom : (μ, μ s)= (0.005e +3, 0.04e +3 ) [m- ] Inclusion : (μ, μ s)= (0.5e +3, 0.04e +3 ) [m- ] Inclusion 3 : (μ, μ s)= (0.005e +3, 0.4e +3 ) [m- ] Inclusion 2 : (μ, μ s)= (0.5e +3, 0.4e +3 ) [m- ] X [m] Fig.. Two dimensions cut of phntom
Modelling of the ner infr-red rdition pulse propgtion in biologicl tissues for medicl imging ppliction 43 Fig. 2. Temporl nd spectrl (FFT: Fst Fourier Trnsform) profile of sources 4. Results nd discussion Y [m] x [m] Fig. 3. Mesh structure for FEM clcultions of 3755 elements. In this section we investigte the influence of the sources for rnge of prmeters, by compring the results for different frequency sources with the sme intensity. Figure 4 shows mximum intensity () nd men vlue of detected TPSF with vrition of detection ngle for three sources simulted from FEM model, the position of detector is clerly shown in figure. We observe tht when the source frequency decrese, the mximum intensity nd men vlue of TPSF decrese, this phenomen demonstrted physiclly by the decrese of the source energy. Indeed, Figure 4 shows the vrition of men time of TPSF detected with vrition of detection ngle for three sources, compres this three curves we observed tht men time increse when the frequency source decrese, this is justified by incresing of width time (WT) of sources (figure 2, temporl profile), for
44 A. Souli, K. Mnsour source WT =0.65*0-9 [s], source2 WT 2 =.4*0-9 [s], source3 WT 3 = 2*0-9 [s], thus the period impulse time influence on men time of TPSF. () To study the impulse propgtion we view intensity mps of three sources in different simultion time, which is clerly shown in Figures 6, 7 nd 8. According to this result, the source with frequency of f =4*0 9 [Hz] nd WT =0.65*0-9 [s], stbilized fter.05*0-9 [s] of his propgtion in phntom, this time present rtio of.6 of WT. But the source2 with frequency of f =5*0 9 [Hz] nd WT =.4*0-9 [s], strted the stbility on the 5*0-9 [s] of his propgtion in phntom, this time present rtio of 3.57 of WT 2. Finlly, the source3 with frequency of f =0.5*0 9 [Hz] nd WT =2*0-9 [s], stbilized fter the time of 8*0-8 [s] of the propgtion in phntom, this time present rtio of 3.8 of WT 3. Thus, ccording to this sttistics, when the frequency increse, the time of signl stbility increse, this hve reltion with detection instrument which hve response time less then 50*0-9 [s] [7], so the choice of the frequency source hve very importnt role in decresing of signl (TPSF) time response to dpted with the technology detection which is lwys in development. () Fig. 4. Vrition of: () Mximum intensity, men vlue of TPSF with vrition of detection ngle for three sources. (c) (d) (e) Fig. 6. Intensity mps of source for different simultion time: () 5.6*0-0 [s], 7*0-0 [s], (c) 8.05*0-0 [s], (d).05*0-9 [s], (e).755*0-9 [s]. Fig. 5. Vrition of men time of TPSF with vrition of detection ngle for three sources.
Modelling of the ner infr-red rdition pulse propgtion in biologicl tissues for medicl imging ppliction 45 5. Conclusion ( (b (c (d The temporl profiles (TPSF) nd mps intensity of photons diffused in highly scttering medi such s biologicl tissue is computed t bse of Comsol Multiphysics softwre. This progrm genertes m-files, intended to be clled by n optimiztion process, written in Mtlb softwre, to reconstruct imges of the phntoms to be investigted with our time-resolved tomogrphy set up. During the reconstruction process, the prmeters of interest, (bsorption nd reduced scttering coefficients, fluorescent probe concentrtion) will be itertively djusted to perform constrined nonliner minimiztion of n objective function of the distnce between mesured nd computed temporl profiles. Applictions re expected to concern the contribution of resonnce mgnetic imging (RMI) in (DOT). Medicl pplictions in cerebrl ctivtion re lso considered. References (e Fig. 7. Intensity mps of source2 for different simultion time: () *0-9 [s],.6*0-9 [s], (c) 2*0-9 [s], (d) 3*0-9 [s], (e) 5*0-9 [s]. () [] L. Horesh, M. Schweiger, M. Bollhöfer, A. Douiri, D.S. Holder, S. R. Arridge, Interntionl Journl Of Informtion And Systems Sciences, 2( 4), 532 (2005). [2] N. G. Chen, Q. Zhu, Optics Express, (25), 3445 (2003). [3] D.T. Delpy, M. Cope, Phil. Trns. Royl Society, 352, 649 (997). [4] S. R. Arridge, M. Cope, D.T. Delpy, Physics in medicine nd biology, 37(7), 53 (992). [5] M. Schweiger, S.R. Arridge, M. Hirok, D.T. Deply, Am. Assoc. Phys. Med, 22, 779 (995). [6] A. Souli, K. Mnsour, IEEE conference proceeding (MMS) th, 7 (20). [7] A. Souli, K. Mnsour, Digest Journl of Nnomterils nd Biostructures, 7(3) 27 (202). [8] A. Souli, K. Mnsour, Advnced Mterils Reserch, 227, 25 (20). * Corresponding uthor Abdou.zezou@yhoo.fr (c) (d) (e) Fig. 8.Intensity mps of source3 for different simultion time: () 7*0-8 [s], 7.4*0-8 [s], (c) 7.6*0-8 [s], (d) 7.8*0-8 [s], (e) 8*0-8 [s].