Functionl tomogrphy using time-gted ICCD cmer Qing Zho, 1 Lorenzo Spinelli, 2 Andre Bssi, 3 Ginluc Vlentini, 2,3 Dvide Contini, 3 Alessndro Torricelli, 3 Rinldo Cubeddu, 2,3 Giovnni Zccnti, 4 Fbrizio Mrtelli, 4 nd Antonio Pifferi 2,3,* 1 Dept Robotics Brin nd Cognitive Sciences, Istituto Itlino di Tecnologi, vi Morego 30, I 16163 Genov, Itly 2 Istituto di Fotonic e Nnotecnologie, Sezione di Milno, Consiglio Nzionle delle Ricerche, pizz Leonrdo d Vinci 32, I-20133 Miln, Itly 3 Diprtimento di Fisic, Politecnico di Milno, pizz Leonrdo d Vinci 32, 20133 Miln, Itly 4 Diprtimento di Fisic e Astronomi, Università degli Studi di Firenze, vi G. Snsone 1, 50019 Sesto Fiorentino, Firenze, Itly *ntonio.pifferi@polimi.it Abstrct: We present system for ner infrred functionl tomogrphy bsed on single pulsed source nd time-gted cmer, for non-contct collection over lrge re. The men penetrtion depth of diffusely reflected photons is dependent on the rrivl time of photons, but not on the source detector distnce. Thus, time-encoded dt cn be used to recover depth informtion while photon exiting point is exploited for lterl locliztion. This pproch ws tested ginst simultions, demonstrting both detection nd locliztion cpbilities. Preliminry mesurements on inhomogeneous phntoms showed good detection sensibility, even for low opticl perturbtion, nd locliztion cpbilities, yet with decresing sptil resolution for incresing depths. Potentil ppliction of this method to in vivo functionl studies on the brin is discussed. 2011 Opticl Society of Americ OCIS codes: (170.5280) Photon migrtion; (170.3890) Medicl optics instrumenttion; (170.6920) Time-resolved imging. References nd links 1. M. S. Ptterson, B. Chnce, nd B. C. Wilson, Time resolved reflectnce nd trnsmittnce for the non-invsive mesurement of tissue opticl properties, Appl. Opt. 28(12), 2331 2336 (1989). 2. J. Steinbrink, H. Wbnitz, H. Obrig, A. Villringer, nd H. Rinneberg, Determining chnges in NIR bsorption using lyered model of the humn hed, Phys. Med. Biol. 46(3), 879 896 (2001). 3. A. Liebert, H. Wbnitz, J. Steinbrink, H. Obrig, M. Möller, R. Mcdonld, A. Villringer, nd H. Rinneberg, Time-resolved multidistnce ner-infrred spectroscopy of the dult hed: intrcerebrl nd extrcerebrl bsorption chnges from moments of distribution of times of flight of photons, Appl. Opt. 43(15), 3037 3047 (2004). 4. D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Pgli, nd R. Cubeddu, Multi-chnnel time-resolved system for functionl ner infrred spectroscopy, Opt. Express 14(12), 5418 5432 (2006). 5. J. Selb, J. J. Stott, M. A. Frnceschini, A. G. Sorensen, nd D. A. Bos, Improved sensitivity to cerebrl hemodynmics during brin ctivtion with time-gted opticl system: nlyticl model nd experimentl vlidtion, J. Biomed. Opt. 10(1), 011013 (2005). 6. J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. Hillmn, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, nd J. S. Wytt, Three-dimensionl opticl tomogrphy of the premture infnt brin, Phys. Med. Biol. 47(23), 4155 4166 (2002). 7. Y. Hoshi, I. Od, Y. Wd, Y. Ito, M. Yutk Ymshit, K. Od, Y. Oht, Ymd, nd Mmoru Tmur, Visuosptil imgery is fruitful strtegy for the digit spn bckwrd tsk: study with ner-infrred opticl tomogrphy, Brin Res. Cogn. Brin Res. 9(3), 339 342 (2000). 8. J. Selb, D. K. Joseph, nd D. A. Bos, Time-gted opticl system for depth-resolved functionl brin imging, J. Biomed. Opt. 11(4), 044008 (2006). 9. J. Selb, E. M. C. Hillmn, D. Joseph, nd D. A. Bos, Discrimintion between superficil nd cerebrl signls during functionl brin imging with time-gted system, presented t the Europen Conferences on Biomedicl Optics (ECBO), Munich, Germny, June 13 16, 2005. 10. J. Selb, A. M. Dle, nd D. A. Bos, Liner 3D reconstruction of time-domin diffuse opticl imging differentil dt: improved depth locliztion nd lterl resolution, Opt. Express 15(25), 16400 16412 (2007). #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 705
11. W. Becker, Advnced TCSPC with Advnced Time-Correlted Single Photon Counting Techniques (Springer, Berlin, Germny 2006). 12. A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Mrtelli, S. Del Binco, nd G. Zccnti, Time-resolved reflectnce t null source-detector seprtion: improving contrst nd resolution in diffuse opticl imging, Phys. Rev. Lett. 95(7), 078101 (2005). 13. A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Mrtelli, G. Zccnti, A. Tosi, A. D. Mor, F. Zpp, nd S. Cov, Time-resolved diffuse reflectnce t null source-detector seprtion using fst gted single-photon vlnche diode, Phys. Rev. Lett. 100(138), 101 (2008). 14. P. Swosz, M. Kcprzk, A. Liebert, nd R. Mniewski, Appliction of time-gted, intensified CCD cmer for imging of bsorption chnges in non-homogenous medium, in 11th Mediterrnen Conference on Medicl nd Biomedicl Engineering nd Computing 2007, T. Jrm, P. Krmr, nd A. Zupnic, eds., vol. 16 of IFMBE Proceedings (Interntionl Federtion for Medicl nd Biologicl Engineering, 2007), pp. 410 412 15. R. B. Schulz, J. Peter, W. Semmler, C. D Andre, G. Vlentini, nd R. Cubeddu, Comprison of noncontct nd fiber-bsed fluorescence-medited tomogrphy, Opt. Lett. 31(6), 769 771 (2006). 16. S. Del Binco, F. Mrtelli, nd G. Zccnti, Penetrtion depth of light re-emitted by diffusive medium: theoreticl nd experimentl investigtion, Phys. Med. Biol. 47(23), 4131 4144 (2002). 17. S. Crrresi, T. S. M. Shtir, F. Mrtelli, nd G. Zccnti, Accurcy of perturbtion model to predict the effect of scttering nd bsorbing inhomogeneities on photon migrtion, Appl. Opt. 40(25), 4622 4632 (2001). 18. S. R. Arridge, Opticl tomogrphy in medicl imging, Inverse Probl. 15(2), R41 R93 (1999). 19. H. W. Engl, M. Hnke, nd A. Neubuer, Regulriztion of Inverse Problems (Kluwer, Dordrecht, 1996). 20. D. Contini, F. Mrtelli, nd G. Zccnti, Photon migrtion through turbid slb described by model bsed on diffusion pproximtion. I. Theory, Appl. Opt. 36(19), 4587 4599 (1997). 21. F. Mrtelli, S. Del Binco, A. Ismelli, nd G. Zccnti, Light Propgtion Through Biologicl Tissue nd Other Diffusive Medi (SPIE, Bellinghm, Wshington, 2010), Chps. 4 nd 7. 22. L. Azizi, K. Zrycht, D. Ettori, E. Tinet, nd J.-M. Tulle, Ultimte sptil resolution with diffuse opticl tomogrphy, Opt. Express 17(14), 12132 12144 (2009). 23. A. Sssroli, F. Mrtelli, nd S. Fntini, Perturbtion theory for the diffusion eqution by use of the moments of the generlized temporl point-spred function. III. Frequency-domin nd time-domin results, J. Opt. Soc. Am. A 27(7), 1723 1742 (2010). 24. L. Spinelli, F. Mrtelli, A. Frin, A. Pifferi, A. Torricelli, R. Cubeddu, nd G. Zccnti, Clibrtion of scttering nd bsorption properties of liquid diffusive medium t NIR wvelengths. Time-resolved method, Opt. Express 15(11), 6589 6604 (2007). 1. Introduction Light is powerful tool for in-vivo investigtion of biologicl tissues. In the 600-1100 nm rnge it is not hrmful for biologicl medi t low power densities (few mw/mm 2 ), permitting design of in vivo non-invsive dignostics. The low tissue bsorption in this wvelength rnge mkes it possible to look into the body t few cm of depth (e.g. the brin cortex) or through more thn 6 cm of tissue in trnsmission (e.g. compressed brest). Furthermore, light crries multiple useful informtion from the visited tissues linked either to bsorption (e.g. tissue composition, oxygention), or to scttering (e.g. tissue microstructure) or even by exploiting selective fluorescent mrkers to specific biochemicl trgets. In the sme spectrl rnge most tissues re highly scttering. This is most severe chllenge cusing scttering to bsorption coupling, strong ttenution of the remitted light with exponentil dependence on the visited depth, blurring effects impiring sptil resolution. An ttrctive pproch to study photon propgtion in highly scttering medi (photon migrtion) is the doption of time-domin scheme [1]. Seprting photons propgted through the medium s function of their trveling time permits to uncouple bsorption from scttering contributions, to probe the medium t incresing men penetrtion depths by collecting longer lived photons, nd to improve sptil resolution using erly less dispersed photons. In prticulr, in the cse of brin imging, ddressed to detection of hemoglobin content nd oxygention, time-domin mesurements hve been proposed s mens to rech deeper structures (brin cortex) uncoupling for the msking effects cused by more superficil tissues [2 7]. Different pproches hve been proposed to exploit time-encoded depth informtion, such s selection of lte time-gtes [4,5,8], subtrction of erly gtes from lte gtes [4,9], derivtion of the vrince of the Distribution of Time of Flight (DTOF) tht is lmost exclusively sensitive to bsorption chnges in deep tissue lyers [3], use of the whole DTOF interpreted with Monte Crlo bsed sensitivity fctors [2], s well s the doption of full 3D reconstruction scheme [6,10]. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 706
At present, in most cses, only tiny frction of the potentilly vilble informtion is retrieved in typicl time-resolved mesurement. The ultimte physicl limittion would correspond to uniform illumintion over the hed with power density corresponding to the sfety limits (few mw/mm 2 ), combined with corresponding collection of the emitted signl from the sme re with n ccepting solid ngle of 2π. Current time-resolved systems re quite fr from this limit. Just smll frction of the vilble signl is collected due to the very poor (<1%) sptil coverge of the hed, both for sources nd detectors. Furthermore, in the cse of Time-Correlted Single-Photon counting (TCSPC) systems, the mximum detectble signl is limited by the mximum count rte of the detection electronics tht t 6 present is t best bout 5 10 counts/s for bord running t 50% of the sturted count rte [11]. This limit is esily reched with source power of bout 1 mw, nd set of collecting bundles with n interfiber distnce of few cm. Thus, it is not possible with clssicl schemes to fully exploit the future vilbility of compct pulsed fiber sources with t lest 100 times more power thn diode lsers, s well s to foresee dense coverge of the hed, or even to tke dvntge of the higher contrst nd sptil resolution offered by very short interfiber distnces [12]. A possibility to overcome these limittions is to use Single-Photon Avlnche Diode (SPAD) operted in time-gted mode [13], even though the smll detector re is t present limiting fctor if single SPAD is employed. Alterntively, it is possible to dopt time-gted Intensified CCD cmer (ICCD) tht hs lower limittions in term of mximum signl level, even though the signl qulity is possibly worse thn for TCSPC systems. This pproch hs been widely studied by Selb et l. [5,8,10] empowering set of bundles of different lengths to smple different propgtion times with single time-gte. Alterntively, Swosz et l. [14] hve dopted completely non-contct scheme with scnning source nd wide field collection. In this pper we hve implemented system cpble to cquire lrge dt set from wide region surrounding single injection point, exploiting the time informtion to recover 3D tomogrphy. The system is bsed on single injection source nd on gted cmer for cquisition. Compred to previous work of Selb et l. [8] here we explore lrge re with non-contct pproch tht could permit better light hrvesting together with higher number of source-detector pirs. In the cse of moleculr imging, wide-field non-contct pproch hs been proven superior to fiber-bsed collection schemes for tomogrphic reconstruction both in terms of sptil resolution nd imge qulity [15]. Also, sequentil cquisition of different time windows permits to chnge light ttenution for ech imge so to properly fill the whole dynmic rnge of the CCD, nd rech better equliztion of the signl t different time gtes. Conversely, with respect to the work of Swosz et l. [14], here we present complete 3D tomogrphic pproch. In ddition, the use of single fixed lunching fiber mkes it possible to recover full 3D tomogrphy in short time, comptible with functionl imging studies. Compred to our current implementtion, the work of Swosz et l. is more ggressive, iming t performing mesurements even t null interfiber distnce, tht permits, lso, to chieve fully non-contct scheme. Here we follow more conservtive pproch, using shield to msk smll circle round the lunching fiber tht prevents to expose the cmer to the high photon flux rising from smll distnces, nd most of ll to reduce rdildependent vritions in signl level. Nevertheless, it will be possible to implement in future sptil filter on the imging optics so to fcilitte fully non-contct mesurements. In the following, we will first revise two concepts tht constitute the bsis of the present work, nd then we will test the vlidity of the method for 3D functionl tomogrphy both on simultions nd on phntom mesurements. Finlly, the possible ppliction to in vivo functionl imging of brin ctivity will be discussed. 2. Concepts The key ides underpinning this work re depicted in Fig. 1, nd Fig. 2. A first concept (Fig. 1) is the use of time to reconstruct 3D tomogrphy. Considering n homogeneous diffusive medium, upon incresing the rrivl time of photons, the men depth of visited tissue increses s well. Most noticebly, the men depth is not ffected by the source-detector #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 707
distnce, being encoded solely in the time. This opens the possibility for 3D tomogrphic scheme with single injection point, where depth informtion is provided by the photon trnsit time, while lterl informtion is gined from the different collection points. The grph in Fig. 1 shows the men penetrtion depth s function of the photon rrivl time, clculted s described in Ref [16]. for homogeneous medium with reduced scttering coefficient ( µ s ' ) of 10 cm 1. The function does not depend neither on the bsorption coefficient ( µ ), nor on the source-detector seprtion ( ρ ). () men depth (cm) 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 (b) 0 1000 2000 3000 4000 time (ps) Fig. 1. Use of time to explore different depths in the medium. Left: upon incresing the photon rrivl time, the probbility function of photon pths (bnn shpe) gets deeper, in sme wy for ll source-detector couples. Right: men depth of photon pths s function of the photon trveling time, clculted for µ ' = 10 cm 1 s described in Ref [16]. The plot is the sme for s ny source-detector seprtion. The second concept is to fully exploit light exiting from the tissue (Fig. 2). In typicl setup for opticl functionl imging, certin number of bundles re used to couple light to nd from the tissue. Sptil coverge is rther poor (bout 0.25%) since reltively lrge sourcedetector distnce is dopted nd only limited number of bundles cn be positioned on the hed. Here we wnt to exploit much lrger filling fctor (bout 90%) by collecting most of the exiting light strting from lower distnce of 1 cm from the injection point up to mximum distnce of 3 cm. The inner region is excluded (shielded) to void sturtion of the ICCD due to the overwhelming number of erly photons t short distnces. Conversely, t lrger distnces, the rdil dependence of signl becomes smoother, prticulrly t lter times. The grph in Fig. 2 shows the rdil dependence of the emitted signl for 5 different delys (1, 2, 3, 4, nd 5 ns). All curves re normlized to the vlue derived for ρ = 1 cm. By pplying these two concepts we wnt to ttin enough informtion to get 3D reconstruction from single injection point nd in short time. These two concepts were shown for homogeneous medium. Similr trends re expected lso for n inhomogeneous cse, with smll perturbtion, since the effect both on depth sensitivity (Fig. 1) nd signl level (Fig. 2) is smll. Out of the smll perturbtion regime, those concepts re still vlid qulittively, lthough the trends could be quite distorted. 3. Reconstruction strtegy 3.1. Forwrd model The geometry of the problem is depicted in Fig. 3. One single source ws used both in simultions nd in phntom experiments. The position of the source ws defined s the origin of the Crtesin coordinte system. Collection points on the medium surfce re identified by r, while r * loctes ny point (voxel) within the diffusive medium. The time t represents the rrivl time of photons t the detector point. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 708
() detection re useful re (φ 6 cm) injection fiber collection bundle (φ 0.3 cm) filling fctor = 0.25% 0.9 0.8 0.7 signl counts (.u.) 1 0.6 0.5 0.4 (b) dynmic rnge of signl 0.3 1 ns 2 ns 0.2 3 ns 0.1 4 ns 5 ns 0 1 1.5 2 2.5 3 rdil distnce (cm) Fig. 2. Use of lrge collection re. Left: ssuming source-detector pir with detector rdius of 0.15 cm, compred to the useful re with rdius of 3 cm, the sptil coverge (detector re over totl re) is only 0.25% of the physicl limit. Right: signl level clculted s function of distnce from the source for different vlues of the photon rrivl time. All curves re normlized to the vlue t 1 cm, which is the minimum distnce used in this pper. Upon incresing time, the signl gets more uniform over the whole collection re. Φ0 r,t reference photon fluence for the unperturbed medium (for n in vivo functionl imging experiment, this cn correspond to n initil rest stte), nd with Φ r,t the perturbed photon fluence obtined when the bsorption coefficient in the medium We indicte with ( ) ( ) µ ( r *) t loction r* is chnged compred to the reference initil stte 0 ( *) mount µ ( r* ) = µ ( r* ) µ ( r *). 0 µ r by the For smll bsorption chnges the problem cn be simplified ssuming linerized perturbtion pproch: smll loclized perturbtion µ ( r *) yields perturbed photon fluence given by [2,3,17]: where ( rr, *,t ) int ( µ ( r ) ( rr t) ) Φ = Φ exp *, *, (1) 0 int is the time-resolved internl men pthlength, tht photons, detected t time t, hve trveled inside the inhomogeneity [17]. Thus, the observed chnge in signl ttenution cn be expressed s: ( µ, rr, *, ) ln ( ) µ ( r* ) ( rr, *, ) A t = ΦΦ 0 = int t (2) Moving from the continuous to the discretized cse, the reconstructed region is volume (6 6 3.6 cm 3 ) centered beneth the injection source, nd divided into n voxels cubic voxels with side 0.3 cm. The xy plne, prllel to the surfce (detector plne), ws discretized t steps of 0.3 cm both in the x nd y directions. Then, ll pixels included in the field of view of the imging system (5.5 7 cm 2 ), nd out of the circulr blck shield ( 2 cm) were selected s detectors, yielding totl of n SD source-detector pirs. For every collection point, set of n gtes mesurements re derived, corresponding to integrtion from n initil time t G up to t G + t, where t is the width of the time-gted window. The width t is kept fixed, while t G is moved t incresed delys, yielding mesurements with incresing verge propgtion times. Mesurements re stored in the rry ΔA, with dimensions n SD n gtes. A globl chnge in the bsorption properties of the medium cn be expressed by the rry Δμ, n elements, defined for every voxel of the medium. Assuming tht the time-resolved with voxels #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 709
fluence resulting from distributed chnge in the bsorption coefficient Δμ cn be obtined s the superposition of loclized perturbtions, from Eq. (2) we cn derive where ( i, j, t G) ΔA = L Δμ (3) Lrr is mtrix with indices ddressing the detector position r i, the voxel position r j, nd the time window G nsd ngtes nvoxels. Mtrix L represents the men internl pthlengths spent within ech voxel by photons mesured t ech detector position nd ech time gte. Since the longer the men pthlength in given voxel, the lrger the effect produced on the mesurements, the men pthlength mtrix L is lso clled sensitivity mtrix [10]. We clculted it using the nlyticl expression for int ( r, r*,t) provided in Ref. [17], Eq. (6), for homogeneous medium with known opticl properties, evluted t time t G, tht is t the beginning of ech time window. This pproximtion cn be justified for lrger t G tking into ccount tht the mjority of the photons collected in ech time window rrives to the detector t the opening of the gte, being the photon fluence rpidly decying in time. Yet, some lrger discrepncy is expected t erly times. t, nd dimensions ( ) 5.5 cm detector plne 7x5.5 cm 2 shield source O x r detector y 7 cm r* 3.6 cm reconstructed volume 6x6x3.6 cm 3 z 6 cm Fig. 3. Geometry of the problem. A single injection source is set on the origin of the Crtesin system. The volume is divided into n voxels cubic voxels, ddressed by r*. The surfce not covered by the blck circulr shield round the injection source is divided into n SD squre detectors, ddressed by r. 3.2. Inverse problem The estimted imge of [18,19]: Δμ in Eq. (3) ws reconstructed using the Tikhonov regulriztion T ( ) 1 T Δμ = L LL +αi ΔOD (4) 6 cm The prmeter α in Eq. (4) ws used to restrin the sensitivity of Δμ to the noise level of the dt. Let s go bck now to the two leding concepts formulted in the previous prgrph. Regrding Fig. 1, we observe tht the men photon internl pthlength int in deeper voxels increses upon incresing the photon rrivl times t, resulting in higher sensitivity of the mesurement to the locl perturbtion (see Fig. 10 in Ref. [17]). Thus the L mtrix provides higher weight for deeper voxels upon incresing t G. In the CW cse, for ech detector position #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 710
single mesurement is chieved, nd the L mtrix contins the internl men pthlengths corresponding to n verge propgtion time t. Thus, deeper regions re reched exploiting lrge source-detector distnces tht yield lrger verge propgtion time. Conversely, the use of multiple time gtes permits, for every source-detector couple, to hve multiple mesurements with incresing depth sensitivity. In wy, lterl nd depth sensitivity re seprted, being the former encoded in the detector position, nd the ltter in the time gte t G. Furthermore, depth informtion is reched just by incresing t G, without chnging source-detector position, thus keeping exctly the sme collection efficiency. Regrding Fig. 2, we observe tht incresing the detection coverge we increse both the totl collected signl nd the sptil coverge of the mesurement ΔA. Since depth informtion is lredy provided by time, this should help in mending the ill-posed nture of the problem. The determintion of the optiml sectioning of the detection surfce nd the optiml choice of the time gtes is not obvious nd depends on deeper nlysis of the mtrix L nd of the vilble SNR, nd goes beyond the scope of the present pper. Conversely, we hve dopted simple choice by sectioning the detection surfce with the sme size of the voxels, nd tking number of time-gtes comptible with rel-time in vivo cquisition. Anyhow, it is resonble tht the mximum informtion is gined when the entire signl exiting the surfce is collected, nd tht spre coverge, s the one depicted in the left of Fig. 2 in the cse of the bundle is quite fr from the ultimte limit. 4. Mterils nd methods 4.1. Simultions The photon fluence Φ, simulting locl perturbtion, ws clculted using n higher order perturbtive pproch yielding better ccurcy thn the purely liner eqution [17]: ( ) ( ) int int 0 ( ) ( ) µ ( ) ( ( ) µ ( )) Φ r, t = 1 rr,, t r exp rr,, t r Φ r, t (5) where the photon fluence for the unperturbed stte Φ 0 ws clculted using the timedependent diffusion eqution solved for homogeneous slb pplying the extrpolted boundry conditions [20,21], while int ws clculted gin using Eq. (6) of Ref 17. Then, Φ ( r,t) ws integrted between t G nd t G + t for ech dely. Since, both for simultions nd phntom mesurements the slb thickness ws rther lrge, identicl results would be obtined using the semi-infinite model. The perturbtions were simulted by sphere (rdius 0.6 cm) embedded in homogeneous -1-1 medium with µ = 0.1 cm, µ s ' = 10 cm n medium = 1.33, n externl = 1 nd slb thickness of 15 cm (lmost semi-infinite). The reduced scttering coefficient of the inclusion ws kept the INC sme s the bckground, while 5 different vlues for the bsorption coefficient ( µ ) were considered, nmely 0.1 cm 1 (1 µ ), sme s bckground, 0.2 cm 1 ( 2 µ ), 0.4 cm 1 ( 4 µ ), 0.8 cm 1 ( 8 µ ), nd 2.0 cm 1 ( 20 µ ), to mimic completely bsorbing inclusion. Position in the xy plne ws (0,1) cm. Along the direction z, four depths were tested: 0.5, 1.0, 1.5, nd 2.0 cm. Eight time-delys t G were used (2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4 ns), while keeping fixed the width t = 500 ps. Poisson noise ws dded to the simultion in ccordnce to wht expected for the mesurements with the ICCD. In detil, simulted imges were multiplied by proper fctor so to yield given signl intensity. At ech detector position, the signl-to-noise rtio (SNR) ws clculted s the squre root of the number of counts, thus ssuming purely Poisson noise. Then, the globl SNR ws derived s the medin of the SNR t ech detector position nd ech dely. The ctul dynmic rnge of the ICCD ws effectively tken into ccount by #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 711
limiting the pek vlue in ech simulted imge to the mximum counts, nd normlizing the entire imge ccordingly. 4.2. Experimentl set-up A scheme of the experimentl set-up is depicted in Fig. 4. A pulsed diode lser (PDL800B, PicoQunt, Germny), operting t 690 nm, with pulse width 200 ps, nd repetition rte of 80 MHz ws used s the illuminting source. Light ws delivered to the tissue by mens of 50 μm core grded index fiber, nd expnded to few mm 2 using spcer. The mximum power impinging onto the phntom or onto the tissue ws 1 mw. The lunching fiber ws inserted into blck cylinder ( = 2 cm) so to msk the region too close to the injection point tht could sturte the cmer t n erly gte. The cylinder ws kept over the surfce, with the PVC in contct with the wter solution. Detection ws chieved using time-gted intensifier tube (HRI, Kentech, Didcot, UK), coupled to low-noise, Peltier cooled CCD cmer (PCO GmbH, Gottingen, Germny), set t distnce of 20 cm over the surfce nd collecting diffusely remitted light from n re centered in the injection point. The cmer ws operted with 500 ps wide gte nd rising edge of 120 ps set t given progrmmble dely with respect to the lser pulse. A hrdwre binning of 2x2 pixels ws pplied to the ICCD so to reduce the incidence of the red-out noise. All opertions involved in the mesurement were utomted, tht re: i) moving the opticl inhomogeneity using trnslting stge; ii) djusting the gte dely; iii) rotting the circulr vrible ttenutor to reduce injected power t erly delys; iv) setting the intensifier gin; v) cquiring nd sving the imges. The imging region of the ICCD ws 5.5 7.0 cm 2. Before processing, softwre binning procedure ws pplied by dding pixels in 0.3 0.3 cm 2 blocks (28 28 pixels) to reduce noise level. To eliminte the defocused shding effect of the lunching fiber crossing the imged field, prt of the rw imge ws removed. The remining 205 pixels were selected s detectors. The imging region for reconstruction ws 6 6 cm 2, s indicted by the red squre block in Fig. 4(b). The blck circle indictes the position of the blck cylinder. The region enclosed by the blck lines nd the bottom line of the rectngle ws removed to void influence of the opticl fiber. 5. Results nd Discussion 5.1. Vlidtion on simulted dt sets The proposed method ws tested first on simultions. Figure 5 shows verticl yz sections of the 3D reconstructions of µ t x = 0 for incresing vlues of µ INC (rows) nd of the perturbtion depth z (columns) recovered from simulted dt. For the sme depth, the reconstructed µ ugments for incresing vlues of µ INC (ech column hs the sme colorbr). The perturbtion cn be detected t ll depths, lthough with decresing contrst nd worse sptil resolution. Also, the lterl nd xil positions of the perturbtion re recovered with resonble greement. The SNR of simultions in Fig. 5 is 1000, leding to choice of α = 0.01. To investigte the relevnce of the signl level on the outcome of the reconstruction, we hve repeted the exercise using SNR = 40. The reconstructed µ is reported in Fig. 6. Although detection is still possible, compred to higher SNR simultions (Fig. 5), sptil locliztion is worsened, since the perturbed re is quite lrge, nd depth dependence is lost. This confirms tht sptil resolution in diffuse opticl tomogrphy is ultimtely limited by the vilble SNR [22]. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 712
Fig. 4. () Experimentl set-up. Light source: pulsed diode lser, operted t 690 nm with 80 MHz repetition rte. Detection: time-gted intensified CCD cmer, gte width 1 ns, risetime 120 ps. The lunching fiber is embedded into blck cylinder (1 cm rdius) to shield the cmer from erly photons t short source-detector distnces. (b) One rw imge cptured by the ICCD cmer. The red rectngle shows the imging region in X-Y plne for reconstruction. The blck circle indictes the position of the blck cylinder. The region enclosed by the blck lines nd the bottom line of the rectngle ws removed to void influence of the opticl fiber. It must be reclled tht the reconstruction model is bsed on the ssumption of smll perturbtion. It hs been shown [17], tht for sphere with 0.5 cm rdius set t depth of 2 cm, this pproximtion strts deviting from the rel cse for µ = 0.2 cm 1. Lrger perturbtions could be better described using higher order perturbtion pproch [23]. Yet, this would led to non-liner problem, to be solved with n itertive pproch. 5.2. Phntom mesurements For the homogeneous medium we used wter solution of Intrlipid nd blck ink with -1-1 µ = 0.1 cm nd µ s ' = 10 cm [24], poured in lrge tnk (surfce 15x20 cm 2, height 19 cm). A totl of 5 blck PVC cylindricl (height equl to dimeter) inclusions, with incresing volume (0.021, 0.050, 0.098, 0.270, 0.400 cm 3 ) were hold beneth the point (0,1.5) cm of the xy plne t 4 incresing depths z : 0.5, 1.0, 1.5 nd 2.0 cm (mesured from the upper surfce of the inclusion). The gting window pplied to the ICCD ws shifted in time t 8 incresing time-delys t G (2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4 ns), while the gte width t ws fixed t 500 ps. The cquisition time of the CCD cmer ws 2.5 s for ech dely. Figure 7 shows verticl yz sections of the 3D reconstructions of µ t x = 0 for incresing volumes of the PVC cylinder (rows) nd of depth z (columns). The perturbtion cn be detected with enough contrst up to the lrger depth (2.0 cm). Furthermore, there is resonble dependence of the reconstructed µ on the mount of perturbtion (PVC volume). Locliztion properties re lso dequte both for the y coordinte, nd for the depth z dependence. Sptil resolution suffers for the lower contrst t lrger depths, with swelling nd decresing of mximum µ upon incresing z. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 713
Fig. 5. Verticl section long the yz plne of 3D reconstructions of µ from simulted dt, using α = 0.01. A loclized perturbtion (sphere with rdius 0.6 cm) with incresing vlues of INC µ compred to µ (rows) is set t incresing depths z (columns). The first nd lst row INC represent completely homogeneous cse ( µ = 1 µ ), nd very high (completely INC bsorbing) inhomogeneity ( µ = 20 µ ), respectively. Axis dimensions re in cm, while colorbr is in cm 1. The use of blck PVC cylinders ws motivted by the need to produce controllble perturbtions. Different solutions hve been proposed to simulte opticl inhomogeneities, such s glss/plstic tubes or gloves filled with liquid solution, yet some rrngements re prone to light-guiding effects, others re difficult to hndle or to control in shpe nd position. Conversely, we hve checked vi Monte Crlo simultions tht smll totlly bsorbing inhomogeneities produce perturbtion on the DTOF of the sme shpe nd mplitude of relistic bsorption chnges provided tht the depth of the inhomogeneity is equl to or lrger thn 1 cm. Although phntom mesurements hve been crried out lso for the depth z = 0.5 cm, in this sitution, for which the inhomogeneity my be very close to source or detector, the perturbtions of blck PVC cylinders is not equivlent to tht of relistic bsorption chnges. Conversely, for z 1cm, the equivlence holds true. For instnce, totl bsorber with volume of 0.250 cm 3 yields temporl perturbtion quite similr to n opticl inhomogeneity with volume of 1 cm 3-1 nd µ = 0.5 cm (dt not shown). Aprt from the centrl blck disk, the medium boundry ws ir (92% of the imged re), thus n ext = 1 ws used for the refrctive index of the externl medium. Yet, some perturbtions cused by the different refrctive index of the blck holder cnnot be ruled out. The vilble source power in this experiment ws rther low (1 mw). Results presented on simultions show tht gin in SNR could indeed led to better sptil resolution nd locliztion. Thus, there is lrge spce for improvement, considering tht round 100 mw of source power could be used in vivo, provided tht the source dimeter is enlrged (e.g. 0.5-0.7 cm) so to sty within the sfety limits. Yet, the power stbility of the source needs to be well controlled so to permit detection of time-gted intensity chnges s low s 1%. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 714
Fig. 6. Verticl section long the yz plne of 3D reconstructions of µ from simulted dt, generted s in Fig. 5, prt from lower SNR = 40 nd vlue of α = 0.1. A loclized perturbtion (sphere with rdius 0.6 cm) with incresing vlues of µ INC compred to µ (rows) is set t incresing depths z (columns). The first nd lst row represent completely INC homogeneous cse ( µ = 1 µ ), nd very high (completely bsorbing) inhomogeneity INC ( µ = 20 µ ), respectively. Axis dimensions re in cm, colorbr is in cm 1. 5.3. Potentil ppliction to functionl imging of the brin One of the key dvntges of the proposed pproch is the exploittion of both significnt light hrvesting s well s optiml collection of vilble informtion. As consequence full 3D cquisition is fesible in reltively short time. Phntom mesurements hve been demonstrted with totl cquisition time per reconstructed imge of 15 s. The vilble power ws just 1 mw, with room for relistic gin by 2 orders of mgnitude, possibly resulting in better imge qulity nd/or reduced cquisition time. This mkes the technique prticulrly ppeling for in vivo functionl imging, involving the reconstruction of bsorption chnges compred to n initil reference stte. The study of the pplicbility of this pproch to in vivo functionl imging will be ddressed in the ner future with the id of more powerful source. By now we just performed some preliminry tests on shved subject leding to 3 observtions: i) when the subject is lying on bed, it is rther esy to keep the sme working distnce of the cmer from the hed (20 cm) nd field of view (5.5x7.0 cm 2 ) s for phntom mesurements; ii) the signl level t 690 nm is similr to wht observed on phntoms; iii) movement rtifcts seem not to be so criticl, with shift in the position of the lunching fiber, identified by the blck cylinder fiber holder, less thn the size of one voxel (<3 mm) during 15 min. Clerly, the presence of hir could hmper prcticl pplicbility of the proposed pproch. In ny cse, ll mesurements performed on the forehed (e.g. those relted to cognitive tsks) could be esily mnged. Also, on regions covered by hir, proper combing could crete rows or zones of exposed skin. We will study whether this kind of reduced dt set is still vluble to provide 3D reconstruction. #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 715
Fig. 7. Verticl section long the yz plne with x = 0 cm of tomogrphies of µ from phntom mesurements, using α = 0.1. From left to right the depth (Z) of the inclusion is incresed. From top to bottom, the volume of the PVC cylinder is incresed. Axis dimensions re in cm, while colorbr is in cm 1. 6. Conclusion We hve proposed novel scheme to functionl tomogrphy bsed on single source injection point nd on time-gted ICCD cmer for detection. A non-contct modlity is dopted for collection, with direct imging of the medium surfce vi the cmer lens. Shielding of smll region round the lunching fiber helps preventing reduction of the useful dynmic rnge. Simultions of loclized perturbtion of the bsorption coefficient demonstrte the fesibility of the proposed pproch both for detection nd locliztion of smll perturbtion, with n imge qulity clerly dependent on the SNR. Phntom mesurements using blck PVC cylinders demonstrte detection of 0.050 cm 3 perturbtion down to depth of 2 cm within diffusive tissue-like medium. Also, firly good locliztion is chieved both in depth nd lterl direction, while sptil resolution nd contrst is degrded for incresing depth. Totl cquisition time to cquire full 3D dt set ws 15 s for n injected power of 1 mw. Work is in progress to study the pplicbility of this method to in vivo functionl imging of the brin nd to exploit more powerful (100 mw) sources. Acknowledgments The reserch leding to these results hs been prtilly funded by the Europen Community s Seventh Frmework Progrmme under the neuropt project (FP7-HEALTH-2007-201076). #140186 - $15.00 USD Received 23 Dec 2010; revised 18 Feb 2011; ccepted 19 Feb 2011; published 25 Feb 2011 (C) 2011 OSA 1 Mrch 2011 / Vol. 2, No. 3 / BIOMEDICAL OPTICS EXPRESS 716