Abstract

A Monte Carlo method for photon transport has gained wide popularity in biomedical optics for studying light behaviour in tissue. Nowadays, typical computation times range from a few minutes to hours. Although various implementations of the Monte Carlo algorithm exist, there is only a limited number of free software available. In addition, these packages may require substantial learning efforts. To address these issues, we present a new Monte Carlo software with a user-friendly interface. The simulation geometry is defined using an unstructured (triangular or tetrahedral) mesh. The program solves the photon fluence in the computation domain and the exitance at the domain boundary. It is capable of simulating complex measurement geometries with spatially varying optical parameter distributions and supports several types of light sources as well as intensity modulated light. Furthermore, attention is given to ease of use and fast problem set up with a MATLAB (The MathWorks Inc., Natick, MA) interface. The simulation code is written in C++ and parallelized using OpenMP. The simulation code has been validated against analytical and numerical solutions of radiative transfer equation and other Monte Carlo software in good agreement. The software is available for download from the homepage https://inverselight.github.io/ValoMC/ and the source code from GitHub https://github.com/InverseLight/ValoMC.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

J. Cassidy, A. Nouri, V. Betz, and L. Lilge, “High-performance, robustly verified Monte Carlo simulation with FullMonte,” J. Biomed. Opt. 23(8), 1 (2018).
[Crossref]

L. Yu, F. Nina-Paravecino, D. Kaeli, and Q. Fang, “Scalable and massively parallel Monte Carlo photon transport simulations for heterogeneous computing platforms,” J. Biomed. Opt. 23(1), 1 (2018).
[Crossref]

D. Ancora, L. Qiu, G. Zacharakis, L. Spinelli, A. Torricelli, and A. Pifferi, “Noninvasive optical estimation of CSF thickness for brain-atrophy monitoring,” Biomed. Opt. Express 9(9), 4094 (2018).
[Crossref]

2017 (4)

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

H. Xiang, B. Chen, W. Wu, Y. Zhang, and H. Jia, “An integral MPS model of blood coagulation by laser irradiation: Application to the optimization of multi-pulse Nd:YAG laser treatment of port-wine stains,” Int. J. Heat Mass Transfer 114, 1220–1233 (2017).
[Crossref]

A. Correia, P. Hanselaer, H. Cornelissen, and Y. Meuret, “Radiance based method for accurate determination of volume scattering parameters using GPU-accelerated Monte Carlo,” Opt. Express 25(19), 22575–22586 (2017).
[Crossref]

V. Periyasamy and M. Pramanik, “Advances in Monte Carlo simulation for light propagation in tissue,” IEEE Rev. Biomed. Eng. 10, 122–135 (2017).
[Crossref]

2016 (5)

Y. Liu, H. Jiang, and Z. Yuan, “Two schemes for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 3987–3997 (2016).
[Crossref]

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6(1), 27057 (2016).
[Crossref]

D. Wangpraseurt, S. L. Jacques, T. Petrie, and M. Kühl, “Monte Carlo modeling of photon propagation reveals highly scattering coral tissue,” Front. Plant. Sci. 7, 1404 (2016).
[Crossref]

R. Yao, X. Intes, and Q. Fang, “Generalized mesh-based Monte Carlo for widefield illumination and detection via mesh retessellation,” Biomed. Opt. Express 7(1), 171–184 (2016).
[Crossref]

R. Hochuli, S. Powell, S. Arridge, and B. Cox, “Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance,” J. Biomed. Opt. 21(12), 126004 (2016).
[Crossref]

2015 (4)

Y. Liu, S. Jacques, M. Azimipour, J. Rogers, R. Pashaie, and K. Eliceiri, “OptogenSIM: a 3D Monte Carlo simulation platform for light delivery design in optogenetics,” Biomed. Opt. Express 6(12), 4859–4870 (2015).
[Crossref]

J. Cassidy, V. Betz, and L. Lilgem, “Treatment plan evaluation for interstitial photodynamic therapy in a mouse model by Monte Carlo simulation with FullMonte,” Front. Phys. 3, 6 (2015).
[Crossref]

L. Vinckenbosch, C. Lacaux, S. Tindel, M. Thomassin, and T. Obara, “Monte Carlo methods for lightpropagation in biological tissues,” Math. Biosci. 269, 48–60 (2015).
[Crossref]

O. Lehtikangas, T. Tarvainen, A. Kim, and S. Arridge, “Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index,” J. Comput. Phys. 282, 345–359 (2015).
[Crossref]

2014 (6)

J. J. Selb, D. A. Boas, S. T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
[Crossref]

A. Pulkkinen, V. Kolehmainen, J. Kaipio, B. Cox, S. Arridge, and T. Tarvainen, “Approximate marginalization of unknown scattering in quantitative photoacoustic tomography,” Inv. Probl. Imag. 8(3), 811–829 (2014).
[Crossref]

M. Schweiger and S. R. Arridge, “The Toast++ software suite for forward and inverse modeling in optical tomography,” J. Biomed. Opt. 19(4), 040801 (2014).
[Crossref]

S. L. Jacques, “Coupling 3D Monte Carlo light transport in optically heterogeneous tissues to photoacoustic signal generation,” Photoacoustics 2(4), 137–142 (2014).
[Crossref]

C. Hayakawa, J. Spanier, and V. Venugopalan, “Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media,” J. Opt. Soc. Am. A 31(2), 301–311 (2014).
[Crossref]

V. Periyasamya and M. Pramanik, “Monte Carlo simulation of light transport in turbid medium with embedded object - spherical, cylindrical, ellipsoidal, or cuboidal objects embedded within multilayered tissues,” J. Biomed. Opt. 19(4), 045003 (2014).
[Crossref]

2013 (4)

2012 (4)

A. Liemert and A. Kienle, “Analytical approach for solving the radiative transfer equation in two-dimensional layered media,” J. Quant. Spectrosc. Radiat. Transfer 113(7), 559–564 (2012).
[Crossref]

Q. Fang and D. Kaeli, “Accelerating mesh-based Monte Carlo method on modern CPU architectures,” Biomed. Opt. Express 3(12), 3223–3230 (2012).
[Crossref]

S. Powell and T. Leung, “Highly parallel Monte-Carlo simulations of the acousto-optic effect in heterogeneous turbid media,” J. Biomed. Opt. 17(4), 045002 (2012).
[Crossref]

A. Sassaroli and F. Martelli, “Equivalence of four Monte Carlo methods for photon migration in turbid media,” J. Opt. Soc. Am. A 29(10), 2110–2117 (2012).
[Crossref]

2011 (3)

J. Chen, V. Venugopal, and X. Intes, “Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates,” Biomed. Opt. Express 2(4), 871–886 (2011).
[Crossref]

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency,” Phys. Med. Biol. 38, 5788–5798 (2011).
[Crossref]

P. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

2010 (6)

B. Treeby and B. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref]

O. Lehtikangas, T. Tarvainen, V. Kolehmainen, A. Pulkkinen, S. Arridge, and J. Kaipio, “Finite element approximation of the Fokker-Planck equation for diffuse optical tomography,” J. Quant. Spectrosc. Radiat. Transfer 111(10), 1406–1417 (2010).
[Crossref]

T. Leung and S. Powell, “Fast Monte Carlo simulations of ultrasound-modulated light using a graphics processing unit,” J. Biomed. Opt. 15(5), 055007 (2010).
[Crossref]

Q. Fang, “Mesh-based Monte Carlo method using fast ray-tracing in Plücker coordinates,” Biomed. Opt. Express 1(1), 165–175 (2010).
[Crossref]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
[Crossref]

H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. 55(4), 947–962 (2010).
[Crossref]

2009 (1)

2008 (1)

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: Influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[Crossref]

2007 (1)

2005 (3)

2003 (1)

2002 (1)

2001 (1)

1998 (1)

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[Crossref]

1997 (2)

1996 (1)

T. Pfefer, J. K. Barton, E. Chan, M. Ducros, B. Sorg, T. Milner, J. Nelson, and A. Welch, “A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue,” IEEE J. Sel. Top. Quantum Electron. 2(4), 934–942 (1996).
[Crossref]

1995 (1)

L. Wang, S. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref]

1993 (1)

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. Arridge, P. van der Zee, and D. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Ajichi, Y.

Ancora, D.

D. Ancora, L. Qiu, G. Zacharakis, L. Spinelli, A. Torricelli, and A. Pifferi, “Noninvasive optical estimation of CSF thickness for brain-atrophy monitoring,” Biomed. Opt. Express 9(9), 4094 (2018).
[Crossref]

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

Arridge, S.

R. Hochuli, S. Powell, S. Arridge, and B. Cox, “Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance,” J. Biomed. Opt. 21(12), 126004 (2016).
[Crossref]

O. Lehtikangas, T. Tarvainen, A. Kim, and S. Arridge, “Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index,” J. Comput. Phys. 282, 345–359 (2015).
[Crossref]

A. Pulkkinen, V. Kolehmainen, J. Kaipio, B. Cox, S. Arridge, and T. Tarvainen, “Approximate marginalization of unknown scattering in quantitative photoacoustic tomography,” Inv. Probl. Imag. 8(3), 811–829 (2014).
[Crossref]

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[Crossref]

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F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6(1), 27057 (2016).
[Crossref]

Powell, S.

R. Hochuli, S. Powell, S. Arridge, and B. Cox, “Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance,” J. Biomed. Opt. 21(12), 126004 (2016).
[Crossref]

S. Powell and T. Leung, “Highly parallel Monte-Carlo simulations of the acousto-optic effect in heterogeneous turbid media,” J. Biomed. Opt. 17(4), 045002 (2012).
[Crossref]

T. Leung and S. Powell, “Fast Monte Carlo simulations of ultrasound-modulated light using a graphics processing unit,” J. Biomed. Opt. 15(5), 055007 (2010).
[Crossref]

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in “SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology,” G. Müller and D. Sliney, eds. (1989), vol. IS 5, pp. 102–111.

Pramanik, M.

V. Periyasamy and M. Pramanik, “Advances in Monte Carlo simulation for light propagation in tissue,” IEEE Rev. Biomed. Eng. 10, 122–135 (2017).
[Crossref]

V. Periyasamya and M. Pramanik, “Monte Carlo simulation of light transport in turbid medium with embedded object - spherical, cylindrical, ellipsoidal, or cuboidal objects embedded within multilayered tissues,” J. Biomed. Opt. 19(4), 045003 (2014).
[Crossref]

Prohaska, S.

J. Buchmann, B. A. Kaplan, S. Prohaska, and J. Laufer, “Experimental validation of a Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography,” in “Photons Plus Ultrasound: Imaging and Sensing 2017, Proc. of SPIE,” A. Oraevsky and L. Wang, eds. (2017), vol. 10064, p. 1006416.

B. A. Kaplan, J. Buchmann, S. Prohaska, and J. Laufer, “Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography,” in “Photons Plus Ultrasound: Imaging and Sensing 2017, Proc. of SPIE,” A. Oraevsky and L. Wang, eds. (2017), vol. 10064, pp. 100645J–1.

Pulkkinen, A.

A. Pulkkinen, V. Kolehmainen, J. Kaipio, B. Cox, S. Arridge, and T. Tarvainen, “Approximate marginalization of unknown scattering in quantitative photoacoustic tomography,” Inv. Probl. Imag. 8(3), 811–829 (2014).
[Crossref]

A. Pulkkinen and T. Tarvainen, “Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements,” J. Opt. Soc. Am. A 30(3), 470–478 (2013).
[Crossref]

P. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

O. Lehtikangas, T. Tarvainen, V. Kolehmainen, A. Pulkkinen, S. Arridge, and J. Kaipio, “Finite element approximation of the Fokker-Planck equation for diffuse optical tomography,” J. Quant. Spectrosc. Radiat. Transfer 111(10), 1406–1417 (2010).
[Crossref]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
[Crossref]

T. Tarvainen, A. Pulkkinen, B. Cox, J. Kaipio, and S. Arridge, “Image reconstruction in quantitative photoacoustic tomography using the radiative transfer equation and the diffusion approximation,” in “Opto-Acoustic Methods and Applications, Proc. of OSA Biomedical Optics-SPIE,” V. Ntziachristos and C. Lin, eds. (2013), vol. 8800, pp. 880006–1.

Qiu, L.

Relue, P.

S. Patwardhan, A. Dhawan, and P. Relue, “Monte Carlo simulation of light-tissue interaction: Three-dimensional simulation for trans-illumination-based imaging of skin lesions,” IEEE Trans. Biomed. Eng. 52(7), 1227–1236 (2005).
[Crossref]

Ripoll, J.

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

Rogers, J.

Rüfenacht, D.

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: Influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[Crossref]

Sassaroli, A.

Schöberl, J.

J. Schöberl, “NETGEN an advancing front 2d/3d-mesh generator based on abstract rules,” Comput. Visualization Sci. 1(1), 41–52 (1997).
[Crossref]

Schweiger, M.

M. Schweiger and S. R. Arridge, “The Toast++ software suite for forward and inverse modeling in optical tomography,” J. Biomed. Opt. 19(4), 040801 (2014).
[Crossref]

P. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
[Crossref]

Selb, J. J.

J. J. Selb, D. A. Boas, S. T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
[Crossref]

Shen, H.

H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. 55(4), 947–962 (2010).
[Crossref]

Somersalo, E.

Sorg, B.

T. Pfefer, J. K. Barton, E. Chan, M. Ducros, B. Sorg, T. Milner, J. Nelson, and A. Welch, “A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue,” IEEE J. Sel. Top. Quantum Electron. 2(4), 934–942 (1996).
[Crossref]

Spanier, J.

Spinelli, L.

D. Ancora, L. Qiu, G. Zacharakis, L. Spinelli, A. Torricelli, and A. Pifferi, “Noninvasive optical estimation of CSF thickness for brain-atrophy monitoring,” Biomed. Opt. Express 9(9), 4094 (2018).
[Crossref]

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6(1), 27057 (2016).
[Crossref]

Stott, J.

Tarvainen, T.

O. Lehtikangas, T. Tarvainen, A. Kim, and S. Arridge, “Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index,” J. Comput. Phys. 282, 345–359 (2015).
[Crossref]

A. Pulkkinen, V. Kolehmainen, J. Kaipio, B. Cox, S. Arridge, and T. Tarvainen, “Approximate marginalization of unknown scattering in quantitative photoacoustic tomography,” Inv. Probl. Imag. 8(3), 811–829 (2014).
[Crossref]

A. Pulkkinen and T. Tarvainen, “Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements,” J. Opt. Soc. Am. A 30(3), 470–478 (2013).
[Crossref]

P. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

O. Lehtikangas, T. Tarvainen, V. Kolehmainen, A. Pulkkinen, S. Arridge, and J. Kaipio, “Finite element approximation of the Fokker-Planck equation for diffuse optical tomography,” J. Quant. Spectrosc. Radiat. Transfer 111(10), 1406–1417 (2010).
[Crossref]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
[Crossref]

T. Tarvainen, A. Pulkkinen, B. Cox, J. Kaipio, and S. Arridge, “Image reconstruction in quantitative photoacoustic tomography using the radiative transfer equation and the diffusion approximation,” in “Opto-Acoustic Methods and Applications, Proc. of OSA Biomedical Optics-SPIE,” V. Ntziachristos and C. Lin, eds. (2013), vol. 8800, pp. 880006–1.

Thomassin, M.

L. Vinckenbosch, C. Lacaux, S. Tindel, M. Thomassin, and T. Obara, “Monte Carlo methods for lightpropagation in biological tissues,” Math. Biosci. 269, 48–60 (2015).
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Tindel, S.

L. Vinckenbosch, C. Lacaux, S. Tindel, M. Thomassin, and T. Obara, “Monte Carlo methods for lightpropagation in biological tissues,” Math. Biosci. 269, 48–60 (2015).
[Crossref]

Torricelli, A.

D. Ancora, L. Qiu, G. Zacharakis, L. Spinelli, A. Torricelli, and A. Pifferi, “Noninvasive optical estimation of CSF thickness for brain-atrophy monitoring,” Biomed. Opt. Express 9(9), 4094 (2018).
[Crossref]

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6(1), 27057 (2016).
[Crossref]

Treeby, B.

B. Treeby and B. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref]

van der Zee, P.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. Arridge, P. van der Zee, and D. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Vauhkonen, M.

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
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Venugopal, V.

Venugopalan, V.

Vinckenbosch, L.

L. Vinckenbosch, C. Lacaux, S. Tindel, M. Thomassin, and T. Obara, “Monte Carlo methods for lightpropagation in biological tissues,” Math. Biosci. 269, 48–60 (2015).
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Vitkin, I.

Wang, G.

H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. 55(4), 947–962 (2010).
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L. Wang, R. Nordquist, and W. Chen, “Optimal beam size for light delivery to absorption-enhanced tumors buried in biological tissues and effect of multiple-beam delivery: a Monte Carlo study,” Appl. Opt. 36(31), 8286–8291 (1997).
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L. Wang, S. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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L. V. Wang, Diffuse Optical Tomography (Wiley-Blackwell, 2012), chap. 11, pp. 249–281.

Wangpraseurt, D.

D. Wangpraseurt, S. L. Jacques, T. Petrie, and M. Kühl, “Monte Carlo modeling of photon propagation reveals highly scattering coral tissue,” Front. Plant. Sci. 7, 1404 (2016).
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Welch, A.

T. Pfefer, J. K. Barton, E. Chan, M. Ducros, B. Sorg, T. Milner, J. Nelson, and A. Welch, “A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue,” IEEE J. Sel. Top. Quantum Electron. 2(4), 934–942 (1996).
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Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in “SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology,” G. Müller and D. Sliney, eds. (1989), vol. IS 5, pp. 102–111.

Wu, W.

H. Xiang, B. Chen, W. Wu, Y. Zhang, and H. Jia, “An integral MPS model of blood coagulation by laser irradiation: Application to the optimization of multi-pulse Nd:YAG laser treatment of port-wine stains,” Int. J. Heat Mass Transfer 114, 1220–1233 (2017).
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Xiang, H.

H. Xiang, B. Chen, W. Wu, Y. Zhang, and H. Jia, “An integral MPS model of blood coagulation by laser irradiation: Application to the optimization of multi-pulse Nd:YAG laser treatment of port-wine stains,” Int. J. Heat Mass Transfer 114, 1220–1233 (2017).
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Yang, O.

Yao, R.

Yu, L.

L. Yu, F. Nina-Paravecino, D. Kaeli, and Q. Fang, “Scalable and massively parallel Monte Carlo photon transport simulations for heterogeneous computing platforms,” J. Biomed. Opt. 23(1), 1 (2018).
[Crossref]

Yuan, Z.

Y. Liu, H. Jiang, and Z. Yuan, “Two schemes for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 3987–3997 (2016).
[Crossref]

Zacharakis, G.

D. Ancora, L. Qiu, G. Zacharakis, L. Spinelli, A. Torricelli, and A. Pifferi, “Noninvasive optical estimation of CSF thickness for brain-atrophy monitoring,” Biomed. Opt. Express 9(9), 4094 (2018).
[Crossref]

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

Zacharopoulos, A.

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

Zhang, Y.

H. Xiang, B. Chen, W. Wu, Y. Zhang, and H. Jia, “An integral MPS model of blood coagulation by laser irradiation: Application to the optimization of multi-pulse Nd:YAG laser treatment of port-wine stains,” Int. J. Heat Mass Transfer 114, 1220–1233 (2017).
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L. Wang, S. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
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T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: Influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
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L. Wang, S. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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J. Schöberl, “NETGEN an advancing front 2d/3d-mesh generator based on abstract rules,” Comput. Visualization Sci. 1(1), 41–52 (1997).
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J. Cassidy, V. Betz, and L. Lilgem, “Treatment plan evaluation for interstitial photodynamic therapy in a mouse model by Monte Carlo simulation with FullMonte,” Front. Phys. 3, 6 (2015).
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D. Wangpraseurt, S. L. Jacques, T. Petrie, and M. Kühl, “Monte Carlo modeling of photon propagation reveals highly scattering coral tissue,” Front. Plant. Sci. 7, 1404 (2016).
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IEEE J. Sel. Top. Quantum Electron. (1)

T. Pfefer, J. K. Barton, E. Chan, M. Ducros, B. Sorg, T. Milner, J. Nelson, and A. Welch, “A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue,” IEEE J. Sel. Top. Quantum Electron. 2(4), 934–942 (1996).
[Crossref]

IEEE Rev. Biomed. Eng. (1)

V. Periyasamy and M. Pramanik, “Advances in Monte Carlo simulation for light propagation in tissue,” IEEE Rev. Biomed. Eng. 10, 122–135 (2017).
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S. Patwardhan, A. Dhawan, and P. Relue, “Monte Carlo simulation of light-tissue interaction: Three-dimensional simulation for trans-illumination-based imaging of skin lesions,” IEEE Trans. Biomed. Eng. 52(7), 1227–1236 (2005).
[Crossref]

IEEE Trans. Med. Imaging. (1)

D. Ancora, A. Zacharopoulos, J. Ripoll, and G. Zacharakis, “Fluorescence diffusion in the presence of optically clear tissues in a mouse head model,” IEEE Trans. Med. Imaging. 36(5), 1086–1093 (2017).
[Crossref]

Int. J. Heat Mass Transfer (1)

H. Xiang, B. Chen, W. Wu, Y. Zhang, and H. Jia, “An integral MPS model of blood coagulation by laser irradiation: Application to the optimization of multi-pulse Nd:YAG laser treatment of port-wine stains,” Int. J. Heat Mass Transfer 114, 1220–1233 (2017).
[Crossref]

Inv. Probl. (1)

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inv. Probl. 26(1), 015005 (2010).
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Y. Marzouk, I. Langmore, and G. Bal, “Bayesian inverse problems with Monte Carlo forward models,” Inv. Probl. Imag. 7(1), 81–105 (2013).
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A. Pulkkinen, V. Kolehmainen, J. Kaipio, B. Cox, S. Arridge, and T. Tarvainen, “Approximate marginalization of unknown scattering in quantitative photoacoustic tomography,” Inv. Probl. Imag. 8(3), 811–829 (2014).
[Crossref]

J. Biomed. Opt. (9)

M. Schweiger and S. R. Arridge, “The Toast++ software suite for forward and inverse modeling in optical tomography,” J. Biomed. Opt. 19(4), 040801 (2014).
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B. Treeby and B. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref]

J. Cassidy, A. Nouri, V. Betz, and L. Lilge, “High-performance, robustly verified Monte Carlo simulation with FullMonte,” J. Biomed. Opt. 23(8), 1 (2018).
[Crossref]

S. Powell and T. Leung, “Highly parallel Monte-Carlo simulations of the acousto-optic effect in heterogeneous turbid media,” J. Biomed. Opt. 17(4), 045002 (2012).
[Crossref]

T. Leung and S. Powell, “Fast Monte Carlo simulations of ultrasound-modulated light using a graphics processing unit,” J. Biomed. Opt. 15(5), 055007 (2010).
[Crossref]

L. Yu, F. Nina-Paravecino, D. Kaeli, and Q. Fang, “Scalable and massively parallel Monte Carlo photon transport simulations for heterogeneous computing platforms,” J. Biomed. Opt. 23(1), 1 (2018).
[Crossref]

R. Hochuli, S. Powell, S. Arridge, and B. Cox, “Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance,” J. Biomed. Opt. 21(12), 126004 (2016).
[Crossref]

V. Periyasamya and M. Pramanik, “Monte Carlo simulation of light transport in turbid medium with embedded object - spherical, cylindrical, ellipsoidal, or cuboidal objects embedded within multilayered tissues,” J. Biomed. Opt. 19(4), 045003 (2014).
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C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
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J. Comput. Phys. (2)

O. Lehtikangas, T. Tarvainen, A. Kim, and S. Arridge, “Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index,” J. Comput. Phys. 282, 345–359 (2015).
[Crossref]

P. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
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L. Vinckenbosch, C. Lacaux, S. Tindel, M. Thomassin, and T. Obara, “Monte Carlo methods for lightpropagation in biological tissues,” Math. Biosci. 269, 48–60 (2015).
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Med. Phys. (1)

Y. Liu, H. Jiang, and Z. Yuan, “Two schemes for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 3987–3997 (2016).
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J. J. Selb, D. A. Boas, S. T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
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H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. 55(4), 947–962 (2010).
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B. A. Kaplan, J. Buchmann, S. Prohaska, and J. Laufer, “Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography,” in “Photons Plus Ultrasound: Imaging and Sensing 2017, Proc. of SPIE,” A. Oraevsky and L. Wang, eds. (2017), vol. 10064, pp. 100645J–1.

J. Buchmann, B. A. Kaplan, S. Prohaska, and J. Laufer, “Experimental validation of a Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography,” in “Photons Plus Ultrasound: Imaging and Sensing 2017, Proc. of SPIE,” A. Oraevsky and L. Wang, eds. (2017), vol. 10064, p. 1006416.

T. Tarvainen, A. Pulkkinen, B. Cox, J. Kaipio, and S. Arridge, “Image reconstruction in quantitative photoacoustic tomography using the radiative transfer equation and the diffusion approximation,” in “Opto-Acoustic Methods and Applications, Proc. of OSA Biomedical Optics-SPIE,” V. Ntziachristos and C. Lin, eds. (2013), vol. 8800, pp. 880006–1.

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Figures (5)

Fig. 1.
Fig. 1. Illustration of the matrices $r$ (coordinates), $H$ (element topology) and $B_H$ (boundary element topology). (a) Shown is a 2D circle constructed from triangles. (b) The geometry for the simple example discussed in the text. (c) 3D half-sphere constructed from tetrahedrons. (d) A tetrahedron $H_1 = (\,1\enspace 3\enspace 5\enspace 2\,)$ indicated with coloured region and a boundary element ${B_H}_1 = (\,1\enspace 3\enspace \,5)$ indicated with a dashed line.
Fig. 2.
Fig. 2. Flowchart of the algorithm.
Fig. 3.
Fig. 3. Comparison of ValoMC against the analytical solution of the radiative transfer equation in a semi-infinte layered medium. The unit of exitance ($1/\textrm {mm}$) is used for consistency with Ref. [65]. The data for the analytical solution was provided by A. Liemert and A. Kienle [65].
Fig. 4.
Fig. 4. Comparison of ValoMC against Mesh-based Monte Carlo (MMC) [19]. (a) Fluence distribution when the refractive index of the sphere was set to $n = 1.0$ calculated with ValoMC. (b) Difference (relative error) between fluence obtained using ValoMC and MMC with different number of photon packets calculated using Eqn. (10). (c) Total energy absorption rate in the sphere as a function of its refractive index calculated with ValoMC and MMC.
Fig. 5.
Fig. 5. Frequency domain calculation in 2D. Coloured image shows the phase of the photon fluence. The blue line shows the amplitude of the exitance.

Tables (3)

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Table 1. A summary of currently implemented features in ValoMC.

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Table 2. List of the mandatory fields in the input and output of the main function of ValoMC. More detailed options are provided in the homepage and documentation.

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Table 3. List of the environments ValoMC has been tested on.

Equations (10)

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r = ( r 1 r 2 r 3 r 4 ) = ( 0.8 0.7 0.2 1.4 1.6 1.2 1.8 1 )
H = ( H 1 H 2 ) = ( 1 2 3 3 4 1 ) .
B H = ( B H 1 B H 2 B H 3 B H 4 ) = ( 1 2 2 3 3 4 4 1 )
H N = ( 1 2 2 3 4 1 )
P ( s ) = μ s , curr exp ( μ s , curr s )
w w exp ( μ a , curr Δ s )
Φ i = W i μ a , i N V i
J j + = W j N A j
w w exp [ ( μ a , curr + i ω n curr c 0 ) Δ s ]
E = 100 % R ( f ( r ) f ref ( r ) ) 2 d r R f ref ( r ) 2 d r

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