A GPU accelerated study of aqueous humor dynamics in human eyes using the lattice Boltzmann method

Gang Huang; Qianlin Ye; Hao Tang; Zhangrong Qin; Gang Huang; Qianlin Ye; Hao Tang; Zhangrong Qin

doi:10.3934/mbe.2023372

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 8476-8497. doi: 10.3934/mbe.2023372

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A GPU accelerated study of aqueous humor dynamics in human eyes using the lattice Boltzmann method

1.
Business School, Jiangxi University of Science and Technology, Jiangxi, China
2.
Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin 541004, China

Academic Editor: Xiang-Sheng Wang

Received: 23 November 2022 Revised: 16 February 2023 Accepted: 22 February 2023 Published: 02 March 2023

In this paper, we presented a 3D human eyes aqueous humor (AH) dynamics model, and additionally, designed and optimized it using GPU technology. First, the feasibility of the model is demonstrated through validation. Then, the effect of different factors on AH flow was investigated using the validated model. The experimental results showed that AH flow more rapidly when standing than supine; the intraocular temperature has the greatest effect on AH flow compared to other factors; the AH secretion rate and trabecular meshwork (TM) permeability had a greater effect on intraocular pressure (IOP). Corneal indentation and ovoid anterior chamber (AC) can also affect AH flow. Finally, the PartSparse algorithm based GPU can save more than 50% of the memory consumption and achieves a performance of 1491.29 MLUPS and a Speedup of 837.61 times.
- lattice Boltzmann method,
- aqueous humor dynamics,
- GPU,
- sparse matrix
Citation: Gang Huang, Qianlin Ye, Hao Tang, Zhangrong Qin. A GPU accelerated study of aqueous humor dynamics in human eyes using the lattice Boltzmann method[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8476-8497. doi: 10.3934/mbe.2023372

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Abstract

In this paper, we presented a 3D human eyes aqueous humor (AH) dynamics model, and additionally, designed and optimized it using GPU technology. First, the feasibility of the model is demonstrated through validation. Then, the effect of different factors on AH flow was investigated using the validated model. The experimental results showed that AH flow more rapidly when standing than supine; the intraocular temperature has the greatest effect on AH flow compared to other factors; the AH secretion rate and trabecular meshwork (TM) permeability had a greater effect on intraocular pressure (IOP). Corneal indentation and ovoid anterior chamber (AC) can also affect AH flow. Finally, the PartSparse algorithm based GPU can save more than 50% of the memory consumption and achieves a performance of 1491.29 MLUPS and a Speedup of 837.61 times.

References

[1]	C. R. Canning, M. J. Greaney, J. N. Dewynne, A. D. Fitt, Fluid flow in the anterior chamber of a human eye, Math. Med. Biol., 19 (2002), 31−60. https://doi.org/10.1093/imammb/19.1.31 doi: 10.1093/imammb/19.1.31
[2]	J. J. Heys, V. H. Barocas, A boussinesq model of natural convection in the human eye and the formation of Krukenberg's spindle, Ann. Biomed. Eng., 30 (2002), 392−401. https://doi.org/10.1114/1.1477447 doi: 10.1114/1.1477447
[3]	A. D. Fitt, G. Gonzalez, Fluid mechanics of the human eye: Aqueous humour flow in the anterior chamber, Bull. Math. Biol., 68 (2006), 53−71. https://doi.org/10.1007/s11538-005-9015-2 doi: 10.1007/s11538-005-9015-2
[4]	T. R. Crowder, V. J. Ervin, Numerical simulations of fluid pressure in the human eye, Appl. Math. Comput., 219 (2013), 11119−11133. https://doi.org/10.1016/j.amc.2013.04.060 doi: 10.1016/j.amc.2013.04.060
[5]	S. Kumar, S. Acharya, R. Beuerman, A. Palkama, Numerical solution of ocular fluid dynamics in a rabbit eye: parametric effects, Ann. Biomed. Eng., 34 (2006), 530. https://doi.org/10.1007/s10439-005-9048-6 doi: 10.1007/s10439-005-9048-6
[6]	J. A. Ferreira, P. De Oliveira, P. M. Da Silva, J. N. Murta, Numerical simulation of aqueous humor flow: from healthy to pathologic situations, Appl. Math. Comput., 226 (2014), 777−792. https://doi.org/10.1016/j.amc.2013.10.070 doi: 10.1016/j.amc.2013.10.070
[7]	G. R. Mcnamara, G. Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61 (1988), 2332−2335. https://doi.org/10.1103/PhysRevLett.61.2332 doi: 10.1103/PhysRevLett.61.2332
[8]	S. Y. Chen, H. D. Chen, D. Martinez, W. Matthaeus, Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett., 67 (1991), 3776−3779. https://doi.org/10.1103/PhysRevLett.67.3776 doi: 10.1103/PhysRevLett.67.3776
[9]	Y. H. Qian, D. D'Humières, P. Lallemand, Lattice bgk models for navier-stokes equation, Europhys. Lett., 17 (1992), 479−484. https://doi.org/10.1209/0295-5075/17/6/001 doi: 10.1209/0295-5075/17/6/001
[10]	Y. H. Qian, Simulating thermohydrodynamics with lattice BGK models, J. Sci. Comput., 8 (1993), 231−242. https://doi.org/10.1007/BF01060932 doi: 10.1007/BF01060932
[11]	Z. Guo, B. Shi, C. Zheng, A coupled lattice BGK model for the Boussinesq equations, Int. J. Numer. Methods Fluids, 39 (2002), 325−342. https://doi.org/10.1002/fld.337 doi: 10.1002/fld.337
[12]	Z. Guo, T. Zhao, A lattice Boltzmann model for convection heat transfer in porous media, Numer. Heat Transfer, Part B, 47 (2005), 157−177. https://doi.org/10.1080/10407790590883405 doi: 10.1080/10407790590883405
[13]	Z. Qin, L. Meng, F. Yang, C. Zhang, B. Wen, Aqueous humor dynamics in human eye: a lattice Boltzmann study, Math. Biosci. Eng., 18 (2021), 5006−5028. https://doi.org/10.3934/mbe.2021255 doi: 10.3934/mbe.2021255
[14]	E. Lindholm, J. Nickolls, S. Oberman, J. Montrym, NVIDIA Tesla: a unified graphics and computing architecture, IEEE Micro, 28 (2008), 39−55. https://doi.org/10.1109/MM.2008.31 doi: 10.1109/MM.2008.31
[15]	J. Tölke, Implementation of a Lattice Boltzmann kernel using the compute unified device architecture developed by Nvidia, Comput. Visualization Sci., 13 (2008), 29−39. https://doi.org/10.1007/s00791-008-0120-2 doi: 10.1007/s00791-008-0120-2
[16]	F. Kuznik, C. Obrecht, G. Rusaouen, J. J. Roux, LBM based flow simulation using GPU computing processor, Comput. Math. Appl., 59 (2010), 2380−2392. https://doi.org/10.1016/j.camwa.2009.08.052 doi: 10.1016/j.camwa.2009.08.052
[17]	J. Habich, T. Zeiser, G. Hager, G. Wellein, Performance analysis and optimization strategies for a D3Q19 lattice Boltzmann kernel on nVIDIA GPUs using CUDA, Adv. Eng. Software, 42 (2011), 266−272. https://doi.org/10.1016/j.advengsoft.2010.10.007 doi: 10.1016/j.advengsoft.2010.10.007
[18]	P. R. Rinaldi, E. A. Dari, M. J. Vénere, A. Clausse, A lattice-Boltzmann solver for 3D fluid simulation on GPU, Simul. Modell. Pract. Theory, 25 (2012), 163−171. https://doi.org/10.1016/j.simpat.2012.03.004 doi: 10.1016/j.simpat.2012.03.004
[19]	Z. Wang, Y. Zhao, A. P. Sawchuck, M. C. Dalsing, H. Yu, GPU acceleration of Volumetric Lattice Boltzmann Method for patient-specific computational hemodynamics, Comput. Fluids, 115 (2015), 192−200. https://doi.org/10.1016/j.compfluid.2015.04.004 doi: 10.1016/j.compfluid.2015.04.004
[20]	A. Xu, L. Shi, T. S. Zhao, Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management, Int. J. Heat Mass Transfer, 109 (2017), 577−588. https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.032 doi: 10.1016/j.ijheatmasstransfer.2017.02.032
[21]	B. Ma, L. Shi, C. Huang, Q. Xu, Effects of nanoscale pore structure on permeability and relative permeability loss analyzed by GPU enhanced Multiple-Relaxation-Time LBM, Int. J. Heat Mass Transfer, 117 (2018), 584−594. https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.136 doi: 10.1016/j.ijheatmasstransfer.2017.09.136
[22]	Á, Salinas, C. Torres, O. Ayala, A fast and efficient integration of boundary conditions into a unified CUDA Kernel for a shallow water solver lattice Boltzmann method, Comput. Phys. Commun., 249 (2020). https://doi.org/10.1016/j.cpc.2019.107009 doi: 10.1016/j.cpc.2019.107009
[23]	J. J. Heys, V. H. Barocas, M. J. Taravella, Modeling passive mechanical interaction between aqueous humor and iris, J. Biomech. Eng., 123 (2001), 540−547. https://doi.org/10.1115/1.1411972 doi: 10.1115/1.1411972
[24]	O. Abouali, A. Modareszadeh, A. Ghaffarieh, J. Tu, Investigation of saccadic eye movement effects on the fluid dynamic in the anterior chamber, J. Biomech. Eng., 134 (2012). https://doi.org/10.1115/1.4005762 doi: 10.1115/1.4005762
[25]	C. Lin, F. Yuan, Numerical simulations of ethacrynic acid transport from precorneal region to trabecular meshwork, Ann. Biomed. Eng., 38 (2010), 935−944. https://doi.org/10.1007/s10439-010-9947-z doi: 10.1007/s10439-010-9947-z
[26]	N. Heussner, L. Holl, T. Nowak, T. Beuth, M. S. Spitzer, W. Stork, Prediction of temperature and damage in an irradiated human eye—Utilization of a detailed computer model which includes a vectorial blood stream in the choroid, Comput. Biol. Med., 51 (2014), 35−43. https://doi.org/10.1016/j.compbiomed.2014.04.021 doi: 10.1016/j.compbiomed.2014.04.021
[27]	Z. Guo, C. Zheng, B. Shi, Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin. Phys., 11 (2002), 366. https://doi.org/10.1088/1009-1963/11/4/310 doi: 10.1088/1009-1963/11/4/310
[28]	M. Astorino, J. B. Sagredo, A. Quarteroni, A modular lattice boltzmann solver for GPU computing processors, SeMA J., 59 (2013), 53−78. https://doi.org/10.1007/BF03322610 doi: 10.1007/BF03322610
[29]	C. Nita, L. M. Itu, C. Suciu, GPU accelerated blood flow computation using the Lattice Boltzmann method, in 2013 IEEE High Performance Extreme Computing Conference (HPEC), IEEE, 2013. https://doi.org/10.1109/HPEC.2013.6670324
[30]	A. G. Shet, S. H. Sorathiya, S. Krithivasan, A. M. Deshpande, B. Kaul, S. D. Sherlekar, et al., Data structure and movement for lattice-based simulations, Phys. Rev. E, 88 (2013), 013314. https://doi.org/10.1103/PhysRevE.88.013314 doi: 10.1103/PhysRevE.88.013314
[31]	M. J. Mawson, A. J. Revell, Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs, Comput. Phys. Commun., 185 (2014), 2566−2574. https://doi.org/10.1016/j.cpc.2014.06.003 doi: 10.1016/j.cpc.2014.06.003
[32]	C. Huang, B. Shi, Z. Guo, Z. Chai, Multi-GPU based Lattice Boltzmann method for hemodynamic simulation in patient-specific cerebral aneurysm, Commun. Comput. Phys., 17 (2015), 960−974. https://doi.org/10.4208/cicp.2014.m342 doi: 10.4208/cicp.2014.m342
[33]	A. Karampatzakis, T. Samaras, Numerical model of heat transfer in the human eye with consideration of fluid dynamics of the aqueous humour, Phys. Med. Biol., 55 (2010), 5653−5665. https://doi.org/10.1088/0031-9155/55/19/003 doi: 10.1088/0031-9155/55/19/003
[34]	Y. Zhao, B. Chen, D. Li, Optimization of surgical protocol for laser iridotomy based on the numerical simulation of aqueous flow, Math. Biosci. Eng., 16 (2019), 7405−7420. https://doi.org/10.3934/mbe.2019370 doi: 10.3934/mbe.2019370

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