Anatomically porous-media heat transfer modeling for multi-organ supercooling perfusion cryopreservation

Zaize Liu , Xiaoshuai Wang , Jie Zhang , Sirui Yang , Huili Zhang , Zixin Li , Yan Wang , Fan Yang , Yi Hou , Minghui Guo , Wei Rao

Thermo-X ›› 2026, Vol. 2 ›› Issue (2) : 202610

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Thermo-X ›› 2026, Vol. 2 ›› Issue (2) :202610 DOI: 10.70401/tx.2026.0018
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Anatomically porous-media heat transfer modeling for multi-organ supercooling perfusion cryopreservation
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Abstract

Supercooling perfusion extends organ-preservation time by maintaining grafts ice-free below 0 °C, but thermal non-uniformity and limited intra-organ temperature observability hinder protocol design, especially at large-organ scales. We developed an anatomically based thermo-fluidic modeling framework for supercooled perfusion of the liver, heart, and kidney in a recirculating multi-organ configuration and validated the model experimentally. Three-dimensional organ geometries from the BodyParts3D repository were combined with a porous-media tissue representation and realistic perfusion boundary conditions to resolve transient intra-parenchymal temperature fields. A self-developed variable-frequency supercooled machine perfusion (MP) platform was used to measure temperatures in porcine livers, hearts, and kidneys using multiple thermocouples placed at anatomically corresponding locations. Simulated temperature trajectories agreed with measurements across organs, with mean absolute errors of 0.24 °C for the liver, 2.63 °C for the heart, and 0.4 °C for the kidney, and reproduced initial cooling followed by progressive approach to the perfusate temperature and stabilization. Spatial temperature maps captured organ-specific gradients consistent with convective heat extraction by perfusate delivery and conductive transport within tissue. Using the validated model, we performed parametric sweeps of the inlet perfusion parameter, perfusate thermophysical properties, and external convective heat-transfer coefficient to quantify their effects on cooling rate and temperature uniformity. Based on quantitative metrics, these parameters were found to influence cooling rate and intra-organ temperature uniformity to different degrees, while the magnitude of improvement differed among organs due to size and vascular characteristics. This study provides a validated, under the tested conditions, tool to predict intra-organ temperature evolution and a guide for thermodynamically optimizing supercooled MP protocols in multi-organ preservation.

Keywords

Supercooled machine perfusion / organ preservation / heat transfer / porous media model / intra-organ temperature field

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Zaize Liu, Xiaoshuai Wang, Jie Zhang, Sirui Yang, Huili Zhang, Zixin Li, Yan Wang, Fan Yang, Yi Hou, Minghui Guo, Wei Rao. Anatomically porous-media heat transfer modeling for multi-organ supercooling perfusion cryopreservation. Thermo-X, 2026, 2 (2) : 202610 DOI:10.70401/tx.2026.0018

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References

[1]

Atfeh J, Guerre P, Sebbag L, Pozzi M, Huot L. Economic burden and healthcare trajectories of patients awaiting heart transplantation in a French tertiary center. Transpl Int. 2025; 38:13703.

[2]

Tonelli M, Wiebe N, Knoll G, Bello A, Browne S, Jadhav D, et al. Systematic review: Kidney transplantation compared with dialysis in clinically relevant outcomes. Am J Transplant. 2011; 11(10):2093-2109.

[3]

Girish V, Mousa OY. Liver transplantation. In: StatPearls. Treasure Island: StatPearls Publishing; 2026.

[4]

Tan SY, Merchant J. Joseph Murray (1919-2012): First transplant surgeon. Singapore Med J. 2019; 60(4):162-163.

[5]

Dery KJ, Yao S, Cheng B, Kupiec-Weglinski JW. New therapeutic concepts against ischemia-reperfusion injury in organ transplantation. Expert Rev Clin Immunol. 2023; 19(10):1205-1224.

[6]

Hess NR, Ziegler LA, Kaczorowski DJ. Heart donation and preservation: Historical perspectives, current technologies, and future directions. J Clin Med. 2022; 11(19):5762.

[7]

DeFilippis EM, Khush KK, Farr MA, Fiedler A, Kilic A, Givertz MM. Evolving characteristics of heart transplantation donors and recipients: JACC Focus Seminar. J Am Coll Cardiol. 2022; 79(11):1108-1123.

[8]

Jing L, Yao L, Zhao M, Peng LP, Liu M. Organ preservation: From the past to the future. Acta Pharmacol Sin. 2018; 39(5):845-857.

[9]

Bruinsma BG, Uygun K. Subzero organ preservation: The dawn of a new ice age? Curr Opin Organ Transplant. 2017; 22(3):281-286.

[10]

de Vries RJ, Tessier SN, Banik PD, Nagpal S, Cronin SEJ, Ozer S, et al. Subzero non-frozen preservation of human livers in the supercooled state. Nat Protoc. 2020; 15(6):2024-2040.

[11]

Durán M, Calleja R, Hann A, Clarke G, Ciria R, Nutu A, et al. Machine perfusion and the prevention of ischemic type biliary lesions following liver transplant: What is the evidence? World J Gastroenterol. 2023; 29(20):3066-3083.

[12]

Li J, Wang W, Li C, Kuang L, Huang Z, Chen X, et al. Anti-icing organogel enables quasi-homogeneous supercooling preservation of mouse hearts. Adv Sci. 2025; 12(37):e06968.

[13]

de Vries RJ, Tessier SN, Banik PD, Nagpal S, Cronin SEJ, Ozer S, et al. Supercooling extends preservation time of human livers. Nat Biotechnol. 2019; 37(10):1131-1136.

[14]

Filz von Reiterdank I, Dinicu AT, Rosales I, Cetrulo CL, Coert JH, et al.Mink van der Molen AB, Supercooling preservation of vascularized composite allografts through CPA optimization, thermal tracking, and stepwise loading techniques. Sci Rep. 2024; 14(1):22339.

[15]

Molema G, Aird WC. Vascular heterogeneity in the kidney. Semin Nephrol. 2012; 32(2):145-155.

[16]

Abdoli A, Dulikravich GS, Bajaj C, Stowe DF, Jahania MS. Human heart conjugate cooling simulation: Unsteady thermo-fluid-stress analysis. Int J Numer Method Biomed Eng. 2014; 30(11):1372-1386.

[17]

Wang Y, Zhu K, Liang F, Zhang Y. Thermal-structure coupling simulation during ex-vivo hypothermic perfusion of kidney. Appl Therm Eng. 2014; 67:250-257.

[18]

Emerson D, Rabin Y, Kara LB. A simplified computational liver perfusion model, with applications to organ preservation. Sci Rep. 2025; 15(1):2178.

[19]

Berendsen TA, Bruinsma BG, Puts CF, Saeidi N, Usta OB, Uygun BE, et al. Supercooling enables long-term transplantation survival following 4 days of liver preservation. Nat Med. 2014; 20(7):790-793.

[20]

Ozgur OS, Taggart M, Mojoudi M, Pendexter C, Filz von Reiterdank I, Kharga A, et al. Optimized partial freezing protocol enables 10-day storage of rat livers. Sci Rep. 2024; 14(1):25260.

[21]

Quader M, Torrado JF, Mangino MJ, Toldo S. Temperature and flow rate limit the optimal ex-vivo perfusion of the heart-an experimental study. J Cardiothorac Surg. 2020; 15:180.

[22]

Deng W, Tsubota KI. Numerical simulation of the vascular structure dependence of blood flow in the kidney. Med Eng Phys. 2022; 104(1):103809.

[23]

Ehrlich LE, Fahy GM, Wowk BG, Malen JA, Rabin Y. Thermal analyses of a human kidney and a rabbit kidney during cryopreservation by vitrification. J Biomech Eng. 2018; 140(1):0110051-0110058.

[24]

Nguyen MC, Li X, Linares N, Jadlowiec C, Moss A, Reddy KS, et al. Ex-situ machine perfusion in clinical liver transplantation: Current practices and future directions. Liver Transpl. 2025; 31(4):531-544.

[25]

de Vries Y, Brüggenwirth IMA, Karangwa SA, von Meijenfeldt FA, van Leeuwen OB, Burlage LC, et al. Dual versus single oxygenated hypothermic machine perfusion of porcine livers: Impact on hepatobiliary and endothelial cell injury. Transplant Direct. 2021; 7(9):e741.

[26]

Elliott GD, Wang S, Fuller BJ. Cryoprotectants: A review of the actions and applications of cryoprotective solutes that modulate cell recovery from ultra-low temperatures. Cryobiology. 2017; 76:74-91.

[27]

Varble NA, Bakhutashvili I, Reed SL, Delgado J, Tokoutsi Z, Frackowiak B, et al. Morphometric characterization and temporal temperature measurements during hepatic microwave ablation in swine. PLoS One. 2023; 18(8):e0289674.

[28]

Lee JM, Han JK, Lee JY, Kim SH, Choi JY, Lee MW, et al. Hepatic radiofrequency ablation using multiple probes: Ex vivo and in vivo comparative studies of monopolar versus multipolar modes. Korean J Radiol. 2006; 7(2):106-117.

[29]

Obara H, Matsuno N, Shigeta T, Enosawa S, Hirano T, Mizunuma H. Rewarming machine perfusion system for liver transplantation. J Med Devices. 2013; 7(4):041011.

[30]

Swift LM, Jaimes R 3rd, McCullough D, Burke M, Reilly M, Maeda T, et al. Optocardiography and electrophysiology studies of ex vivo langendorff-perfused hearts. J Vis Exp. 2019; 153:60472.

[31]

Marom R, Dau JJ, Ghani KR, Hall TL, Roberts WW. Assessing renal tissue temperature changes and perfusion effects during laser activation in an in vivo porcine model. World J Urol. 2024; 42(1):197.

[32]

Mitsuhashi N, Fujieda K, Tamura T, Kawamoto S, Takagi T, Okubo K. BodyParts3D: 3D structure database for anatomical concepts. Nucleic Acids Res. 2009; 37:D782-D785.

[33]

Nakayama A, Kuwahara F. A general bioheat transfer model based on the theory of porous media. Int J Heat Mass Transf. 2008; 51:3190-3199.

[34]

Khaled ARA, Vafai K. The role of porous media in modeling flow and heat transfer in biological tissues. Int J Heat Mass Transf. 2003; 46(26):4989-5003.

[35]

Iasiello M, Andreozzi A, Bianco N, Vafai K. Effects of pulsed radiofrequency source on cardiac ablation. Bioengineering. 2023; 10(2):227.

[36]

Sun W, Dong X, Wang X, Yuan P, Gong M. Numerical thermal analysis and optimization of vitrification cooling strategies for porcine heart cryopreservation. Cryobiology. 2026; 122:105570.

[37]

Andreozzi A, Brunese L, Iasiello M, Tucci C, Peter Vanoli G. Bioheat transfer in a spherical biological tissue: A comparison among various models. J Phys Conf Ser. 2019; 1224(1):012001.

[38]

Solanki PK, Bischof JC, Rabin Y. Thermo-mechanical stress analysis of cryopreservation in cryobags and the potential benefit of nanowarming. Cryobiology. 2017; 76:129-139.

[39]

Manuchehrabadi N, Shi M, Roy P, Han Z, Qiu J, Xu F, et al. Ultrarapid inductive rewarming of vitrified biomaterials with thin metal forms. Ann Biomed Eng. 2018; 46(11):1857-1869.

[40]

Hasgall PA, Di Gennaro F, Baumgartner C, Neufeld E, Lloyd B, Gosselin MC, et al. Tissue Properties Database V5.0 [Internet]. Zurich: IT'IS Foundation; 2025. Available from: https://itis.swiss/virtual-population/tissue-properties/downloads/database-v5-0

[41]

Qi X, Hatami S, Bozso S, Buchko M, Forgie KA, Olafson C, et al. The evaluation of constant coronary artery flow versus constant coronary perfusion pressure during normothermic ex situ heart perfusion. J Heart Lung Transplant. 2022; 41(12):1738-1750.

[42]

Brüggenwirth IMA, Lantinga VA, Lascaris B, Thorne AM, Meerdink M, de Kleine RH, et al. Prolonged hypothermic machine perfusion enables daytime liver transplantation-an IDEAL stage 2 prospective clinical trial. eClinicalMedicine. 2024; 68:102411.

[43]

Eça L, Hoekstra M. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. J Comput Phys. 2014; 262:104-130.

[44]

O’Connor J, Laizet S, Wynn A, Edeling W, Coveney PV. Quantifying uncertainties in direct numerical simulations of a turbulent channel flow. Comput Fluids. 2024; 268:106108.

[45]

Tueni N, Allain JM, Genet M. On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis. J Mech Behav Biomed Mater. 2023; 138:105600.

[46]

Valvano JW, Cochran JR, Diller KR. Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors. Int J Thermophys. 1985; 6(3):301-311.

[47]

Mohammadi A, Bianchi L, Asadi S, Saccomandi P. Measurement of ex vivo liver, brain and pancreas thermal properties as function of temperature. Sensors. 2021; 21(12):4236.

[48]

Zhan L, Han Z, Shao Q, Etheridge ML, Hays T, Bischof JC. Rapid joule heating improves vitrification based cryopreservation. Nat Commun. 2022; 13(1):6017.

[49]

Han Z, Bischof JC. Critical cooling and warming rates as a function of CPA concentration. CryoLetters. 2020; 41(4):185-193.

[50]

Solanki PK, Rabin Y. Thermomechanical stress analysis of rabbit kidney and human kidney during cryopreservation by vitrification with the application of radiofrequency heating. Cryobiology. 2021; 100:180-192.

[51]

Sun X. Development of an improved thermal model of the human body and an experimental investigation of heat transfer from a moving cylinder [dissertation]. Manhattan: Kansas State University; 2012. Available from: https://www.proquest.com/openview

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