lable at ScienceDirect

Applied Thermal Engineering 67 (2014) 250e257

Contents lists avai

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Thermal-structure coupling simulation during ex-vivo hypothermicperfusion of kidney

Yabo Wang a,c, Kai Zhu b,c,*, Fei Liang b, Yamin Zhang d

a School of Environmental Science and Engineering, Tianjin University, Tianjin 300072, Chinab Tianjin Key Laboratory of Refrigeration Technology, Tianjin University of Commerce, Tianjin, ChinacKey Laboratory of Efficient Utilization of Low and Medium Grade Energy, MOE, Tianjin University, Tianjin 300072, Chinad Tianjin First Center Hospital, Tianjin, China

h i g h l i g h t s

� The anatomical CAD model of vessels was developed according to the vascular cast.� The continuous flow was formed by treating capillaries and tissue as porous media.� Thermal-structure simulation helps clinicians to better predict flushing process.� Larger perfusion rates could cause kidney injury due to large distortion.� The perfusion rates should be strictly set to achieve the optimal preservation effect.

a r t i c l e i n f o

Article history:Received 30 January 2014Accepted 16 March 2014Available online 25 March 2014

Keywords:Hypothermic perfusionKidneyTemperature fieldThermal stressDeformation

* Corresponding author. Tianjin Key LaboratoryTianjin University of Commerce, Tianjin, China.

E-mail address: zhukai210@tju.edu.cn (K. Zhu).

http://dx.doi.org/10.1016/j.applthermaleng.2014.03.021359-4311/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

In this paper, the temperature variation and consequent thermal stress and deformation during hypo-thermic perfusion are numerically investigated. Hypothermic perfusion is the first step of preservationtechniques that washes out of the vascular system and provides the supply of substrates and cools thekidney to the preservation temperature. A three-dimensional (3D) finite element analysis using theanatomical CAD model of kidney is developed to accurately simulate the hypothermic perfusion process.Based on the temperature field, the time evolution of thermal stress and deformation distribution areobtained. In addition, we analyze the effect on the thermal stress and deformationwhich cannot be easilyacquired through clinical experiments. The results indicate that the thermal effects of large blood vesselscould remarkably affect the temperature, thermal stress and deformation distributions. Increasing theperfusion rate could enlarge the thermal deformation, which causes the injury to the kidney. Theseresults provide a guideline to the basic and applied research for the thermal effect on the hypothermicperfusion of kidney.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Organ transplantation has been one of the most significant ad-vances in medicine in the latter half of the 20th century and re-mains in many cases the only effective therapy for end-stage organfailure [1]. Hypothermia is employed for organ preservation toreduce the kinetics of metabolic activities. Cooling is induced by abrief flush with a chilled preservation solution after the organ isremoved from the donor. Kazuhiro et al. [2] pointed out that theinitial flush is equally as important as the storage itself. The

of Refrigeration Technology,

9

improvement of this process could minimize preservation injuryand supply the organ of high quality and efficacy [3,4]. Until now,most studies about hypothermia perfusion are conducted by thebiologists or clinicians [5,6]. Therefore, the demand for a detailedunderstanding of the temperature history of the organ in order tomonitor the extent of cryopreservation is compelling. In the recent,kidney transplantation is one of the most common and successfulorgan transplantation [7]. In this paper, we focus on the initialflushing of kidney before storage.

During the process of hypothermic perfusion (initial flushing),the chilled preservation solution is infused through renal artery andflows out of the kidney through the renal vein after passing througha series of capillary vessels. Large blood vessels can produce steeptemperature gradients in biological tissue, resulting in uneven

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257 251

thermal contraction of different region of tissue and correspondingthermal stress. The severe thermal deformation may cause thevulnerable cell or component losing the function. In recent years,many researchers have done numerical simulation and experi-mental analysis on thermal stress and fracture problems in freezingpreservation of organs [8e11]. However, the biomechanical effectduring hypothermic perfusion has received little attention up tonow.

This paper is dedicated to present a comprehensive investiga-tion on the thermal effects on the temperature profile and thermalstress during hypothermic perfusion using a series of thermal-structure simulations. In the simulation of temperature field, theconfiguration of large blood vessels and tissues are preciselydetermined; therefore, the heat and mass transfer between largeblood vessels and tissues could be well simulated compared tosimplified structures [12e16]. The different perfusion rate which isone of the factors effecting on initial flushing is analyzed. This studyultimately aims to provide information to clinicians for betterpredicting hypothermic perfusion process and making more reli-able treatment decisions.

2. Methods of simulation

2.1. Physical model and mesh generation

The kidney is shaped much like a bean. The renal vessel tree is acomplex vascular net irrigating the renal tissue. Accurate bio-thermal modeling requires accurate modeling of tissue andvascular anatomy. The vascular cast was got by experimentalmethod [17] as shown in Fig. 1. The blue ones (in the web version)represent the veins and the red ones represent the arteries. We usethe 3D scanner (Shining3D, China) and Geomagic Studio 10.0software (Geomagic, North Carolina, USA) to reconstruct the ar-teries, veins and tissue respectively [18e20]. Taking the arteries asexample, we firstly obtain the image of arteries from 3D scanner,which is then input to the Geomagic Studio 10.0 software to switchto 3D model. All parts of the reconstructed subjects are saved asIGES format for importing into pro/E4.0. The 3D geometric model ofporcine kidney comprising tissue, large arterial and venous vesselsare shown in Fig. 2. After Boolean operation and assembly, themodel is switched to ICEM CFD 13.0(ANSYS, Inc., Canonsburg, PA,USA) for computational meshing. Unstructured tetrahedral mesh-ing scheme is used. We first generate meshes for artery and veinand then we generate meshes for tissue domains to ensure highquality of mesh in each component. The surface meshes from thefluid domain are used in the solid domain to enable a better

Fig. 1. Renal vascular cast.

interpolation of fluidesolid interfaces. The number of total tetra-hedral elements is 2,692,000. For arteries, veins and tissue domain,the number of elements for each component of kidney are1,009,367, 455,782 and 1,226,851.

After creating meshes for each component, the governingequations together with boundary conditions are solved usingAnsys CFX 13.0(ANSYS, Inc., Canonsburg, PA, USA), which is acommercially available software package and extensively utilizedto address a variety of practical engineering problems nowadays.The flow and temperature analysis are solved according to SIMPLEand second order upwind algorithms. The first order implicit timediscretization scheme is used for time evolution. All simulationsadopt parallel model and run on the DAWNING workstation with30 core CPUs and eight memories (1 GB each).

2.2. Thermal modeling

A hypothermic perfusion experiment was conducted accordingto clinic procedure. The boundary and initial conditions were setaccording to this experiment. The details of this experiment areshown in Ref. [21]. During the hypothermic perfusion, the kidney isflushed at ambient room temperature with the solution precooledto þ1 �C and the average perfusion rate was 50 ml/min (0.05 m/s).The coolant fluid enters the kidneys through the renal artery andleaves the kidneys through the renal vein after passing through aseries of capillaries. We focus on the temperature changes duringthe hypothermic perfusion process, so the physiological salinerather than expensive organ preservation solution is used in theexperiment.

2.2.1. Fluid domain modelThe metabolic heat generation is not considered in the simula-

tion, for cooling could reduce the metabolic activities effectively.The medium is continuous, and the governing equations consist ofcontinuity, momentum and energy conservation equations.

Continuity equation:

v

vxiðruiÞ ¼ 0 (1)

Momentum equation:

v

vtðruiÞ þ

v

vxj

�rujui

� ¼ �vPvxi

þ v

vxj

m

vuivxj

!!(2)

Energy equation:

v

vtðrTÞ þ v

vxiðruiTÞ ¼ v

vxi

�kcp

�vTvxi

��(3)

The uniform velocity profile is adopted at the entrance of artery.The coolant is physiological saline whose temperature is 1 �C andvelocity is 0.5 m/s. The maximum Reynolds numbers of perfusionmodel, based on the inlet diameter which is 245 and thus the flowwas treated as laminar. The outlets of artery and the inlets of veinembedded in the kidney are set as interface in the CFX. In thesimulation, the initial temperature of the biological tissue andblood is 37 �C. On the whole, the physiological saline properties arealmost identical to that of water which is assumed as incom-pressible and Newtonian flow with a constant density of 1000 kg/m3 and a constant dynamic viscosity of 1.7921 � 10�3 Pa s.

2.2.2. Porous modelKidney is composed of more capillary blood vessels with di-

ameters ranging from 10 to 300 mm. The capillary blood vessels aredifficult to reconstruct.We treat thewhole extravascular region as a

Table 1Mechanical parameters of kidney.

Modulus of elasticity Poisson’s ratio Thermal expansion coefficient

0.43 (MPa) 0.33 2.46 � 10�5 (1/�C)

Fig. 2. The physical model established by Proe.

Fig. 3. The streamline of coolant in the kidney.

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257252

fluid-saturated porous medium, through which the coolant in-filtrates. Taking the tissue as porous media could establish thecontinuous transport channel in the kidney in the simulation. Theporous media approach involves the application of the principle ofheat transfer and fluid mechanics in a fluid-saturated perfusedtissue to obtain a model of equation that will govern heat transferand fluid flow in a biological system (living tissue). It is assumedthat the tissue is isotropic. The porosity (volume fraction of thevascular space) is 0.2 [22,23] and the thermal conductivity is 0.5W/(m K) [24].

As the isolated kidney is exposed in the air during coolantperfusion, the boundary condition for kidney surface adopts theconvective boundary condition:

�kvTsvn

¼ haðTs � TaÞ (4)

where Ts is the renal surface temperature ha ¼ 10 W/(m2 K), andTa ¼ 26 �C are the convective heat transfer coefficient and tem-perature of air in ambient.

2.3. Coupled thermo-structure analysis

In this study, we assume that the bio-materials have elasticmechanical properties and are isotropic in nature. Thermal strain isan elastic strain that results from expansion with increasing tem-perature, or contraction with decreasing temperature. When tem-perature changes from T0 to T, the thermal strain (ε) of the elementdue to the temperature change is:

ε ¼ aðT � T0Þ ¼ aðDTÞ (5)

where a is the thermal expansion coefficient. The initial tempera-ture of kidney (T0) is 37 �C. The elastic deformation is satisfied byHooke’s law; hence the thermal stress (s) can be written as:

s ¼ EaðDTÞ ¼ Eε (6)

where E is Young’ modulus.The temperature and stress distributions caused by hypother-

mic perfusion are three-dimensional and transient. Ansys Work-bench provides the capability of performing indirect sequentiallycoupled thermo-structure analysis for both heat and stress analysis.In this study, the thermal and structural analysis are performedusing Ansys CFX and Ansys Mechanical through Workbench(ANSYS, Inc., Canonsburg, PA, USA). A transient thermal analysis isperformed first to obtain the global temperature history generated

during the cold perfusion, which is then input as a body load for themechanical analysis to determine the stress distribution anddeformation [25e29]. The modulus of elasticity, Poisson’s ratio andcoefficient of thermal expansion respectively are obtained by ex-periments [30] as shown in Table 1.

3. Result and discussion

The cold perfusion by introducing chilled solutions in sufficientvolumes (clinically this requires in the region of 200e400 ml ofchilled solutions) into the major vascular channels canwashout theblood and achieve moderate cooling. The coupled calculationsprovide a complete set of data including temperature and me-chanical data on the tissue during the whole hypothermic perfu-sion process.

3.1. Temperature field of kidney

As mentioned above, a hypothermic perfusion experiment wasconducted by the clinician. The hypothermic perfusion lasted 300 sand the infrared images of kidney were taken at every 15 s duringthe hypothermic perfusion process as shown in Fig. 4A.

The CFD simulation focuses on the three domains: arteries,tissue, and veins, which are modeled as a conjugate heat transferproblem. During the perfusion process, coolant fluid enters thekidneys through the renal artery and leaves the kidneys throughthe renal vein after passing through a series of capillaries. Fig. 3 isthe streamline of the coolant fluid which shows this flowing pro-cess. Fig. 4B shows the variation in the temperature versus timeduring the total time simulation of perfusion process for a kidney. Itis assumed that the temperature distribution on the whole kidneyis uniform at 37 �C when the perfusion begins. The kidney tem-perature is decreased by flushing with the chilled fluid which cantake away the heat. The minimal temperature is localized aroundthe artery entrance. The temperature continues to decline withperfusion and the irregular configuration of renal vessels leads toan uneven temperature distribution on the kidney surface. We canconclude that the configuration of vessels is an essential factor inthe study of biological heat transfer.

Fig. 4. Surface temperature field obtained from numerical simulation and infraredimage.

Fig. 5. Total distortion distribution at different time.

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257 253

Table 2 gives the temperature range of surface temperature atdifferent moments. The difference between the maximum andminimum surface temperature of the kidney at 20, 30, 60, 120, 180,240 and 300 s is 17.6, 15.2, 9.9, 4.6, 2.8, 2.1 and 1.8 �C, respectively. Itis obvious that the temperature difference decreases as time in-creases. That is to say, the temperature gradient is larger at thebeginning and the temperature achieves uniform temperature ofw4 �C at the end of perfusion. The comparison between thesimulation results and the infrared thermal images shows that thetemperature distribution on kidney surface is roughly the sameduring the cooling process, which could ensure the accuracy ofsubsequent calculations.

3.2. Thermal deformation of kidney

Fig. 5 gives the distribution of the total distortion in the wholekidney for various moments of simulation. For these figures, thescale of values of the deformation varies from 0 to 1.39 mm. The

Table 2Temperature range at different time during cooling.

20 s 30 s 60 s

Temp. range (�C) 30.8e13.2 27.0e11.8 18.6e8.7Temp. different (�C) 17.6 15.2 9.9

decrease in temperature causes an enlargement of deformation onthe kidney. The value of the maximum displacement recordedduring this simulation is at the moment t ¼ 300 s, which corre-sponds to the time of the end of the perfusion. At the beginning ofthe perfusion, the deformation of external surface presents stronginhomogeneity. After a period of time, the central part of kidneyshows the uniform distribution, gradually. Indeed, during aperfusion, the temperature distribution depends almost entirelyon the structure of vessels; this complicated structure of vessels

120 s 180 s 240 s 300 s

10.3e5.7 7.4e4.6 6.3e4.2 5.9e4.14.6 2.8 2.1 1.8

Fig. 6. Von Mises stress distribution of kidney.

Fig. 7. Sketch map of cross section and longitudinal section.

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257254

will generate an asymmetry temperature distribution of the outersurface of kidney which will cause the uneven deformation ofkidney. The decline of temperature intensifies the tissue contrac-tion. With the temperature becoming equilibrium gradually, thedeformation of kidney reaches the maximum value and keepsconstant.

Fig. 8. The coupling result of cross-section when perfusing for 240 s.

Fig. 9. The coupling result of longitudinal section when perfusing for 240 s.

Fig. 10. Von Mises stress and thermal deformation of cross-section.

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257 255

3.3. Von Mises stress distribution

Fig. 6 presents the distribution of the constraint equivalent ofVonMises stress to various moments of simulation, and the scale ofvalues varies from 0 KPa to 12.88 KPa. The surface thermal stress isuniform and of theminimumvalue at anymoments. This is becausethe temperature gradient of the outer surface is less than innerkidney.

The renal tissue behaves very soft when the stress is lower than1.16 MPa whereas after that the tissue suddenly stiffens [31]. Themaximum value recorded during this simulation of the thermo-mechanical coupling is far less than the extreme pressure to keepthe soft structure. Although themaximumvalue of VonMises stressis much smaller than the stiffen strength of kidney in contractionprocess, the phenomenon of non-uniform thermal stress in thekidney might introduce unfavorable cell injury.

Fig. 11. Von Mises stress and thermal deformation of longitudinal section.

3.4. The coupling result of internal kidney

The cross-section and longitudinal section were chosen asresearch object and shown in Fig. 7. Large blood vessels buriedwithin the kidney through the contribution to heat transfer bycryoprotectant flow could lead to the significant temperaturenonuniformity around the vessel and steepy temperature gradientas shown in Figs. 8A and 9A. Due to the nonuniform cooling of thekidney, the maximum thermal stresses are localized around the

vessels. It is found that the Von Mises stress decreases graduallyalong the radial direction of vessels. The tissue away from thevessels produce less thermal stress due to the seepage flow ofporous media leading to more uniform temperature distribution.The inner distortions aremore dependent on the vessel structure asshown in Figs. 8C and 9C. The very outer edge of the kidney showsthemaximum thermal deformation, especially for the left and rightedge of the kidney in Fig. 9C. The cooling causes the contraction ofthe tissue. The displacement of internal tissue is constrained by thetraction of surrounding tissue, while tensile stress imposed on theouter tissue all come from internal of kidney. The thermal defor-mation of external surface is the comprehensive reflection of in-ternal deformation of kidney during perfusion. Each of the kidneysis about 10 cm long and 5.5 cmwide. So the maximum deformationoccurs in the longitudinal direction. The left and right tip of thekidney should deform seriously.

The two curves in Fig. 10 are the average value of Von Misesstress and deformationwith time of cross-sectionwhile Fig.11 is forthe longitudinal section. Fig. 10 shows that the thermal stress anddeformation keep rapidly increasing at the beginning 60 s of theperfusion and then the values increase slowly. From the tempera-ture simulation, the temperature changes apparently at the initialstage of perfusion. The temperature variation at 20 s is about 17.6 �Cfrom 30.8 �C to 13.2 �C while this temperature range decreases to

Fig. 12. Comparison of average Von Mises stress and deformation of cross-section ofdifferent perfusion rate.

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257256

about 1 �C when the perfusion lasted for 300 s as shown in Table 2.The steepy temperature gradient occurred at the initial stage. Thedisappearance of the temperature gradient will not generate ther-mal stresses and consequent deformation. Fig. 11 shows the similarresult that the thermal stress and deformation increase with time.From the comparison between Figs. 10 and 11, the Von Mises stressand deformation of the longitudinal section are always greater thanthat of the cross section. The maximum thermal stress of cross-section after perfusion is 4.8 KPa lower than that of longitudinalsection (7.7 KPa). From Figs. 8 and 9, the area of vessel sections inthe longitudinal section is larger than that in the cross-section. Andthe more complicated vessel structure in the longitudinal sectionwill result in more steepy temperature gradient and consequentlarger thermal stress and deformation.

Fig. 13. Comparison of average Von Mises stress and deformation of longitudinalsection of different perfusion rate.

3.5. The effect of different perfusion rate

Perfusion rate could influence the thermal effect of large bloodvessels. In order to investigate its impact, another case is simulatedunder the same conditions. The perfusion rate increases to 2 fold ofthe original one. The entrance velocity increases to 100 ml/min

(0.1 m/s). It is shown in Figs. 12 and 13 that the elevation ofperfusion rate increases the magnitude of displacement of kidneyand effective stress. The 1-fold increase of perfusion rate makesabout 0.6 KPa increase of thermal stress in cross section and1.32 KPa increase in the longitudinal section. The average de-formations increase in the cross and longitudinal section are0.10 mm and 0.17 mm respectively. The reason is that with the flowvelocity of coolant increasing, the cooling rate in tissue becomeslarger, which enlarge the temperature gradient in the tissues. Moreblood vessels section in the longitudinal section makes larger in-crease of thermal stress and deformation. Comparing the twocurves in Figs. 12 and 13, the effective thermal stress and defor-mation almost reach equilibrium when flushing with higher ve-locity after flushing for 200 s while the values still slowly increasefor original condition. Because it costs less time to reach uniformtemperature distribution when flushing with higher velocity.

Jacobsen et al. [4] reported that a highly deleterious effect onpost-transplant function of rapid cooling of rabbit kidney beforestorage. They attribute this to patchy necrosis of proximal tubularcells as well as considerable amounts of cellular debris in tubularlumina. The proximal tubular occupies the cortical labyrinth, where

Y. Wang et al. / Applied Thermal Engineering 67 (2014) 250e257 257

the larger deformation takes place according to thermal structuresimulation. We conclude that the rapid cooling during washout ofkidney grafts before cold storage is undesirable as such coolingproduces a larger magnitude of displacement and consequentnonfunctioning transplants. VanWagensveld et al. [32] pointed outthat flushing at 37 �C following cold storage could attenuate thereperfusion injury in preserved rat livers. Flushing at 37 �C couldavoid the generation of temperature gradient. Thus, this is anotherevidence to illustrate that kidney injury occurs due to the tem-perature gradient and consequent deformation. In another view,using lower flow velocity during the initial flush may lead toirregular distribution of the solution and incomplete flushing ofblood components from vascular beds [33]. Thus, there exists anoptimal perfusion rate. The coupling calculation of the temperaturefield and thermal stress distribution provide a platform to optimizethe perfusion protocol by simulation method.

4. Conclusions

This paper presents a comprehensive investigation on 3-D tissuetemperature profile of kidney during hypothermia perfusion andconsequent thermal stress and deformation based on a thermalstructure coupling calculation for an anatomical model of kidney. Inthe simulation of temperature field, the large blood vessels arereconstructed according to anatomical structure and the micro-capillaries and tissue are treated as the porous media so as toform the continuous channel of the vessel in the kidney. Thecomparisons between calculation result and infrared images takenduring cold perfusion illustrate that this kind of calculation can givea true reflection of temperature.

The numerical simulation for the coupled transient thermal fieldand stress field is carried out by sequentially thermal-structuralcoupled method based on ANSYS Workbench to evaluate thestress fields and deformations which are established in the kidneyduring hypothermia perfusion. The simulation results shows thatthe thermal effects of large blood vessels remarkably affect thetemperature, thermal stress and deformation distribution of kid-ney. The maximum thermal stress occurs near the vessel and thelargest deformation takes place around the tips of the tissue sur-face. Additionally, increasing the perfusion rate could significantlyaffect the magnitude of the thermal effects of large blood vessels.The rapid cooling of kidney could enlarge the thermal stress anddeformation, which cause the injury to vulnerable cells andcomponent. It is worth to further analyze the thermal effect on thekidney injury during hypothermia perfusion and optimize theperfusion protocol.

Acknowledgements

This work is supported by Project (No. 51076117) of NationalNatural Science Foundation of China.

References

[1] J.F. Barry, C.Y. Lee, Hypothermic perfusion preservation: the future of organpreservation revisited, Cryobiology 54 (2007) 129e145.

[2] S. Kazuhiro, I. Hideaki, T. Toru, M. Yasuo, The effect of initial flush for coolingand coronary vascular washout in heart preservation, Int. J. Angiology 6(1997) 67e70.

[3] M.D. Kay, S.A. Hosgood, S.J. Harper, A. Bagul, H.L. Waller, M.L. Nicholson,Normothermic versus hypothermic ex vivo flush using a novel phosphate-freepreservation solution (AQIX) in porcine kidneys, J. Surg. Res. 171 (2011) 275e282.

[4] I.A. Jacobsen, J. Chemnitz, E. Kemp, The effect of cooling rate in flush preser-vation of rabbit kidneys, Organ Preserv. (1982) 179e182.

[5] C.J. Imber, S.D. St Peter, C.I. Lopez, D. Pigott, T. James, R. Taylor, J. Mcguire,D. Hughes, A. Butler, M. Rees, P.J. Friend, Advantages of normothermic

perfusion over cold storage in liver preservation, Transplantation 73 (2002)701e709.

[6] J.I. Yamauchi, S. Rivhiter, B. Vollmar, M.D. Menger, T. Minor, Warm preflushwith treptokinase improves microvascular procurement and tissue integrityin liver graft retrieval from non-heart-beating donors, Tranplantation 69(2000) 1780e1784.

[7] J.F. Mcanulty, Hyperthermic organ preservation by static storage methods:current status and a views to the future, Cryobiology 60 (2010) S13eS19.

[8] S. Lin, D.Y. Gao, X.C. Yu, Thermal stress induced by water solidification in acylindrical tube, ASME J. Heat Transfer 112 (1990) 1079e1082.

[9] D. Lei, J.H. Zhao, L.A. Tian, Analysis of thermal stressed around the wholeprocess of artery cryopreservation, J. Univ. Sci. Technol. China 34 (2004)328e334.

[10] Y. Zhang, G. Liu, S.Q. Xie, Biomechanical simulation of anterior cruciate liga-ment strain for injury prevention, Comput. Biol. Med. 41 (2011) 159e163.

[11] B. Rubinsky, Thermal stress during solidification, ASME J. Heat Transfer 104(1982) 196e199.

[12] X. Xue, Z.Z. He, J. Liu, Computational study of thermal effects of large bloodvessels in human knee joint, Comput. Biol. Med. 43 (2013) 63e72.

[13] H.W. Huang, C.T. Liauh, T.L. Horng, T.C. Shih, C.F. Chiang, W.L. Lin, Effectiveheating for tumors with thermally significant blood vessels during hyper-thermia treatment, Appl. Therm. Eng. 50 (2013) 837e847.

[14] K. Yue, S.B. Zheng, Y.H. Luo, X.X. Zhang, J.T. Tang, Determination of the 3Dtemperature distribution during ferromagnetic hyperthermia under the in-fluence of blood flow, J. Therm. Biol. 36 (2011) 498e506.

[15] X. Zhao, K.J. Chua, Studying the thermal effects of a clinically-extractedvascular tissue during cryo-freezing, J. Therm. Biol. 37 (2012) 556e563.

[16] J. Shi, Z.Q. Chen, M.H. Shi, Simulation of heat transfer of biological tissueduring cryosurgery based on vascular trees, Appl. Therm. Eng. 29 (2009)1792e1798.

[17] D. Sturm, L.X. Xu, M. Kress, Visualizing the three dimensional vascularstructure of the pig renal cortex, in: Proceeding of the 1994 Interna-tional Mechanical Engineering Congress and Exposition, 1994. Chicago,IL, USA.

[18] M.V. Sousa, E.C. Vasconcelos, G. Janson, D. Garib, A. Pinzan, Accuracy andreproducibility of 3-dimensional digital model measurements, Am. J. Orthod.Dentofacial Orthop. 142 (2012) 269e273.

[19] P. Li, Y. Tang, J. Li, L. Shen, W. Tian, W. Tang, Establishment of sequentialsoftware processing for a biomechanical model of mandibular reconstructionwith custom-made plate, Comput. Methods Programs Biomed. 111 (2013)642e649.

[20] C.V. Bourantas, I.C. Kourtis, M.E. Plissiti, D.I. Fotiadis, C.S. Katsouras,M.I. Papafaklis, L.K. Michalis, A method for 3D reconstruction of coronaryarteries using biplane angiography and intravascular ultrasound images,Comput. Med. Imaging Graph. 29 (2005) 597e606.

[21] A. Yang, K. Zhu, Y.B. Wang, Y.Y. Li, Y.M. Zhang, Experimental study of bio-heattransfer in kidney cold irrigation, J. Eng. Thermophys. 31 (2010) 644e646.

[22] M. Shadi, V. Kambiz, Analytical characterization of heat transport throughbiological media incorporating hyperthermia treatment, Int. J. Heat MassTransfer 52 (2009) 1608e1618.

[23] S.P. Cuo, D.S. Yu, W.T. Wu, Physical characteristics of porous media in theviscera, Acta Mech. Solida Sin. 2 (1983) 284e287.

[24] R.H. Kenneth, R. William, M.C. Michael, Thermal conductivity and H2O contentin rabbit kidney cortex and medulla, J. Therm. Biol. 8 (1983) 311e313.

[25] H. Ahmed, H. Liang, Y. Chunze, E. Richard, Finite element simulation of thetemperature and stress fields in single layers built without-support in selec-tive laser melting, Mater. Des. 52 (2013) 638e647.

[26] B.S. Yilbas, A.F.M. Arif, Material response to thermal loading due to short pulselaser heating, Int. J. Heat Mass Transfer 44 (2001) 3787e3798.

[27] B. Ghadimi, R. Saiedi, F. Kowsary, 3D investigation of thermal stresses in alocomotive ventilated brake disc based on a conjugate thermo-fluidcoupling boundary conditions, Int. Commun. Heat Mass Transfer 49(2013) 104e109.

[28] A. Belhocine, M. Bouchetara, Thermomechanical modeling of dry contacts inautomotive disc brake, Int. J. Therm. Sci. 60 (2012) 161e170.

[29] A. Belhocine, M. Bouchetara, Thermal analysis of a solid brake disc, Appl.Therm. Eng. 32 (2012) 59e67.

[30] N. An, Correlation Study of Thermal Stress Field and Temperature Field inRenal Cold-perfusion Process, Tianjin University of Commerce, Tianjin,2013.

[31] S. Umale, C. Deck, N. Bourdet, P. Dhumane, J. Marescauc, R. Willinger,Experimental mechanical characterization of abdominal organs: liver, kidney,&spleen, J. Mech. Behav. Biomed. Mater. 17 (2013) 22e33.

[32] B.A. Van Wagensveld, M.E. Reinders, T.M. Van Gulik, H.C. Gelderblom,W.M. Frederiks, R.J. Wanders, H. Obertop, Warm flush at 37 �C following coldstorage attenuates reperfusion injury in preserved rat liver, Transplant Int. 11(1998) 38e45.

[33] J. Mohara, H. Tsutsumi, I. Takeyoshi, M. Tokumine, M. Aizaki, S. Ishikawa,K. Matsumoto, Y. Morishita, The optimal pressure for initial flush withUW solution in heart procurement, J. Heart Lung Transplant. 21 (2002)383e390.