Computational Biomechanics Project

Co-Researcher (RIKEN): Ying HE

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Study on the Relationship between Blood Flow and Heat Transfer in biological tissues

Recently, studies on the integrated simulation of the human circulatory system have attracted the attention of many researchers. The phenomena occurring in the blood circulatory system are complex, and they are profoundly involved in the development and progress of diseases such as circulatory disease, diabetes, and cancer [1]. Therefore, an integrated study needs to be conducted on the relationship between blood flow and the phenomena of bioheat and mass transfer with regard to the blood circulatory system and each organ. My studies can be divided mainly into two themes: numerical simulation of the thermofluid dynamics of blood circulation in the peripheral blood vessels and thermal behavior of normal and tumor tissues under laser irradiation.

1. Numerical study on the thermal behavior of the blood circulation and the extremity
The influence of blood flow on body temperature has been studied by many researchers. For example, it has been revealed that smoking and mental stress can cause a decrease in the blood flow rate in peripheral blood vessels, and a subsequent decrease in the finger temperature. Moreover, because of different blood flow regulation ability, body temperature regulation ability is different between male and female.
In this study, the heat transfer of blood circulation in the upper limb and the finger were numerically computed. As the first step, the effect of a cold stimulus on the finger temperature was investigated (--> Download page (1)). Based on an anatomic cross-sectional structure and the model constructed by Yokoyama et al. [2] and [3], a two-dimensional geometrical model of the medius was constructed by including the arteries of the medius. The arterial blood temperature was assumed to be 37°C, and the temperatures of other tissues were computed numerically by Pennues’ bioheat equation [4]. The simulation condition is that after exposing the finger to the air at a normal temperature, it was immersed into 10 oC cold water and then, re-exposed to the air at a normal temperature. Fig. 1 shows the temperature variation of the finger when exposed to the air and in the cold water.

Fig. 1 Isotherms of the finger at different conditions

Fig. 2 Temperature distribution of blood and solid tissues along the longitudinal direction of the finger model

As the second step, the effect of local blood flow on the temperature distribution of the finger was investigated (--> Download page (4)). In order to simulate the bioheat transfer, a computational code was developed based on Shirasaki’s code of two-dimensional finite element method (FEM) for thermohydrodynamic analysis [5]. The blood flow rate in the finger was measured using ultrasound Doppler flowmetry, and the measured data was used as the boundary condition for the calculation. The temperature distribution of the finger in the air at the resting condition was obtained at different Reynolds numbers, and the range of the Reynolds numbers was set between 20 and 100. Fig. 2 shows the temperature distribution of blood and solid tissue along the longitudinal direction of the finger model. The finger temperature tended to increase with the Reynolds number.

As the third step, the global effect of blood flow on the temperature distribution was investigated. Based on the dynamic model [6] constructed by Olufsen et al., a one-dimensional thermofluid model in an elastic blood vessel was constructed (--> Download page (6)), where an energy equation was added with the effect of the flow rate and blood vessel. areas. The blood pressure,flow rate, and temperature in a network of arteries, veins, and capillaries in the human upper limb were numerically computed. With regard to the numercal methods, firstly, the blood flow rates and cross-sections of blood vessels were obtained using the two-step Lax-Wendroff method. The obtained data were next substituted into the energy equation, and the temperature was thus analyzed. (--> Download page (6)).
Fig. 3 shows the schematic of the blood circulation in the human upper limb. The thermal behavior of the extremity was investigated by coupling the one-dimensional blood flow model (--> Download page (8)) and the two-dimensional thermal model of a human finger. (--> Download page (1))
Fig. 4 shows the schematic of the cross-section of the finger model. Figs. 5 and 6 give the blood pressures and temperatures in different blood vessels, respectively, and Fig. 7 shows the temperature distribution in the solid tissues of the finger model. In order to compare the computational results. The time sequential data of the upper limb skin temperature under room condition were taken by an infrared thermography, and the spectra of the data were analyzed using fast Fourier transform (FFT). It is found that there are periodic changes for skin temperature in some places, which is in agreement with the computational results qualitatively. ( --> Download page (8)).

Fig. 3 The schematic of the blood circulation in the human upper limb

Fig. 4 The schematic of the cross-section of the finger model

Fig. 5 Computed pressure signals in different blood vessels.

Fig. 6 Temperatures within the artery, vein, and capillary of the finger model.

Fig. 7 Temperature distribution in the solid tissues of the finger model.

In summary, the hemadynamic effect of the circulation on the heat transfer in biological tissues (human finger) was investigated from different aspects. The physiological information such as the blood pressure, blood flow rate, and temperature in different conditions can be predicted with this model. This study is ecpected to be beneficial for the diagnosis of peripheral circulatory diseases, sports training, automobile driving, and prosthetic hand development.

2. Thermal behavior of normal and tumor tissues and their blood flow under laser irradiation
Tumor blood flow plays an important role in the development, detection, and treatment of tumors. In radiotherapy and chemotherapy, since oxygen and drugs are transported to the tumor tissue through blood, adequate blood flow is required. On the contrary, since thermal energy is lost due to blood circulation, a lower blood flow rate in the tumor is desirable in thermotherapy. Therefore, regulating the blood flow rate would increase the efficiency of cancer treatment. The development of laser technology has contributed to the medical treatment of many diseases. Laser in medical treatment is mainly used as a source of thermal energy. In this study, based on previous studies on laser irradiation [7] and [8] and my study (--> Download page (8)), the changes in the tumor blood flow rate due to laser irradiation were investigated. A cancerous mammry gland under laser irradiation were analyzed. Firstly, the blood perfusion in the tumor and nomal tissues were computed by the blood flow model and transferred to the FE thermal model. Secondly, the average temperature of the cancerous tissues was computed by the FE thermal model and transferred to the blood flow model. These steps were repeated with the time going and the variation of blood flow with the tumor temperature can be obtained .
Fig. 8 shows the temperature distribution and the tumor blood perfusion rate under different power of laser irradiations.
The experimental results obtained in this study are currently limited. In the future, heating-induced changes in the blood flow and oxygen distribution in tumor tissues will be further investigated.

Fig. 8 Tumor blood perfusion rate and temperature distribution in the laser-irradiated tissues.

[1]	****, 31-33.
[2]	W. Kahle, H. Leonhardt, and W. Platzer, Taschenatlas der Anatomie (in Japanese, translated by J. Ochi), 2000 (Chapter 3 ).
[3]	Yokoyama, S. and Ogino, H., 1985, " Developing computer model for analysis of human cold tolerance". The annals of physiological anthropology, Vol. 4, No. 2, pp.183-187.
[4]	Pennes, H. H., 1948, "Analysis of tissue and arterialblood temperatures in the resting human forearm ". J. applied physiology, Vol. 1, No.2, pp.93-122 .
[5]	Sirazaki, M., and Himeno, R., Unified analysis of thermal flows and heat transfer using PC cluster (Japanese). High Performance Computing Symposium, HPCS2002, Tsukuba, Japan, pp. 119-124 (2002).
[6]	M.S. Olufsen, C.S. Peskin, W.Y. Kim, E. R. Pedersen, A. Nadim, and J. Larsen, Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Annals of Biomedical Engineering 28 (2000), 1281-1299.
[7]	****, pp.402-403.
[8]	Majumdar, P. and Sharma R., 2003, Thermal Effects in Laser Irradiated Biological Tissue, The 6th ASMEJSME Thermal Engineering Joint Conference, TED-AJ03-210, Hawaii.