Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31100
Cubic Splines and Fourier Series Approach to Study Temperature Variation in Dermal Layers of Elliptical Shaped Human Limbs

Authors: Mamta Agrawal, Neeru Adlakha, K.R. Pardasani


An attempt has been made to develop a seminumerical model to study temperature variations in dermal layers of human limbs. The model has been developed for two dimensional steady state case. The human limb has been assumed to have elliptical cross section. The dermal region has been divided into three natural layers namely epidermis, dermis and subdermal tissues. The model incorporates the effect of important physiological parameters like blood mass flow rate, metabolic heat generation, and thermal conductivity of the tissues. The outer surface of the limb is exposed to the environment and it is assumed that heat loss takes place at the outer surface by conduction, convection, radiation, and evaporation. The temperature of inner core of the limb also varies at the lower atmospheric temperature. Appropriate boundary conditions have been framed based on the physical conditions of the problem. Cubic splines approach has been employed along radial direction and Fourier series along angular direction to obtain the solution. The numerical results have been computed for different values of eccentricity resembling with the elliptic cross section of the human limbs. The numerical results have been used to obtain the temperature profile and to study the relationships among the various physiological parameters.

Keywords: Fourier Series, blood mass flow rate, Metabolic Heat Generation, Cubic splines and Thermal Conductivity

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1532


[1] W. Perl, "Heat and matter distribution in body tissues and determination of tissue blood flow by local clearance methods," J.Theo. Biol. 2, 201- 235, (1962).
[2] A. M. Patterson, "Measurement of temperature profiles in human skin," S.Afr.J.Sc. 72, 78-79, (1976).
[3] V. P. Saxena, and D. Arya, "Steady state heat distribution in epidermis, dermis and subdermal tissues," Theo. Biol. 89, 423-432, (1981).
[4] V. P. Saxena, .and J. S. Bindra, "Indian J. pure appl.Math.", 18(9), 846- 55, (1987).
[5] K. R. Pardasani, and V. P. Saxena, "Bull. Calcutt Math.Soc." 81,1-8, (1989).
[6] K. R. Pardasani, and N. Adlakha, "Coaxial circular sector elements to study radial and angular heat distribution problem in human limbs," Proc. Nat. ACAD. Sci. India, 68 (A), 1, (1998).
[7] V. P. Saxena, and K. R. Pardasani, "Effect of dermal tumors on temperature distribution in skin with variable blood flow," Mathematical Biology, USA. Vol. 53, No.4, 525-536, (1991).
[8] K. R. Pardasani, and N. Adlakha, "exact solution to a heat flow problem in peripheral tissue layers with a solid tumor in dermis," Ind.J.Pure. Appl. Math.22 (8), 679-682, (1991).
[9] J. W. Mitchell, T. L. Galvez, J. Hengle, G. E. Myers, and K. L. Siebecker, "Thermal response of human legs during cooling " J.Appl. Physiology, U.S.A., 29 (6), 859-865, (1970).
[10] V. P. Saxena, and J. S. Bindra, "Pseudo-analytic finite partition approach to temperature distribution problem in human limbs," Int. J. Math. Sciences. Vol. 12, 403- 408, (1989).
[11] K. R. Pardasani, and N. Adlakha, "Two-dimensional steady state temperature distribution in annular tissue layers of a human or animal body," Ind.J.Pure. Appl. Math. 24(11) 721-728, (1993).
[12] M. K. Jain, S. Iyengar, and R. K. Jain, "Numerical Methods for Scientific and engineering Computation," Wiley Eastern Limited, (1985).
[13] V. P. Saxena., and M. P. Gupta, "Steady state heat migration in radial and angular direction of human limbs," Ind. J. Pure. Appl. Math. 22(8), 657- 668, (1991).
[14] P. Jas, "Finite element approach to the thermal study of malignancies in cylindrical human organs," Ph.D. thesis, MANIT, Bhopal, (2002).
[15] K. R. Pardasani, and M. Shakya, "Three dimensional infinite element model to study thermal disturbances in human peripheral region due to tumor" J. of Biomechanics, Vol. 39, Suppl.1, P.S634, (2006).
[16] K. R. Pardasani, and M. Shakya, "Infinite element thermal model for human dermal regions with tumors." Int. Journal of Applied Sc. & computations, vol. 15 No., PP. 1-10, 1 May 2008.