Cubic Splines and Fourier Series Approach to Study Temperature Variation in Dermal Layers of Elliptical Shaped Human Limbs
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59848", author = "Mamta Agrawal and Neeru Adlakha and K.R. Pardasani", title = "Cubic Splines and Fourier Series Approach to Study Temperature Variation in Dermal Layers of Elliptical Shaped Human Limbs", abstract = "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 = "Blood Mass Flow Rate, Metabolic Heat Generation,
Fourier Series, Cubic splines and Thermal Conductivity.", volume = "2", number = "11", pages = "875-5", }