Total views : 5

One Dimensional Transient State Finite Element Model to Study Thermal Variations due to Transient Vasoconstriction followed by Persistent Vasodilation during Inflammation in Surgical Wound of Peripheral Tissues of Human Limb


  • Department of Mathematics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal – 462003, Madhya Pradesh, India


Objectives: This paper compares theoretically the thermal variations in normal tissues, clean surgical wound and contaminated surgical wound in peripheral tissues of human arm and leg during inflammatory phase of healing. Methods/Statistical Analysis: One dimensional finite element model is developed using Bio-heat equation.Values of arterial blood temperature, core body temperature and heat transfer coefficient have been revised. During inflammation blood perfusion rate and metabolic heat generation rate are considered linearly dependent on temperature and spatial coordinate, and exponentially dependent on time.The effect of vasodilation and effect of rate at which vascular changes occur, on temperature profiles,is investigated by varying value of linear coefficient of temperature dependence and coefficient of time variable respectively. Findings: A computer programme in MATLAB is developed to simulate the results. Skin surface temperature in normal tissue are simulated and validated from published experimental data. Maximum blood perfusion rate at maximum vasodilation calculated theoretically is validated with the published experimental data. Temperature difference in contaminated wound and normal tissue are simulated and validated with the published experimental data. Improvements/Applications: Normal skin temperature and thermal variations during vasodilation are modelled well by revising the values of parameters mentioned above and considering temperature dependent parameters.This information may be useful to biomedical scientists in development of treatment regimen for surgical wounds.


Finite Element Technique, Non-Linear Partial Differential Equation, Temperature Dependent Blood Perfusion Rate, Temperature Dependent Metabolic Heat Generation Rate, Thermal Variations in Peripheral Tissues of Human Limb, Vasodilation.

Full Text:

 |  (PDF views: 9)


  • Li J, Chen J, Kirsner R. Pathophysiology of acute wound healing. Clinics in dermatology. 2007; 25(1): 9–18. Availavle from: Crossref Mid:17276196
  • Diegelmann RF, Evans MC. Wound healing: An overview of acute, fibrotic and delayed healingFront Bioscience. 2004; 9(1): 283–9.
  • Fierheller M, Sibbald RG. A clinical investigation into the relationship between increased periwound skin temperature and local wound infection in patients with chronic leg ulcers. Advances in skin and wound care. 2010; 23(8):369– 79. Available from: Crossref PMid:20631603
  • Gannon R. Fact file: Wound cleansing: sterile water or saline?Nursing Times net. 2007; 103(9): 44.
  • Tweed C. A review of the literature examining the relationship between temperature and infection in surgical wound healing. 2003.
  • Kengne E, Hamouda FB, Lakhssassi A. Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion. Applied Mathematics. 2013; 4(10): 1471. Available from: Crossref
  • Pennes HH. Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of applied physiology. 1948; 1(2): 93–122. PMid:18887578
  • Henriques F, Moritz A. Studies of thermal injury: I. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation*. The American journal of pathology. 1947; 23(4): 530. PMid:19970945 PMCid:PMC1934298
  • Shih T-C, Yuan P, Lin W-L, Kou H-S. Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface. Medical Engineering and Physics. 2007; 29(9): 946–53. Available from: Crossref PMid:17137825
  • Perl W. An extension of the diffusion equation to include clearance by capillary blood flow. Annals of the New York Academy of Sciences. 1963; 108(1): 92–105. Available from: Crossref PMid:13942460
  • Lang J, Erdmann B, Seebass M. Impact of nonlinear heat transfer on temperature control in regional hyperthermia. Transactions on Biomedical Engineering, IEEE 1999; 46(9): 1129–38.
  • Wissler EH. Pennes’ 1948 paper revisited. Journal of Applied Physiology. 1998; 85(1): 35–41. PMid:9655751
  • Saxena V, Bindra J. Quadratic shape functions in variational finite element approach to heat distribution in cutaneous and subcutaneous tissues. Indian Journal of pure Applied Mathematics. 1987; L_8 (9): 846–55.
  • Kengne E, Lakhssassi A, Vaillancourt R, editors. Temperature distribution in living biological tissue simultaneously subjected to oscillatory surface and spatial heating: Analytical and numerical analysis. International Mathematical Forum. 2012.
  • Pardasani K, Shakya M. Three dimensional infinite element model to study thermal disturbances in human peripheral region due to tumor. Journal of Biomechanics. 2006; 39: 634. Available from: Crossref
  • Gowrishankar T, Stewart DA, Martin GT, Weaver JC. Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion. BioMedical Engineering OnLine. 2004; 3(1): 1. Available from: Crossref, Crossref PMid:14746653 PMCid:PMC343291
  • Werner J, Reents T. A contribution to the topography of temperature regulation in man. European journal of applied physiology and occupational physiology. 1980; 45(1): 87–94. Available from: Crossref
  • Jain M, Shakya M. Study of temperature variation in human peripheral region during wound healing process due to plastic surgery. Applied Mathematical Sciences. 2009; 3(54): 2651–62.
  • Jain M, Shakya M. An infinite element model to study temperature variations during wound healing process after plastic surgery. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2011; 14(02): 209–24. Available from: Crossref
  • Gupta N, Shakya M. Transient State Finite Element Model to Analyse Thermal Variations in Peripheral Region of Human Limb undergoing Healing after Surgery. IOSR Journal of Mathematics (IOSR-JM) 2014; 10(6): 66–75.
  • Gupta N, Shakya M. A Two-Dimensional Mathematical Model to Analyze Thermal Variations in Skin and Subcutaneous Tissue Region of Human Limb during Surgical Wound Healing. Applied Mathematics. 2016; 7(02): 145. Available from: Crossref
  • Kamel C, McGahan L, Mierzwinski-Urban M, Embil Journal of Classification of surgical wounds. 2011.
  • Fiala D, Lomas KJ, Stohrer M. A computer model of human thermoregulation for a wide range of environmental conditions: the passive system. Journal of Applied Physiology. 1999; 87(5): 1957–72. PMid:10562642
  • Fiala D, Havenith G, Bröde P, Kampmann B, Jendritzky G. UTCI-Fiala multi-node model of human heat transfer and temperature regulation. International journal of biometeorology. 2012; 56(3): 429–41. Available from: Crossref PMid:21503622
  • Stolwijk JA. A mathematical model of physiological temperature regulation in man. 1971.
  • de Dear RJ, Arens E, Hui Z, Oguro M. Convective and radiative heat transfer coefficients for individual human body segments. International Journal of Biometeorology. 1997; 40(3):141–56.Available from: Crossref PMid:9195861
  • Deodhar AK, Rana R. Surgical physiology of wound healing: a review. Journal of Postgraduate Medicine. 1997; 43(2): 52. PMid:10740722
  • Chin GA, Diegelmann RF, Schultz GS. Cellular and molecular regulation of wound healing. Basic and Clinical Dermatology. 2005; 33:17.
  • Hall JE. Guyton and Hall Textbook of Medical Physiology: Enhanced E-book: Elsevier Health Sciences; 2010.
  • Johnson JM, Minson CT, Kellogg DL. Cutaneous vasodilator and vasoconstrictor mechanisms in temperature regulation. Comprehensive Physiology. 2014. Available from: Crossref PMid:24692134
  • Kellogg D. In vivo mechanisms of cutaneous vasodilation and vasoconstriction in humans during thermoregulatory challenges. Journal of Applied Physiology. 2006; 100(5):1709–18. Available from: Crossref PMid:16614368
  • Charkoudian N. Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans. Journal of Applied Physiology. 2010; 109(4):1221– 8. Available from: Crossref PMCid:PMC2963327
  • Amiya E, Watanabe M, Komuro I. The relationship between vascular function and the autonomic nervous system. Annals of vascular diseases. 2014; 7(2):109. Available from: Crossref PMid:24995054 PMCid:PMC4072858
  • Kumar V, Abbas AK, Fausto N, Mitchell RN. Robbins basic pathology: Elsevier Health Sciences; 2012.
  • Upchurch J. SIRS and sepsis: When the immune system turns traitor 2011 .2015.
  • Gaffney E, Pugh K, Maini P, Arnold F. Investigating a simple model of cutaneous wound healing angiogenesis. Journal of mathematical biology. 2002; 45(4): 337–74. Available from: Crossref PMid:12373343
  • Maggelakis SA. A mathematical model of tissue replacement during epidermal wound healing. Applied Mathematical Modelling. 2003; 27(3):189–96. Available from: Crossref
  • Klabunde R. Cardiovascular physiology concepts: Lippincott Williams and Wilkins; 2011.
  • Ignarro LJ. Endothelium-derived nitric oxide: actions and properties. The FASEB Journal. 1989; 3(1):31–6. PMid:2642868
  • Alberts B, Bray D, Hopkin K, Johnson A, Lewis J, Raff M, et al. Essential cell biology: Garland Science; 2013.
  • Wang X L. Convective heat losses from segments of the human body. Climate Buildings. 1990; 3:8–14.
  • Wang X. Convective heat transfer coefficients from head and arms. Climate Buildings. 1990; 2:3–7.
  • Wang X-L. Free convective heat transfer coefficients of a heated full-scale manikin. Climate Buildings. 1990; 1:17– 31.
  • Kenny GP, Sigal RJ, McGinn R. Body temperature regulation in diabetes. Temperature. 2016;3(1):119–45. Available from: Crossref PMid:27227101 PMCid:PMC4861190
  • Salloum M, Ghaddar N, Ghali K. A new transient bioheat model of the human body and its integration to clothing models. International Journal of Thermal Sciences. 2007; 46(4):371–84. Available from: Crossref


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.