Mathematical Models of Bioheat Transfer

Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm

Pennes, H. H. (1948) · Journal of Applied Physiology · doi:10.1152/jappl.1948.1.2.93 · Cited by 4,655

MICROVASCULAR CONTRIBUTIONS IN TISSUE HEAT TRANSFER

Chen, M. M., & Holmes, K. R. (1980) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1980.tb50742.x · Cited by 501

A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature

Weinbaum, S., & Jiji, L. M. (1985) · Journal of Biomechanical Engineering · doi:10.1115/1.3138533 · Cited by 465

Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part I: Anatomical Foundation and Model Conceptualization

Weinbaum, S., Jiji, L. M., & Lemons, D. E. (1984) · Journal of Biomechanical Engineering · doi:10.1115/1.3138501 · Cited by 310

Heat Transfer in Medicine and Biology

Shitzer, A., & Eberhart, R. C. (1985) · Springer eBooks · doi:10.1007/978-1-4684-8285-0 · Cited by 310

Basal Metabolism, Radiation, Convection and Vaporization at Temperatures of 22 to 35°C.

Hardy, J. D., Bois, E. F. D., & Soderstrom, G. F. (1938) · Journal of Nutrition · doi:10.1093/jn/15.5.477 · Cited by 285

The Energy Conservation Equation for Living Tissue

Wulff, W. (1974) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.1974.324342 · Cited by 279

A Mathematical Model of the Human Temperature Regulatory System - Transient Cold Exposure Response

Gordon, R. G., Roemer, R. B., & Horvath, S. M. (1976) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.1976.324601 · Cited by 246

Advances in Bioengineering

(2020) · Springer eBooks · doi:10.1007/978-981-15-2063-1 · Cited by 243

The Application of the Theory of Heat Flow to the Study of Energy Metabolism

Burton, A. C. (1934) · Journal of Nutrition · doi:10.1093/jn/7.5.497 · Cited by 197

Analysis and Simulation of Dynamic Heat Transfer and Thermal Distribution in Burns with Multilayer Models Using Finite Volumes

Rodríguez-Pérez, A. S., Gilardi-Velázquez, H. E., & Velázquez-Pérez, S. E. (2025) · Dynamics · doi:10.3390/dynamics5040041 · Cited by 1

SAR-Based Thermal Assessment of Dielectrophoretic Pulsed Electromagnetic Stimulation in Tibia Fractures with Metallic Implants

Ertugrul, A. D., Kibritoglu, E., Anil, S., & Yüksel, H. (2026) · Bioengineering · doi:10.3390/bioengineering13030364 · Cited by 1

Influence of emissivity changes on the blood flow rate determined on the basis of heat balance equation

Jasiński, M. (2010) · Cited by 1

Governing Equation and Boundary Conditions of Heat Transfer

(2002) · CRC Press eBooks · doi:10.1201/9780203910184.ch3 · Cited by 1

Using an ultrasound circular transducer to treat Ehrlich ascites carcinoma implanted in mice in vivo and in vitro

Ibrahim, A. T., & Mohamed, M. M. (2013) · International Journal of Biomedical Engineering and Technology · doi:10.1504/ijbet.2013.055675 · Cited by 1

Toward an efficient brain tumor extraction using level set method and pennes bioheat equation

Bousselham, A., Bouattane, O., Youssfi, M., & Raihani, A. (2016) · IEEE Congress on Information Science and Technology (CiSt) · doi:10.1109/cist.2016.7804989 · Cited by 1

Applications of the Use of Infrared Breast Images

Bezerra, L. A., de Melo, J. R. F., Lyra, P., & de Lima, R. D. C. F. (2020) · Advances in bioinformatics and biomedical engineering book series · doi:10.4018/978-1-7998-3456-4.ch012 · Cited by 1

Parametric study of thermal damage in the hyperthermia treatment by radiofrequency

Lopez, J. I., & Member, L. A. B. I.-E. (2021) · IEEE International Congress of Biomedical Engineering and Bioengineering (CI-IB&BI) · doi:10.1109/ci-ibbi54220.2021.9626117 · Cited by 1

Shell Balance Approach for One-Dimensional Bioheat Transport

Roselli, R. J., & Diller, K. R. (2011) · Springer eBooks · doi:10.1007/978-1-4419-8119-6_10 · Cited by 1

Studies of ocular heat transfer using the boundary element method

Ooi, E. H. (2009) · doi:10.32657/10356/19264 · Cited by 1

MULTISCALE ANALYSIS IN DYNAMICAL HEAT TRANSFER PROBLEMS IN BIOLOGICAL TISSUES

Timofte, C. (2009) · Cited by 1

Assessment of the Measurement Repeatability and Sensitivity of a Noninvasive Blood Perfusion Measuring Probe

Comas, C. M. (2005) · VTechWorks (Virginia Tech)

Development and Experimental Validation of Mathematical Tools for Computerized Monitoring of Cryosurgery

Thaokar, C. (2016) · KiltHub Repository · doi:10.1184/r1/6715886

Análise numérica de modelos térmicos envolvendo a estimativa de parâmetros na equação da biotransferência de calor

Figueiredo, A. (2014) · doi:10.14393/ufu.di.2014.394

Uso de Funções de Green no estudo da biotransferência de calor tridimensional considerando efeitos de perfusão sanguínea e metabolismo

de Oliveira, E. P. (2018) · doi:10.14393/ufu.di.2018.1217

Development of a Micro-thermal Sensor Based on 3-omega Technique for Dynamic Freezing Applications

Natesan, H. (2019) · University of Minnesota Digital Conservancy (University of Minnesota)

Mathematical Modeling of Thermal Ablation Treatments in Heart Arrhythmias

Carballo, A. A., Parra, I., Rubio, G., & Valero, E. (2021) · WCCM-ECCOMAS Congress · doi:10.23967/wccm-eccomas.2020.193

Simulação computacional para o problema de dispersão de poluição na lagoa Rodrigo de Freitas

de Barros, J. P. A., de Faria, C. O., & Meyer, J. F. D. C. A. (2021) · Proceeding Series of the Brazilian Society of Computational and Applied Mathematics · doi:10.5540/03.2021.008.01.0473

Microvascular Heat Transfer

Baish, J. W. (2012) · CRC Press eBooks · doi:10.1201/b12937-4

Tissue Damage Control Algorithm for Hyperthermia Based Cancer Treatments

Fatigate, G. R., Neves, R. F. C., Lobosco, M., & Reis, R. F. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-08754-7_57

Estimating the Electrical Conductivity of Human Tissue in Radiofrequency Hyperthermia Therapy

López-Pérez, J. I., & Varón, L. A. B. (2022) · Ingeniería e Investigación · doi:10.15446/ing.investig.92288

Velocity and Blood Perfusion’s Impact on Transient Bioheat Transfer in Human Skin, a Numerical InvestigationPreprint

Hasnain, S., AlRajhi, A. H., Saqib, M., & Abbas, I. (2023) · Research Square · doi:10.21203/rs.3.rs-3447150/v1

Numerical study of bioheat transfer in a vascular bed with counter-flow mechanisms

Sreegowrav, K. R., Indira, R., Puranik, S. M., Jagadeesha, S., Vishwanatha, S. J., & Kumar, K. G. (2025) · Case Studies in Thermal Engineering · doi:10.1016/j.csite.2025.105811

A Numerical Study of Gold-Nanorod-Enhanced Noninvasive Laser Ablation for Central Lung Cancer Using an Optical-Thermal-Fluid Model

Liang, H., Yang, Y., Fang, Z., Cao, L., Zhang, H., Zhang, W., Qian, Z., & Zhang, B. (2025) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.4068094

Impact of inaccuracies of injection positioning for hyperthermia treatment for cancer

Fatigate, G. R., Martins, G. C., Lobosco, M., & Reis, R. F. (2025) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2025.116780

Regional Models: Skin and Deep Tissues

Zhmakin, A. I. (2025) · Springer series in biophysics · doi:10.1007/978-3-031-95459-7_5

Comparison of methods of thermal ablation and endovenous laser coagulation of lower extremity varicose veins in experiment: energy and temperature characteristics of impact on vein and surrounding tissues, effectiveness and safety

Махмутович, М. Д., Borshchev, G. G., Ulbashev, D. S., Sabanaev, R. A., Makhonina, A., & Ermolaev, E. S. (2026) · I P Pavlov Russian Medical Biological Herald · doi:10.17816/pavlovj678356

Étude des interactions par radiofréquence entre multiples dispositifs médicaux pour la compatibilité IRM

Kabil, J. (2018) · doi:10.70675/95bb71d5z8965z4195zb8cfz69706d786535

Analyse thermomécanique du système vasculaire de surface - Application au pied diabétique

Serantoni, V. (2019) · doi:10.70675/089500fczaae9z449bza6cbz784d7f197b10

Dynamic physiological and structural tissue parameters in bioheat models: Enhancing heat transfer realism for hyperthermia therapy

Alamouti, A. K. (2026) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2026.111185

Quantifying thermal-signature equivalence in infrared breast thermography using a modified Pennes bioheat model

Muslim, R., Fardela, R., & Kusuma, T. A. I. (2026) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2026.129785

On the determination of additive source terms in the hyperbolic bio-heat equation

Kinash, N., & Lesnic, D. (2026) · Communications on Analysis and Computation · doi:10.3934/cac.2026015

Fractional two-temperature thermoelastic analysis of electromagnetic heating in skin tissue for thermal damage assessment and safety evaluation

Zhang, X., & Seema (2026) · Nondestructive Testing And Evaluation · doi:10.1080/10589759.2026.2688469

A scoping review of computational models of the diabetic foot

Li, Y., Haron, A. H., Lin, C., Tang, Y., Weightman, A., & Cooper, G. (2026) · PLoS ONE · doi:10.1371/journal.pone.0351638

Computational and MR-Guided Patient-Specific Laser-Induced Thermal Therapy of Cancer

Fuentes, D., Oden, J. T., Diller, K. R., Yung, J., Feng, Y., Hazle, J. D., Shetty, A., & Stafford, R. J. (2026) · Springer eBooks · doi:10.1007/978-3-031-88574-7_17

A first approach to breast temperature profile calculations using physics informed neural network including validation against experimental and numerical data

Filho, E. X. D. V., Bezerra, L. A., & de Lima, R. D. C. F. (2026) · Research on Biomedical Engineering · doi:10.1007/s42600-026-00491-1

Fractional-order thermo-biophysical modeling of soft tissues: analytical, numerical, and experimental insights for thermal therapies

Aref, M. H., Hussein, A. A., Sabry, Y. M., & El-Sharkawy, Y. H. (2026) · Research on Biomedical Engineering · doi:10.1007/s42600-026-00489-9

Gender disparities in thermoregulatory exergy efficiency across the BMI spectrum: Insights from a four-layer human thermal model

Rajeesh, P., Kalaiarasu, B., Tamilarasan, N., Sakthivel, R., & Raghuram, P. (2026) · Array · doi:10.1016/j.array.2026.101154

Infrared Thermography for Non-Contact Monitoring of Physiological Load in Repetitive Work-like Tasks

Fabbiano, L., Morvayovà, A., Gaspari, A., & Morello, R. (2026) · IEEE International Workshop on Metrology for Industry 4.0 & IoT (MetroInd4.0&IoT) · doi:10.1109/metroind4.0iot69397.2026.11653069

Analysis of graphene-coated and uncoated gold nanostars for enhanced photothermal therapy: experimental and simulation

Etemadi, M., Golmohammadi, S., Rasta, S. H., Ahadzadeh, I., & Mardangom, H. N. (2026) · International Journal of Hyperthermia · doi:10.1080/02656736.2026.2722157

Fractional two-temperature dual-phase-lag bioheat transfer under electromagnetic heating: An analytical-physics-informed neural network framework

Hassaballa, A. A., Singhal, A., Elhessewi, G. M. S., & Alanazi, A. A. (2026) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2026.112817

A General Set of Bioheat Transfer Equations Based on the Volume Averaging Theory

Nakayama, A., Kuwahara, F., & Liu, W. (2010) · CRC Press eBooks · doi:10.1201/9781420065428-5 · Cited by 7

Analysis of Bio-Heat Transfer in the System Blood Vessel — Biological Tissue

Majchrzak, E., & Mochnacki, B. (2001) · Springer eBooks · doi:10.1007/978-94-015-9793-7_17 · Cited by 6

NEW DEVELOPMENTS IN BIOHEAT AND MASS TRANSFER MODELING

Xu, L. X. (1999) · Annual Reviews of Heat Transfer · doi:10.1615/annualrevheattransfer.v10.30 · Cited by 8

Analytical Solutions of Pennes Bio-Heat Transfer Equation With a Blood Vessel

Huang, H., Chan, C. L., & Roemer, R. B. (1994) · Journal of Biomechanical Engineering · doi:10.1115/1.2895721 · Cited by 60

Proceedings o/The Fifth Int. Canf. on Environmental Ergonomics THE THERMAL EFFECI ' OF BLOOD FLOW IN A BRANCHING COUNTERCURRENT NETWORK

Brinck, H., & Werner, J. (2015)