This monograph discusses the physical phenomena encountered in the heat transfer in living tissues and mathematical models. It also considers all the relevant information regarding heat transfer in humans, animals and plants in nature and medicine from the whole body down to cellular and sub-cellular models.

Effects of the high or low temperature on the biological systems at the different levels - cells, tissues and organisms - as well a role of the blood circulation and the structure of the vascular network on the heat transfer are considered.

The classic Pennes bioheat equation, a number of the non-Fourier heat transfer models (including the single-phase-lag and dual-phase-lag models), the porous media models, the models based on the fractional differential equations, the discrete vascular models are analyzed and discussed at length.

This book is particularly interesting for graduate students, postdoctoral fellows and researching working on heat transfer in biological systems.

Alexander Zhmakin

Alexander Igorevich Zhmakin was born on March 12, 1951, in Leningrad, USSR. In 1974 he graduated from the Leningrad Polytechnic Institute and joined the Ioffe Institute, where he worked throughout his career, eventually as Leading Researcher of the Computational Physics Laboratory.

In 1980, he defended his Candidate of Physical-Mathematical Sciences (PhD equivalent) thesis on the numerical simulation of non-equilibrium shocked flows. Subsequently, he earned the Doctor of Physical-Mathematical Sciences degree (Dr.Sci.) in 1992 for research in numerical simulation of gas- and liquid-phase epitaxial crystal growth.

Beyond academia, Zhmakin had a longstanding collaboration with Soft-Impact Ltd., a company providing consulting services and developing simulation software for crystal growth processes and semiconductor device modelling. He served as Technical Director from 1997 to 2003, as Research Director from 2004 to 2008, and as Scientific Consultant from 2009 onward. He also collaborated with the St. Petersburg Branch of the Joint Supercomputing Center (JSCC) of the Russian Academy of Sciences.

He mentored numerous undergraduate and graduate students, researchers and engineers.

Zhmakin's early studies (presented in his Candidate thesis) focused on computational fluid dynamics of supersonic magnetohydrodynamic flows and problems of shock-wave interactions with obstacles.

In the mid-1980s, his scientific interests began to shift to low Mach number viscous gas flows and heat transfer and subsequently to crystal growth processes. During this period, Zhmakin developed and applied simulation algorithms for gas-, liquid-, and vapour-phase epitaxy, as well as for bulk and sublimation growth methods, focusing on both entire processes and specific aspects such as fluid dynamics and heat transfer. Furthermore, he co-authored several papers on fluid flows and crystal growth under microgravity.

From the 1990s onward, Zhmakin's research increasingly involved industrial collaborations, largely through his work in Soft-Impact, where he oversaw much of the simulation software development, actively contributing to architecture and research.

In the 2000s, his work expanded to include semiconductor nanostructures (A3B5 compound structure models) and light-emitting diodes based on complex heterostructures. Zhmakin explored interdisciplinary fields such as human motion modelling and cryobiology. His comprehensive monograph, "Fundamentals of Cryobiology: Physical Phenomena and Mathematical Models" (Springer, 2008) covered the state of the art in both theoretical and practical aspects, particularly in cryosurgery and cryoconservation. His interest in human motion modelling was first presented in a 2011 article, and later developed into the book "Human Motion: from Animation to Simulation: A View from the Outside" (Lap Lambert, 2021).

During his final years, Zhmakin increasingly focused on non-classical heat transfer phenomena. His 2023 book "Non-Fourier Heat Conduction: From Phase-Lag Models to Relativistic and Quantum Transport" (Springer) explored advanced theoretical and numerical aspects of heat conduction for scenarios where classical models prove inadequate — such as ultrafast heating and materials with non-homogeneous internal structure, including biological tissues. He later expanded upon this work in "Heat Transfer in Vivo" (2024), a comprehensive analysis of the properties of living organisms from the standpoint of thermal physics.

His books are notable for their precise and thoughtful selection of epigraphs.