Bioheat transfer
Encyclopedia
Bioheat transfer is the study of heat transfer
in biological systems. In simpler terms, it is the study of how heat moves from one compartment, be it within the body or external to the body, to another compartment in the body. Bioheat transfer has its foundations in the engineering discipline of heat transfer and is itself a subfield of biomedical engineering
or bioengineering. In addition, computational techniques to model various bioheat transfer scenarios are widely employed and hold an important place in developing devices and protocols for the medical community.
Of particular importance were the values of specific gravity
, specific heat, thermal conductivity
for the various tissues in the body e.g. skin, fat, muscle, bone, and blood. Today, such values can be easily found in various handbooks and study publications such as the CRC Handbook of Mechanical Engineering (2nd Ed.) or the Report of the task group on reference man (1975).
To illustrate the detailed knowledge that is required by the bioheat transfer community, The CRC Handbook of Mechanical Engineering includes a nearly 2 page table of value for thermal conductivity of various organs including but not limited to: kidney, aorta, arterial plaque, blood, liver, spleen, heart, muscle and tumor.
Because of the importance of blood perfusion on thermal equilibria in the body, blood perfusion values were also pursued early in the history of the field. The CRC Handbook of Mechanical Engineering's chapter on Bioheat Transfer includes a nearly 6 page table of blood perfusion values for a similar variety of tissues as the table for thermal conductivity. Greater discussion on the effect of blood perfusion on heat transfer is given in Section 2.
is the key system by which heat is distributed throughout the body. The blood serves as the vehicle to transport heat from the areas of high heat to areas of lower heat. In general this transfer takes place in the direction from body core to extremities such as the limbs and head. In the case where the extremities are hotter than the core body temperature
, perfusion would serve to transport heat from the extremity back towards the body core. Whether or not the core temperature rises depends on many factors such as the duration of elevated local temperature at the extremity, temperature difference between extremity and core, volume of blood heated above core temperature, and the rate of blood perfusion. This same moderating phenomena of blood perfusion can be applied to local heat transfer problems e.g. heating of a tumor.
Various modalities of energy deposition include: radio frequency
, laser
, high intensity focused ultrasound
, etc. These modalities are commonly used in the minimally invasive surgical treatment of cancer
. One common type is radiofrequency ablation
, a type of hyperthermia therapy
.
form within the cytoplasm of the cell. Bioheat transport equations can also be used to model this process.
.
An example of therapeutic hyperthermia is the ThermaCare HeatWrap by Procter & Gamble
. The application of heat to injured tissues works to heal target tissues by a temperature dependent vasodilation. This vasodilation increases the mass transport of wastes and nutrients from and to the site of injury. Because damaged tissue is more metabolically active the enhanced mass transport can facilitate more rapid healing.
Hypothermia
Heat transfer is not only study of raising temperatures, but also reducing them. It is commonly understood that lower temperatures help to preserve living or "once living" tissue. For example, foods stored in refrigerators last longer because the metabolic processes of cellular decay and bacterial growth
are slowed due to the lower free energy (e.g. heat) in the refrigerator. This principle is often applied in surgical wards to individuals who experience head trauma
.
In cases of head trauma, it is common procedure to reduce the body temperature to about 32°C (90°F) which is about 5°C (8.5°F) lower than normal core temperature of 37°C (98.5°F). This presents a good example of how bioheat transfer engineers can contribute to medical treatments. Such a situation would be broken down first into a system, which in this case would include the entire surface of the body. Assuming the individual is submerged in cold water up to the neck and ears, or otherwise surrounded by an environment that can be modeled as a temperature sink, the engineering would model the body as a composite system composed of skin, fast, muscle bone and possibly organs depending on how complex the model must be. The head could be considered a separate system connected to the body via a third major system, the vasculature. The vasculature would bring cooled blood from the submerged body to the brain where there would be some amount of conductive and convection heat transfer based on the passage of blood through the vessels cooling the vessel via forced convection
and the subsequent cooling of the brain via conduction between blood vessel
and brain tissue. Each of these heat transfer processes i.e. water to body, body to vasculature, and vasculature to brain would require knowledge of the thermal conductivity, specific heat, density, blood perfusion rate, and diameter of blood vessel at the least to predict the temperature history at any point within the body e.g. to know when the temperature at the center of the head trauma reaches 32°C.
Such application of hypothermia is also employed during open heart surgery
where perfusion to the body and brain must stop while cardiac output
is rerouted through a heart lung machine
. Furthermore, biomedical engineers who specialize in bioheat transfer are able to design such medical device
s to perform within a specified range of temperatures and rates of cooling.
From a one-dimensional energy balance in the x-direction:
Where
is the metabolic heat source term and 
is the perfusion heat source term, both per unit volume. The thermal conductivity, 
, is a constant.
Pennes proposed an expression for the perfusion term by assuming that the temperatures of blood entering and exiting capillaries are both constant for any small volume of tissue. We can say that the temperatures of the blood at each state are the same as that of the surroundings, namely the arterial temperature and the local tissue temperature. Now we must define the perfusion rate,
. This is the ratio of the volumetric flow rate of blood per volume of tissue. Thus we have for the perfusion term:
Where
and 
are the density and specific heat capacity of the blood, respectively.
Combining these two equations results in:
Which is the Pennes Bioheat Equation for one-dimensional, steady-state, heat transfer.
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...
in biological systems. In simpler terms, it is the study of how heat moves from one compartment, be it within the body or external to the body, to another compartment in the body. Bioheat transfer has its foundations in the engineering discipline of heat transfer and is itself a subfield of biomedical engineering
Biomedical engineering
Biomedical Engineering is the application of engineering principles and design concepts to medicine and biology. This field seeks to close the gap between engineering and medicine: It combines the design and problem solving skills of engineering with medical and biological sciences to improve...
or bioengineering. In addition, computational techniques to model various bioheat transfer scenarios are widely employed and hold an important place in developing devices and protocols for the medical community.
Constitutive Values
Because modeling bioheat transfer is of the utmost importance in proper device or heating protocol design, constitutive values of various tissues of the body had to be measured early on in the history of bioheat transfer.Of particular importance were the values of specific gravity
Relative density
Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water...
, specific heat, thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
for the various tissues in the body e.g. skin, fat, muscle, bone, and blood. Today, such values can be easily found in various handbooks and study publications such as the CRC Handbook of Mechanical Engineering (2nd Ed.) or the Report of the task group on reference man (1975).
To illustrate the detailed knowledge that is required by the bioheat transfer community, The CRC Handbook of Mechanical Engineering includes a nearly 2 page table of value for thermal conductivity of various organs including but not limited to: kidney, aorta, arterial plaque, blood, liver, spleen, heart, muscle and tumor.
Because of the importance of blood perfusion on thermal equilibria in the body, blood perfusion values were also pursued early in the history of the field. The CRC Handbook of Mechanical Engineering's chapter on Bioheat Transfer includes a nearly 6 page table of blood perfusion values for a similar variety of tissues as the table for thermal conductivity. Greater discussion on the effect of blood perfusion on heat transfer is given in Section 2.
The Cardiovascular System
The cardiovascular systemCirculatory system
The circulatory system is an organ system that passes nutrients , gases, hormones, blood cells, etc...
is the key system by which heat is distributed throughout the body. The blood serves as the vehicle to transport heat from the areas of high heat to areas of lower heat. In general this transfer takes place in the direction from body core to extremities such as the limbs and head. In the case where the extremities are hotter than the core body temperature
Thermoregulation
Thermoregulation is the ability of an organism to keep its body temperature within certain boundaries, even when the surrounding temperature is very different...
, perfusion would serve to transport heat from the extremity back towards the body core. Whether or not the core temperature rises depends on many factors such as the duration of elevated local temperature at the extremity, temperature difference between extremity and core, volume of blood heated above core temperature, and the rate of blood perfusion. This same moderating phenomena of blood perfusion can be applied to local heat transfer problems e.g. heating of a tumor.
Ablative Surgical Procedures
Ablative surgical techniques generally employ some method of energy deposition which destroys cells and tissue with a concomitant increase in temperature at the targeted site. Bioheat transport equations can be applied to the process of energy deposition into the tissue as well as the subsequent conduction/convection heat transport to cells neighboring the targeted site to predict a temperature history and distribution. Such a model could be used to select the most appropriate protocol for the surgery.Various modalities of energy deposition include: radio frequency
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
, laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
, high intensity focused ultrasound
High intensity focused ultrasound
High-Intensity Focused Ultrasound is a highly precise medical procedure using high-intensity focused ultrasound to heat and destroy pathogenic tissue rapidly through ablation...
, etc. These modalities are commonly used in the minimally invasive surgical treatment of cancer
Cancer
Cancer , known medically as a malignant neoplasm, is a large group of different diseases, all involving unregulated cell growth. In cancer, cells divide and grow uncontrollably, forming malignant tumors, and invade nearby parts of the body. The cancer may also spread to more distant parts of the...
. One common type is radiofrequency ablation
Radiofrequency ablation
Radio frequency ablation is a medical procedure where part of the electrical conduction system of the heart, tumor or other dysfunctional tissue is ablated using the heat generated from the high frequency alternating current to treat a medical disorder...
, a type of hyperthermia therapy
Hyperthermia therapy
Hyperthermia therapy is a type of medical treatment in which body tissue is exposed to slightly higher temperatures to damage and kill cancer cells or to make cancer cells more sensitive to the effects of radiation and certain anti-cancer drugs...
.
Cryosurgical Procedures
Cryosugery is a technique which employs the use of low temperatures to destroy cells. The mechanism of death is usually by plasma membrane and protein disruption via physical and osmotic damage when ice crystalsIce crystals
Ice crystals are a small crystalline form of ice including hexagonal columns, hexagonal plates, dendritic crystals, and diamond dust. The highly symmetric shapes are due to depositional growth, namely, direct deposition of water vapour onto the ice crystal...
form within the cytoplasm of the cell. Bioheat transport equations can also be used to model this process.
Therapeutic Hyperthermia & Hypothermia
Heat can be used not only to destroy cells, but also to aid in the recovery of cells and tissues. Such use of heat is sometimes called therapeutic hyperthermia, perhaps to distinguish it from malignant hyperthermiaMalignant hyperthermia
Malignant hyperthermia or malignant hyperpyrexia is a rare life-threatening condition that is usually triggered by exposure to certain drugs used for general anesthesia; specifically, the volatile anesthetic agents and the neuromuscular blocking agent, succinylcholine...
.
An example of therapeutic hyperthermia is the ThermaCare HeatWrap by Procter & Gamble
Procter & Gamble
Procter & Gamble is a Fortune 500 American multinational corporation headquartered in downtown Cincinnati, Ohio and manufactures a wide range of consumer goods....
. The application of heat to injured tissues works to heal target tissues by a temperature dependent vasodilation. This vasodilation increases the mass transport of wastes and nutrients from and to the site of injury. Because damaged tissue is more metabolically active the enhanced mass transport can facilitate more rapid healing.
Hypothermia
Heat transfer is not only study of raising temperatures, but also reducing them. It is commonly understood that lower temperatures help to preserve living or "once living" tissue. For example, foods stored in refrigerators last longer because the metabolic processes of cellular decay and bacterial growth
Bacterial growth
250px|right|thumb|Growth is shown as L = log where numbers is the number of colony forming units per ml, versus T Bacterial growth is the division of one bacterium into two daughter cells in a process called binary fission. Providing no mutational event occurs the resulting daughter cells are...
are slowed due to the lower free energy (e.g. heat) in the refrigerator. This principle is often applied in surgical wards to individuals who experience head trauma
Head injury
Head injury refers to trauma of the head. This may or may not include injury to the brain. However, the terms traumatic brain injury and head injury are often used interchangeably in medical literature....
.
In cases of head trauma, it is common procedure to reduce the body temperature to about 32°C (90°F) which is about 5°C (8.5°F) lower than normal core temperature of 37°C (98.5°F). This presents a good example of how bioheat transfer engineers can contribute to medical treatments. Such a situation would be broken down first into a system, which in this case would include the entire surface of the body. Assuming the individual is submerged in cold water up to the neck and ears, or otherwise surrounded by an environment that can be modeled as a temperature sink, the engineering would model the body as a composite system composed of skin, fast, muscle bone and possibly organs depending on how complex the model must be. The head could be considered a separate system connected to the body via a third major system, the vasculature. The vasculature would bring cooled blood from the submerged body to the brain where there would be some amount of conductive and convection heat transfer based on the passage of blood through the vessels cooling the vessel via forced convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
and the subsequent cooling of the brain via conduction between blood vessel
Blood vessel
The blood vessels are the part of the circulatory system that transports blood throughout the body. There are three major types of blood vessels: the arteries, which carry the blood away from the heart; the capillaries, which enable the actual exchange of water and chemicals between the blood and...
and brain tissue. Each of these heat transfer processes i.e. water to body, body to vasculature, and vasculature to brain would require knowledge of the thermal conductivity, specific heat, density, blood perfusion rate, and diameter of blood vessel at the least to predict the temperature history at any point within the body e.g. to know when the temperature at the center of the head trauma reaches 32°C.
Such application of hypothermia is also employed during open heart surgery
Cardiac surgery
Cardiovascular surgery is surgery on the heart or great vessels performed by cardiac surgeons. Frequently, it is done to treat complications of ischemic heart disease , correct congenital heart disease, or treat valvular heart disease from various causes including endocarditis, rheumatic heart...
where perfusion to the body and brain must stop while cardiac output
Cardiac output
Cardiac output is the volume of blood being pumped by the heart, in particular by a left or right ventricle in the time interval of one minute. CO may be measured in many ways, for example dm3/min...
is rerouted through a heart lung machine
Heart-lung machine
Cardiopulmonary bypass is a technique that temporarily takes over the function of the heart and lungs during surgery, maintaining the circulation of blood and the oxygen content of the body. The CPB pump itself is often referred to as a heart–lung machine or "the pump"...
. Furthermore, biomedical engineers who specialize in bioheat transfer are able to design such medical device
Medical device
A medical device is a product which is used for medical purposes in patients, in diagnosis, therapy or surgery . Whereas medicinal products achieve their principal action by pharmacological, metabolic or immunological means. Medical devices act by other means like physical, mechanical, thermal,...
s to perform within a specified range of temperatures and rates of cooling.
Bioheat Models
Here we present a simplified model of the bioheat equation for steady-state, one-dimensional heat transfer.From a one-dimensional energy balance in the x-direction:
Where
is the metabolic heat source term and is the perfusion heat source term, both per unit volume. The thermal conductivity, , is a constant.Pennes proposed an expression for the perfusion term by assuming that the temperatures of blood entering and exiting capillaries are both constant for any small volume of tissue. We can say that the temperatures of the blood at each state are the same as that of the surroundings, namely the arterial temperature and the local tissue temperature. Now we must define the perfusion rate,
. This is the ratio of the volumetric flow rate of blood per volume of tissue. Thus we have for the perfusion term: Where
and are the density and specific heat capacity of the blood, respectively.Combining these two equations results in:
Which is the Pennes Bioheat Equation for one-dimensional, steady-state, heat transfer.
Training
Most people in that work in the field of bioheat transfer can be considered biomedical engineers. A number of universities grant bachelors degrees in biomedical engineering and bioengineering, but due to the large variety of sub-fields in biomedical engineering the training that undergraduate students receive varies greatly from program to program. Most engineers who have expertise in bioheat transfer received training from academic research labs either as undergraduates or as graduate students.- Undergraduate degreeUndergraduate degreeAn undergraduate degree is a colloquial term for an academic degree taken by a person who has completed undergraduate courses. It is usually offered at an institution of higher education, such as a university...
programs - Graduate degree programs
Bioheat Labs
- The University of Texas at Austin: Kenneth R. Diller, John Pearce, John Hazle
- Virginia Tech: M. Nichole Rylander Christopher G. Rylander
- University of MinnesotaUniversity of MinnesotaThe University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
: Bioheat and Mass Transfer Lab - University of Maryland Baltimore County: Bioheat Transfer Lab
Additional Resources
- CRC Handbook of Mechanical Engineering
- Report of the task group on reference man
- Geigy Scientific Tables