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Study of Thermal relaxation Time (TRT) and the Reason for Non-Consistency of Theoretical Studies with Clinical Reports
Hossein Eshghifard Pasargad Radiation Therapy Co., Jun 2018
Abstract : Thermal Relaxation Time (TRT) was a subject discussed by the concept of selective photothermolysis in treatments that are largely dependent on laser and tissue thermal reactions. Choosing the width of the laser pulse in accordance with the thermal comfort time regardless of the damage function and its related parameters caused a lot of criticism in its effectiveness. Criticisms based on the injury equation and also the thermal transfer equations of the tissue and taking into account the time required for tissue damage at a specified temperature. Each of the articles and clinical records recorded on the weaknesses of the concept of selective photothermolysis that the TRT relies on, and based on this, they have addressed the deficiencies by presenting the opinion, though none of them has a comprehensive look at all factors. Not involved in the correction of the above relationship. The purpose of this article is to investigate the effective variables that have been recorded sporadically in various reports and studies in order to achieve better and more effective clinical outcomes.
Introduction : At the same time, the interaction of laser-tissue and its effects was taken into consideration in the selection of photothermolysis as a result of these studies. Thermal Relaxation Time (TRT) is defined based on this concept, which is selected to determine the appropriate and acceptable pulse width in the treatment and protection of healthy tissue around the target. In this definition, the TRT number is introduced as follows: TRT =
/k
(1)
In which d is the diameter of the target in millimeters and is the thermal emission coefficient in millimeters per second and k is the geometric factor (for a cylindrical target value of 16). Therefore, the pulse length is calculated based on the diameter of the target. Many experiments have shown that if the pulse width is considered only on the basis of the diameter of the target, then the results are not taken correctly. For
example, tests performed by Altshuler et al. [1] were performed on blood vessels and hair follicles. In experiments, it was shown that even with the choice of pulse lengths several times larger than the target TRT, it could be destroyed, so TRT can not be a proper measure for the design of the treatment. The explanation of this paradox is possible based on the thermal transfer equations of the tissue: (2) Where is the time delay in thermal flux and temperature difference in the tissue.
is the time delay for creating a
The general form of the above equation is obtained from a second order Taylor expansion: (3) Energy balance equation The regional equilibrium in the tissue is as follows: +
(4)
Where respectively are the temperature, specific heat capacity, density, and flow rate of the blood flow. is the generated metabolic heat and is the external source of heat. Using equations 3 and 4, we have for the second-order complete equation the heat transfer:
=
(5)
The above equation can be simplified in different conditions and different tissues. For example, in cases where the time delay is small, it is possible to omit quadratic sentences, or even first-order and or, in cases where the time delay is large, one can ignore constant or first-order sentences.
For example, in homogeneous materials with a very small time delay ( to ), the Taylor expansion sentences are deleted and we arrive at the simple equation (1) When the size of laser beam is larger than the thickness of the radiation, onedimensional model of the above equation can be used:
=
(6)
The laser heat source
is defined as follows :
(7) In which
) is the laser beam.
The thermal injury parameter is defined as follows :
= Ln (
(8)
Where is the concentration of tissue protein and degraded
the protein concentration is
When destructive proteins reach 63%, the damage parameter is equal to 1, which means that the tissue is completely damaged.
The injury function equation :
=A
)dt
(9)
A is a repetition factor and E is the activation energy.
Physical - Temperature Parameters of tissue : K = 0.628 w/m.K = 1000 kg/ c = 4187 J/( kg.K ) Physical-thermal parameters of blood: = 1.06 x = 3860 J/ = 1.87 x =
kg/ K /
c
The tissue temperature (T) is a function of the blood flow of the living tissue. The effect of the propagation rate on tissue heat transfer needs more attention. From equation (2) we can conclude that : - .q = k
T
This section shows the heat transfer equation through its conduction The part shows the heat exchange and convection flow. When the tissue temperature is higher than the arterial temperature, the blood circulation has a cooling effect. At first (in the first few seconds), the heat energy transmitted by the blood stream is small. Therefore, surface temperatures do not differ significantly for different values of Over time, the difference in blood flow cooling performance increases. The heat energy transmitted by the blood is proportional to the flow of
blood, thus reducing the temperature with the flow of blood. The temperature obtained from both linear and nonlinear equations is almost the same, but the very small differences cause more severe thermal damage. This suggests that heat injuries in the living tissue are very sensitive to temperature. The metabolic heat generated and blood circulation are important parameters in the living tissue. Blood flow can have a tangible effect on temperature rise. Experiments have shown that the value of the damage parameter is more dependent on the nonlinear heat equation. The reason for this is the effects of the second power of dilatory ( and ) on increasing the temperature of the tissue. Some important points in the above equations are:
1. The energy flux generated does not coincide with the cause of it (temperature change). This is an inconsistency due to the non-homogeneous structure of the biological tissue. 2. The increase in temperature at the target point occurs based on the collection of input and output energy to the target, which enters and exits to various factors, including tissue flow, tissue type, heat source and its physical parameters. 3. The type, location and size of the target play an important role in determining the role of each of the heat transfer methods (conduction, displacement, radiation), and it should be investigated for each specific goal, which of them will have a more effective role. 4. In addition to the heat equations, as shown above, the damage function also plays a very important role in the treatment process. In Equation (9) we can not ignore the time dependence of the introduced parameters. What is fully explained in various articles is the dependence of the temperature necessary to cause irreversible damage to the target's shelf life at that specific temperature. In fact, the only factor determining the irreversible damage to tissue is not temperature. For example, skin destruction at 60 ° C requires a second of time, while the same damage occurs at 70 ° C for 33 milliseconds [2]. Therefore, for the reasons mentioned above, due to the inability of TRT to investigate and analyze the heat treatment processes, the definition of thermal injury time (TDT) was introduced in laboratory and clinical studies to take into account the time needed to change the nature of the protein in one Specific temperatures, and eventually
damaging or protecting the adjacent tissue from damage, can eliminate the defect of the TRT. Of course, this does not mean abandoning TRT, but rather to correct and complete it. Many articles have been published based on the definition of TDT, and various therapeutic protocols have been presented. For example, in a paper published by Murphy and colleagues [2], he addresses the issue of considering the damage function and its non-relation to TRT, which, like many other papers in this field, uses pulse widths based on the concept of TDT And its positive role, especially in choosing longer pulse lengths than what TRT introduces, is better in treatment outcomes. In a comparison, two definitions of TRT and TDT can be summarized as follows: The thermal relaxation time states that if the pulses are longer than the relaxation time, the desired target will not be degraded, and if the pulse length is shorter than the relaxation time, the energy will be blocked at the target and the tissue will be destroyed. This definition is based on the concept of photo thermolysis and is related to the target size. The time of the thermal damage indicates that it is necessary for the target proteins to be irreversibly damaged, which is related to the genus and type of tissue and is defined by the Arrhenius variables. In fact, what should be considered in treatment is destroying the target tissue and protecting adjacent tissues. Protecting adjacent tissues is roughly based on TRT and target tissue damage based on TDT. Recent articles have shown that TDT can be much larger than TRT, which means that it is not necessary to use the minimum width of the pulse defined by TRT to damage the target tissue. Many experiments have shown that pulse widths are much larger than TRT. Especially in the treatment of small vessels, which can be damaged by small pulse widths such as purpura. In fact, the use of high pulse through the protection of the surrounding tissue provides the possibility of using more energy flux to damage the target tissue. Unfortunately, the topic that has not been mentioned in any of the papers is a general look and consideration of all variables involved in treatment. The reason for the use of longer pulses is to allow enough time to damage the protein at a lower temperature. That means using long pulses can be targeted at sufficient time for the destruction process at a suitable temperature, and along with this long pulse can also protect the adjacent tissues.
It is a mistake to note that by increasing the pulses that are used, adjacent tissues will experience longer periods of time at a given temperature, and that the increase in flux along with the increase in pulse length can affect the long-term thermal effects of the adjacent control tissue Is a topic that has not been investigated. As long pulses give the target more chance of staying at the appropriate temperature for destruction, this time can further damage the adjacent tissue. Therefore, simultaneous consideration of TDT for target tissue and TRT for adjacent tissue is necessary. The role of heat transfer methods and the effect of each of them in different tissues should be considered more. For example, the effect of thermal conductivity in the skin is more than blood and deep tissue. The following table summarizes the role of each heat transfer method in different tissues [3] Table (1) The Importance of Heat Transfer Modes in Live Systems [3]
Conduction Tissues important Bone important Blood Vessels Low important Skin unimportant
Transfer ( in liquid ) Low important unimportant important important
Radiation unimportant unimportant unimportant important
A comprehensive theory that can fully reflect the role of all the variables involved in the treatment process should be based on the thermal equation of the tissue, the physical and optical properties of the surrounding tissues, the Arrhenius constants, and the shape and target size of the target. We can not consider the role of long pulses in creating enough time to destroy the target, but ignore the potential damage caused by the same time in the surrounding tissue. The effects of the heat transfer modes, as described in Table 1 in qualitative terms, need to be included in the equations with exact quantities. here are many variables in the body that a certain number can not be considered for them. Even the conditions of the disease, stress and environmental factors also interfere with the accurate determination of the variables, which means that the process of treatment of the presented protocols is also approximated and the physician's skill (knowledge and experience) plays an important role in the outcome of the treatment.
Reference 1. 2.
3.
Altshuler GB.Zenzie HH . Erofeev AV, Smirnov MZ,Anderson, RR, Dierckx C. Contact cooling of the skin.Phys Med Biol 1999:44:1003-1023. M. J. Murphy . P. A. Torstensson, Thermal relaxation time : an outdated concept in photothermal treatments, Laser Med Sci . DOI 10.1007/s10103-013-1445-8 Huang-Wen Huang, Tzyy-Lng Horng . Bioheat Transfer and Thermal Heating fot Tumor Treatment.
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