JBUR-4239; No. of Pages 7 burns xxx (2014) xxx–xxx
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/burns
Rationalization of thermal injury quantification methods: Application to skin burns Benjamin L. Viglianti a, Mark W. Dewhirst b, John P. Abraham c,*, John M. Gorman c, Eph M. Sparrow d a
Department of Radiology, University of Michigan, Ann Arbor, MI 48108, United States Department of Radiation Oncology, Duke University Medical Center, Durham, NC 27710, United States c School of Engineering, University of St. Thomas, St. Paul, MN 55105, United States d Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, United States b
article info
abstract
Article history:
Classification of thermal injury is typically accomplished either through the use of an
Accepted 8 December 2013
equivalent dosimetry method (equivalent minutes at 43 8C, CEM43 8C) or through a thermalinjury-damage metric (the Arrhenius method). For lower-temperature levels, the equivalent
Keywords:
dosimetry approach is typically employed while higher-temperature applications are most
CEM438C
often categorized by injury-damage calculations. The two methods derive from common
Thermal dosimetry
thermodynamic/physical chemistry origins. To facilitate the development of the interre-
Thermal injury
lationships between the two metrics, application is made to the case of skin burns. This
Thermal injury index
thermal insult has been quantified by numerical simulation, and the extracted time-
Hyperthermia
temperature results served for the evaluation of the respective characterizations. The
Thermal ablation
simulations were performed for skin-surface exposure temperatures ranging from 60 to 90 8C, where each surface temperature was held constant for durations extending from 10 to 110 s. It was demonstrated that values of CEM43 at the basal layer of the skin were highly correlated with the depth of injury calculated from a thermal injury integral. Local values of CEM43 were connected to the local cell survival rate, and a correlating equation was developed relating CEM43 with the decrease in cell survival from 90% to 10%. Finally, it was shown that the cell survival/CEM43 relationship for the cases investigated here most closely aligns with isothermal exposure of tissue to temperatures of 50 8C. # 2013 Elsevier Ltd and ISBI. All rights reserved.
1.
Introduction
Quantification of thermal injury to tissue is important for a wide variety of intentional and unintentional thermal exposures. Unintentional exposures lead to burns to skin or internal body regions and the extent of injury must be properly quantified in order for adequate therapy to be applied. On the other hand, many modern medical applications involve the intentional increase of tissue temperature.
Elevating tissue temperature for the purpose of providing therapy for pathological diseases and malfunctions has been practiced for thousands of years [1]. In the oncological environment, for example, hyperthermia is used either as a direct treatment modality or as an adjuvant to enhance other therapies. Direct treatment relies on thermal energy to cause denaturation of the targeted cells. Indirect methods utilize thermal energy as an adjunct to improve the efficacy of the direct cytotoxic therapy [1], such as radiation or chemotherapy [2–5].
* Corresponding author. Tel.: +1 612 963 2169. E-mail addresses: [email protected] (B.L. Viglianti), [email protected] (J.P. Abraham). 0305-4179/$36.00 # 2013 Elsevier Ltd and ISBI. All rights reserved. http://dx.doi.org/10.1016/j.burns.2013.12.005 Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
2
burns xxx (2014) xxx–xxx
Generally, thermal-based treatments are subdivided into two groups with respect to the targeted tissue temperature. Generally, as well as for discussion here, tissue temperatures above 50 8C are reserved for direct treatment, and the therapy is termed ablation. When the target temperatures are between 40 and 45 8C, the term hyperthermia is used to describe the therapy [1,6]. Ablation therapy relies on the direct cytotoxic effect of temperature elevation. This mechanism of cell death is related to denaturing both functional and structural proteins (intra and extra cellular) [6]. The major extracellular structural protein constituent is collagen of various types, all with similar sensitivities to thermal injury [7,8]. Thermal denaturation of collagen is a high-temperature metric of severe thermal damage and represents an upperbound target process in ablation treatments that, when reached, is a sure sign of cellular death and severe vascular disruption. Hyperthermia-based therapies rely on elevating the tissue temperature to relatively non-cytotoxic levels to alter the local physiological environment and/or cellular functions in a way that enhances other treatments. The details of these changes are extensive and have been reviewed elsewhere [1,6,9,10]. The dominant physiological changes involve improved blood flow and oxygenation, stimulation of immune cell migration, and increased vascular permeability. Independent of the heating method used, standardized metrics are needed to quantify the relationship between thermal exposure and damage. This is particularly important when comparing results from different studies, quantifying tissue-dependent sensitivities to heat, or attempting to repeat studies for the purpose therapeutic implementation. Two methods have come into general use for quantifying the deposited thermal energy. The ablation community often uses the damage index or the 50 8C isothermal contour, whereas the hyperthermia community typically uses cumulative equivalent minutes at 43 8C, or the CEM43 method [6,10,11]. Both the damage index and CEM43 methods are based on the underlying premise that tissue damage follows an irreversible first-order chemical reaction with the rate constant following the Arrhenius relationship. Despite this commonality, the two methods are used differently: one to predict the degree of necrosis and the other to guide treatment duration. These methods have been used for the last quarter century, with some rationalizations between them reported in the published literature [11–16]. Here, the two methods are reconciled in what is believed to be a definitive manner. In particular, a specific case study is carried out to facilitate a highly detailed rationalization. Furthermore, for the seemingly the first time, the CEM43 method is used to predict the depth of skin burns. It will also be shown how cell survival results for disparate thermal histories can be brought together and correlated. The application used here for the demonstration has particular importance for the treatment of burns and the results will be compared with literature information on scald wounds. On the other hand, it is expected that the method can also be applied for other situations, such as the intentional application of heat in medical treatments.
2.
Injury quantification methods
2.1.
CEM43 8C method
Cumulative equivalent minutes of thermal treatment at 43 8C (CEM43 8C) (first proposed by Sapareto and Dewey [11]) is commonly used as a standard in the hyperthermia literature to compare different thermal treatment histories to an equivalent heating time at 43 8C. This procedure is discussed in depth in [6,10]. Although the analysis is based on the assumption that thermal damage follows an irreversible first-order chemical reaction, experimental data have demonstrated that observed damage is approximately linear with temperature over a narrow range. Additionally, the dose response curve has inflection points (‘‘breaks’’); the break is related to increased tolerance to thermal injury that is developed during heating [6,10]. There is insufficient data for human tissue to accurately define the breakpoint; most data show that it varies from 43.5 to 47 8C [6,10]. However, Lepock et al. [16] concluded that 43 8C in cell culture likely represents the upper limit at which thermal tolerance can be induced in human cells. For intentional thermal treatments, tissues are often heated to the lower end of the injury-causing temperature range so that the breakpoint has particular importance. On the other hand, for scald wounds where temperatures usually greatly exceed the breakpoint values, its consideration is much less important. In those circumstances, the bulk of the injury occurs well above 43 8C. Because of the presence of a breakpoint, the calculation of CEM43 has to occur in two steps using Eq. (1) separately above and below the breakpoint. CEM43 C ¼ t½RCEM ð43TÞ
(1)
The symbol t is the time of thermal exposure. The timescaling ratio RCEM is the number of minutes needed to compensate for a 1 8C change in the applied therapeutic temperature, either above or below the breakpoint, and T is temperature in degrees Celsius. The breakpoint of 43.5 8C is chosen here, with an RCEM below the breakpoint of 0.233 and above the breakpoint of 0.428. Eq. (1) can also be used in a differential and/or a discretized form if the thermal history is dynamic and known. Z t N X ½RCEM ð43TðtÞÞ dt ¼ ½RCEM ð43Ti Þ Dti (2) CEM43 C ¼ 0
i¼1
However, the process of integration/summation has to account for temperatures that occur both above and below the breakpoint.
2.2.
Damage index/injury integral method
The second metric used to quantify thermal exposure and cell injury is the damage index V. This metric has been widely adopted by tissue ablation practitioners. Thermal ablation generally occurs at higher temperatures than does hyperthermia. Collagen is in high abundance and is, therefore, assumed to be one of the main proteins that are involved with thermal damage at these higher temperatures. The typical thermal
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
3
burns xxx (2014) xxx–xxx
damage process is protein denaturation that follows a firstorder chemical reaction. The reaction state equation, combined with the temperature-dependent reaction rate, gives Z t Cð0Þ Ae½Ea =RTðtÞ dt ¼ Damage index ¼ VðtÞ ¼ ln CðtÞ 0 X Ea ¼ A exp (3) Dt RTðtÞ The damage index V defined by Eq. (3) is the logarithm of the ratio between the number of undamaged cells C(0) present prior to the start of the treatment to the remaining number of undamaged cells at time t indicated by C(t). For example, a damage index V = 0.1 would indicate that 90% of the cells are still viable at the end of the given treatment period, whereas V = 1 would correspond to 36% of the cells still viable. In Eq. (3), A is the frequency factor (1/s), Ea is the activation energy (J/mol), R is the universal gas constant (8.3143 J/mol-K), T is the temperature in Kelvin, and t is the time (s) [7,8,11,12]. If the temperature–time curve is discretized, the right-hand member of Eq. (3) can be used.
2.3.
Relationship between the two methods
The CEM43 and the Damage Index both originate from Arrhenius’ experimental observations in the 1880s [17,18]. The results and their interrelationship are very well described by [19–22]. Eyring’s introduction of the activation energy concept in the 1930s [20–24], that the reactants must surmount an activation energy barrier in order to form product, explained Arrhenius’ experimental observations and resulted in the theory of absolute reaction rates. When the time-scaling ratio RCEM is derived from the constant-rate region of cell survival curves where the slope is D0(T) and where the surviving fraction is C(t)/C(0), the relationship between CEM43 and V is deceptively simple, that is V¼
3.
CEM43 D0 ð43Þ
(4)
Application to skin burns
With the foregoing as background, attention will now be turned to a case study in which the thermal damage to skin will be quantified by both the already identified dosimetry methods. The situation in question is the heating of the exposed surface of the skin by a heat source which imposes a constant elevated temperature for a prescribed duration. Previous analyses of this situation [25,26] were handicapped by incorrect information from the literature relevant to the evaluation of the cell damage index of Eq. (3). Those investigators used Ea of 6.27 105 J/mole and A = 3.1 1098 1/s as originally presented by Henriques and Moritz in their classic studies of skin burns [27–30]. Although these values have been used for many years by numerous investigators, it has been shown that they actually do not fit the Henriques– Moritz data very well. Diller and Klutke [31] reanalyzed the data for temperatures below 52 8C and provided revised coefficients of Ea of 6.04 105 J/mole and A = 1.30 1095 1/s.
Fig. 1 – Image of the tissue layers used in the computational model.
The present analysis of the problem covered the range of prescribed skin surface temperatures from 60 to 90 8C and exposure times from 10 to 110 s. The adopted tissue model consisted of four layers: epidermis, dermis, subcutaneous tissue, and muscle, as illustrated in Fig. 1. The thicknesses of the various layers used in the simulations are shown in Table 1, and the values of the thermal properties for each layer are listed in Table 2. These properties and layer thicknesses were carefully selected from a comprehensive review of the available literature. The Pennes bioheat equation [32] was used to model thermal transport in the tissue bed. ðrcÞt
@Tt @Tt ¼ Kt 2 þ ðrcÞb vðTcore Tt Þ @t @x
(5)
The bioheat equation takes into account the time-dependent heat transfer due to thermal conduction with k as the thermal conductivity and blood perfusion as v. The quantity rc represents the volumetric heat capacity, and the subscripts t and b respectively refer to tissue and blood. The term (Tcore Tt) is the temperature difference between the incoming blood and the local tissue temperature. Results from the solution of Eq. (5) provided the temperature profiles Tt(x,t) needed for the evaluation of the damage index as a function of location and time. With the use of this same timetemperature data, the CEM43 8C at the basal layer and the depth of thermal injury can also be extracted. The basal-layer location was chosen as the reference for the CEM43 8C calculations because of its consistent use by practitioners to characterize thermal injury [33,34], and it is the location of the stem cells that generate the dermis/epidermis skin. Thermal necrosis was defined as corresponding to V = 1 (i.e., the cell damage process is 63.2% complete). The basis for the selection of this value of V is partly from historical
Table 1 – Thicknesses of tissue layers used in model (mm). Epidermis
Dermis
SubQ
Muscle
0.08
2
10
30
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
4
burns xxx (2014) xxx–xxx
Table 2 – Summary of properties used in numerical simulations. Property
Epidermis
Dermis
SubQ
Muscle
k (W/m 8C) c (kJ/kg 8C) r (kg/m3) v (1/s)
0.22 3.6 1200 0
0.4 3.6 1200 0.00125
0.2 2.5 1000 0.00125
0.45 3.8 1000 0.00125
tradition which related temperatures at the basal layer to complete epidermal necrosis. Furthermore, since the injury parameters used in the model were based on experiments of [33,34], it is appropriate to use that measure. The V = 1 criterion corresponding to local cell death has been widely used (e.g., [35–39]); whereas in other studies, values of V = 0.53, 1.0, and 104 have been used to characterize first-, second-, and third-degree burns, respectively (e.g., [40–44]). Temperature solutions were obtained for 12 individual thermal situations, and a listing of these cases is provided in Table 3. A representative temperature distribution is shown in Fig. 2 which shows temperatures at various tissue depths and at various times after the onset of heating. In this case, the duration of heating was 10 s with the surface temperature maintained constant at a 60 8C. After the initial 10-s exposure, convective heat loss occurs characterized by a convective coefficient of 10 W/m2 8C to a fluid environment at 20 8C. At a later time (20 s), the surface temperature is seen to have decreased and the thermal penetration within the tissue has spread, representing the propagation of the thermal energy into the tissue. The CEM43 8C at the basal location was found numerically using Eq. (2) and the in-vitro parameters (R = 0.233 below 43.5 8C and 0.428 above 43.5 8C). The results of these calculations are shown in Fig. 3. There, values of the log(CEM43 8C) are correlated with the burn injury depth divided by the square root of the time following the onset of the thermal insult. The scaling by the square root of time is encountered in the analytical solution for the thermal wave penetration problem and is a common approach in thermal modeling. It is seen that there is a consistent relationship between the quantities of interest, despite the very wide variation of exposure temperatures and exposure durations used to generate the correlation.
In Fig. 3, an algebraic trendline is included to quantify the correlation, facilitating prediction of the extent of the burn injury if the CEM43 8C at the base of the epidermal layer is known along with the exposure time. While it is generally understood that the CEM43 8C method can be used to relate thermal exposures over a limited range of temperatures, its utilization for higher-temperature cases is novel. The finding that there is a clear relationship between burn depth and CEM43 8C at the basal layer is independent of the temperature range over which CEM43 8C comparisons can be made. It is believed that this finding has not been demonstrated before and is significant because of its simplicity and universality. Another connection between the CEM43 8C and the injury integral is the development of local CEM43 8C thresholds that
Fig. 2 – Tissue temperature results for a skin surface temperature of 60 8C for an exposure time of 10 s.
Table 3 – Summary of conditions used for the calculations. Case number 1 2 3 4 5 6 7 8 9 10 11 12
Exposure temp. (8C)
Exposure duration (s)
60 60 60 70 70 70 80 80 80 90 90 90
10 20 110 10 20 110 10 20 110 10 20 110
Fig. 3 – Relationship between CEM43 8C at the basal layer to the depth of burn injury and the time of exposure. Burn depth values are in mm and exposure time is in seconds.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7 burns xxx (2014) xxx–xxx
5
Fig. 4 – Relationship between % of cells surviving thermal insult and CEM43 8C.
correspond to V = 1. Such an analysis will now be described. The distribution of the CEM43 8C throughout the tissue layers following thermal insult is plotted against the predicted cell survival (with Ea = 6.04 105 J/mole and A = 1.30 1095 1/s, taken from [31]). The outcome of this confluence is shown in Fig. 4. The general trend conveyed by the figure is expected, high cell survival for low CEM43 8C, and cell survival decreasing markedly as CEM43 8C increases. It is seen that there is a significant decrease in cell viability as CEM43 8C approaches and exceeds 100 min. The inset in Fig. 4 shows a subset of the data which extends from CEM43 8C of approximately 100–10,000. This range was selected because it corresponds to a decrease in cell viability from approximately 90% to 10%. In this range, it was possible to correlate local cell survival with local CEM43 8C values. Such a correlation is indicated in the inset of Fig. 4. For CEM43 8C values less than approximately 100, almost all cells survive whereas for CEM43 8C values exceeding approximately 10,000, virtually all cells have been destroyed. Although the data shown in Fig. 4 have not collapsed upon a single curve and there is some variation among the data points, the extent of congruence is remarkable. The high degree of the agreement is made more apparent by comparing the results of Fig. 4 with the results that would have been obtained if the fraction of surviving cells (calculated by the injury integral) were compared with CEM values for isothermal exposures (local tissue temperatures brought to and held fixed at an elevated temperature). Such a comparison is shown in Fig. 5. There, it is envisioned that cells are raised instantaneously and homogeneously to one of the temperatures indicated in the figure and held at that temperature indefinitely. This is contrasted with the situation of Fig. 4 where the skin surface is heated and the heat flows by diffusion to the deeper tissue regions. For the instantaneous/homogenous case, Eqs. (1) and (3) are applied for the duration of the exposure to fixed temperature values. It can be seen from the figure that there is a very wide variation in the relationship between CEM and cell survival under this condition. For the temperatures listed in
the figure, none of the curves are coincident. This finding suggests that for isothermal exposures at these temperatures, there is no unique relationship between CEM values and the accumulated injury. Overlaid on the graph of Fig. 5 are the results from Fig. 4. It is seen that the discrete points which correspond to the skinsurface-heating case are most similar to isothermal exposures in the 50 8C range. This appraisal was made by evaluating the equivalent isothermal temperatures for which the largest amount of cellular damage occurred (from 100% survival to 10% survival). While at first it might be surprising that the results coincided in a very small range of isothermal dose injury models, upon reflection there is sound justification for this. The thermal exposures used in the calculations ranged from 10 to 110 s. For durations of this duration, temperatures of 50 8C are required for thermal necrosis.
Fig. 5 – Relationship between % of cells surviving thermal insult and CEM43 8C for exposures that are instantaneous and isothermal at temperature levels designated in the graph. Also shown on the graph are results from Fig. 4 which are outcomes of the present simulations.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
6
burns xxx (2014) xxx–xxx
rate, and a correlating equation was developed for the decrease in cell survival from 90% to 10%. Finally, it was shown that the cell survival/CEM43 relationship for the cases investigated here most closely aligns with isothermal exposure of tissue to temperatures of 50 8C.
Conflict of interest statement The authors declare no conflict of interest.
references Fig. 6 – Relationship between local CEM43 8C and % surviving cells for the range 1000 < CEM43 8C < 10,000.
From a clinical treatment standpoint, another way to use the results of this modeling technique is through a relationship of the burn depth to the exposure temperature and the exposure duration. Such a relationship was developed in [25] and is repeated here as Burn depth ¼ 2:9302 þ 0:0473T 0:0317t þ 0:000913Tt
(6)
Where the burn depth is in mm, the time is in seconds, and the temperature in 8C. This equation, or the equation shown in Fig. 3 allow a treating physician to quickly estimate a burn depth based on the skin surface experience. Here, as elsewhere, burn depth was defined as V = 1 however [25] showed that this quantification closely matched the burn injury depths observed by treating physicians in clinical setting. Finally, it is useful to graphically present the correlation from Fig. 4 in an expanded format. That presentation, shown in Fig. 6, relates the percentage of surviving cells to the instantaneous CEM43 8C value. As expected, as the CEM 43 8C increases, the survival rate decreases. The graph helps provide perspective for the results of the prior images by relating the CEM43 8C quantity to a physiologic outcome.
4.
Concluding remarks
The focus of this research has been to unearth and quantify interrelationships between the two established means of classifying thermal injury. Those means, CEM43 8C and the thermal injury index, have been respectively employed by practitioners of the hyperthermic temperature range and those concerned with tissue ablation. Although it is well established that these two metrics stem from a common base, other interrelations between them for a practical situation (for skin burns) have not heretofore been disclosed. The implementation of the research was accomplished by means of numerical simulation. The variations of temperature with time and with sub-surface depth provided the inputs needed for the reconciliation of the two indices. It was demonstrated that values of CEM43 at the basal layer of the skin were highly correlated with the depth of injury calculated from an injury integral. In addition, relationships between local values of CEM43 were connected to the local cell survival
[1] Hong WK. American Association for Cancer Research. Cancer Medicine, 8th ed., Shelton, Connecticut: People’s Medical Pub. House; 2010. [2] Kong G, Braun RD, Dewhirst MW. Characterization of the effect of hyperthermia on nanoparticle extravasation from tumor vasculature. Cancer Research 2001;61(7):3027–32. [3] Ponce AM, Viglianti BL, Yu D, Yarmolenko PS, Michelich CR, Woo J, et al. Magnetic resonance imaging of temperaturesensitive liposome release: drug dose painting and antitumor effects. Journal of the National Cancer Institute 2007;99(1):53–63. [4] Brizel DM, Scully SP, Harrelson JM, Layfield LJ, Dodge RK, Charles HC, et al. Radiation therapy and hyperthermia improve the oxygenation of human soft tissue sarcomas. Cancer Research 1996;56(23):5347–50. [5] Brizel DM, Scully SP, Harrelson JM, Layfield LJ, Bean JM, Prosnitz LR, et al. Tumor oxygenation predicts for the likelihood of distant metastases in human soft tissue sarcoma. Cancer Research 1996;56(5):941–3. [6] Dewhirst MW, Viglianti BL, Lora-Michiels M, Hanson M, Hoopes PJ. Basic principles of thermal dosimetry and thermal thresholds for tissue damage from hyperthermia. International Journal of Hyperthermia 2003;19(3):267–94. [7] Pearce JA, Thomsen S. Kinetic models of laser-tissue fusion processes. Biomedical Sciences Instrumentation 1993;29:355–60. [8] McMurray T, Pearce JA. Thermal damage quantification utilizing tissue birefringence color image analysis. Biomedical Sciences Instrumentation 1993;29:235–42. [9] Dewhirst MW, Lora-Michiels M, Viglianti BL, Dewey WC, Repacholi M. Carcinogenic effects of hyperthermia. International Journal of Hyperthermia 2003;19(3):236–51. [10] Yarmolenko PS, Moon EJ, Landon C, Manzoor A, Hochman DW, Viglianti BL, et al. Thresholds for thermal damage to normal tissues: an update. International Journal of Hyperthermia 2011;27(4):320–43. [11] Sapareto SA, Dewey WC. Thermal dose determination in cancer therapy. International Journal of Radiation Oncology Biology Physics 1984;10(6):787–800. [12] He X, Bhowmick S, Bischof JC. Thermal therapy in urologic systems: a comparison of Arrhenius and thermal isoeffective dose models in predicting hyperthermic injury. Journal of Biomechanical Engineering 2009;131: 71–7450. [13] Prakash P, Ciederich CJ. Considerations for theoretical modeling of thermal ablation with catheter-based ultrasonic sources: implications for treatment, planning, monitoring, and control. International Journal of Hyperthermia 2012;28:69–86. [14] Reddy G, Dreher MR, Rossman C, Wood BJ, Haemmerich D. Cytotoxicity of hepatocellular carcinoma cells to hyperthermic and ablative temperature exposures: in vitro
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7 burns xxx (2014) xxx–xxx
[15]
[16]
[17]
[18] [19]
[20]
[21] [22]
[23] [24]
[25]
[26]
[27]
[28]
[29]
studies and mathematical modelling. International Journal of Hyperthermia 2013;29:318–23. Pearce JA. Comparative analysis of mathematical models of cell death and thermal damage processes. International Journal of Hyperthermia 2013;29:262–80. Lepock JR. Cellular effects of hyperthermia: relevance to the minimum dose for thermal damage. International Journal of Hyperthermia 2003;19(3):252–66. Arrhenius S. Uber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Sauren On the reaction rate in the inversion of cane sugar by acids Zeitschrift fur Physikalische Chemie 1889;4:226–48. Arrhenius S. Quantitative laws in biological chemistry. London: G. Bell & Sons; 1915: 184. Johnson FH, Eyring H, Stover BJ. The theory of rate processes in biology and medicine. New York: John Wiley & Sons; 1974. Eyring H. The energy of activation for bimolecular reactions involving hydrogen and the halogens, according to quantum mechanics. Journal of the American Chemical Society 1931;53:2537–49. Eyring H. The activated complex in chemical reactions. Journal of Chemical Physics 1935;3(2):107–15. ¨ ber Einfache Gasreaktionen On Eyring H, Polyani M. U simple gas reactions Zeitschrift fur Physikalische Chemie B 1931;12:279–311. Polyani M. Atomic reactions. London: Williams and Norgate; 1932. Pearce JA. Relationship between Arrhenius models of thermal damage and the CEM 43 thermal dose. Energybased Treatment of Tissue and Assessment V, vol. 7181. San Jose, CA, United States: SPIE, P.O. Box 10, Bellingham, WA 98227-0010, United States; 2009. 718104-718101–718104718115. Abraham JP, Hennessey MP, Minkowycz WJ. A simple algebraic model to predict burn depth and injury. International Communications in Heat and Mass Transfer 2011;38:1169–71. Johnson NN, Abraham JP, Helgeson ZI, Minkowycz WJ, Sparrow M. An archive of skin-layer thicknesses and properties and calculations of scald burns with comparisons to experimental observations. Journal of Thermal Science and Engineering Applications 2011;3:011003. Henriques FC. Studies of thermal injury, V. The predictability and significance of thermally induced rate processes leading to irreversible epidermal injury. Archives of Pathology 1947;43:489–502. Henriques FC, Moritz AR. Studies of thermal injury in the conduction of heat to and through skin and the temperatures attained therein: a theoretical and experimental investigation. American Journal of Pathology 1947;23:531–49. Moritz AR. Studies of thermal injury III. The pathology and pathogenesis of cutaneous burns: an experimental
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42] [43]
[44]
study. American Journal of Pathology 1947; 23:915–34. Moritz AR, Henriques FC. Studies in thermal injury II: the relative importance of time and surface temperature in the causation of cutaneous burns. American Journal of Pathology 1947;23:695–720. Diller KR, Klutke GA. Accuracy analysis of the Henriques model for predicting thermal burn injury. Advances in Bioheat and Mass Transfer Volume HTD 268: ASME Heat Transfer Division 1993;117–23. Pennes HH. Analysis of tissue and arterial blood temperatures in resting human forearm. Journal of Applied Physics 1948;1:93–133. Henriques FC, Moritz AR. 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):530–49. Henriques Jr FC. Studies of thermal injury; the predictability and the significance of thermally induced rate processes leading to irreversible epidermal injury. Archives of Pathology 1947;43(5):489–502. Agah R, Pearce JA, Welch AJ, Motamedi M. Rate process model for arterial tissue thermal damage: implications on vessel photocoagulation. Lasers in Surgery and Medicine 1994;15(2):176–84. Rylander MN, Diller KR, Wang S, Aggarwal SJ. Correlation of HSP70 expression and cell viability following thermal stimulation of bovine aortic endothelial cells. Journal of Biomechanical Engineering 2005;127(5):751–7. Stoll AM, Greene LC. Relationship between pain and tissue damage due to thermal radiation. Journal of Applied Physiology 1959;14(3):373–82. Torpea BI, Lee RC. Thermal injury kinetics in electrical trauma. Journal of Biomechanical Engineering 1992;114:241–50. Zhang A, Xu LX. Numerical bioheat transfer in tumor detection and treatment. In: Advances in numerical heat transfer. New York, NY: CRC Press; 2009. Dai W, Wang H, Jordan PM, Mickens RE, Bejan A. A mathematical model for skin burn injury induced by radiation heating. International Journal of Heat and Mass Transfer 2008;51:5497–510. Diller KR, Hayes LJ. Analysis of tissue injury by burning: comparison of in situ and skin flat models. International Journal of Heat and Mass Transfer 1991;34:1393–406. Roselli RJ, Diller KR. Biotransport: principles and applications. New York, NY: Springer; 2011. Rubinsky B. Numerical bioheat transfer. In: Handbook of numerical heat transfer. Hoboken, NJ: John Wiley and Sons; 2006. Sun J, Zhang A, Xu LX. Evaluation of alternative cooling and heating for tumor treatment. International Journal of Heat and Mass Transfer 2008;51:5478–85.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
7
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/burns
Rationalization of thermal injury quantification methods: Application to skin burns Benjamin L. Viglianti a, Mark W. Dewhirst b, John P. Abraham c,*, John M. Gorman c, Eph M. Sparrow d a
Department of Radiology, University of Michigan, Ann Arbor, MI 48108, United States Department of Radiation Oncology, Duke University Medical Center, Durham, NC 27710, United States c School of Engineering, University of St. Thomas, St. Paul, MN 55105, United States d Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, United States b
article info
abstract
Article history:
Classification of thermal injury is typically accomplished either through the use of an
Accepted 8 December 2013
equivalent dosimetry method (equivalent minutes at 43 8C, CEM43 8C) or through a thermalinjury-damage metric (the Arrhenius method). For lower-temperature levels, the equivalent
Keywords:
dosimetry approach is typically employed while higher-temperature applications are most
CEM438C
often categorized by injury-damage calculations. The two methods derive from common
Thermal dosimetry
thermodynamic/physical chemistry origins. To facilitate the development of the interre-
Thermal injury
lationships between the two metrics, application is made to the case of skin burns. This
Thermal injury index
thermal insult has been quantified by numerical simulation, and the extracted time-
Hyperthermia
temperature results served for the evaluation of the respective characterizations. The
Thermal ablation
simulations were performed for skin-surface exposure temperatures ranging from 60 to 90 8C, where each surface temperature was held constant for durations extending from 10 to 110 s. It was demonstrated that values of CEM43 at the basal layer of the skin were highly correlated with the depth of injury calculated from a thermal injury integral. Local values of CEM43 were connected to the local cell survival rate, and a correlating equation was developed relating CEM43 with the decrease in cell survival from 90% to 10%. Finally, it was shown that the cell survival/CEM43 relationship for the cases investigated here most closely aligns with isothermal exposure of tissue to temperatures of 50 8C. # 2013 Elsevier Ltd and ISBI. All rights reserved.
1.
Introduction
Quantification of thermal injury to tissue is important for a wide variety of intentional and unintentional thermal exposures. Unintentional exposures lead to burns to skin or internal body regions and the extent of injury must be properly quantified in order for adequate therapy to be applied. On the other hand, many modern medical applications involve the intentional increase of tissue temperature.
Elevating tissue temperature for the purpose of providing therapy for pathological diseases and malfunctions has been practiced for thousands of years [1]. In the oncological environment, for example, hyperthermia is used either as a direct treatment modality or as an adjuvant to enhance other therapies. Direct treatment relies on thermal energy to cause denaturation of the targeted cells. Indirect methods utilize thermal energy as an adjunct to improve the efficacy of the direct cytotoxic therapy [1], such as radiation or chemotherapy [2–5].
* Corresponding author. Tel.: +1 612 963 2169. E-mail addresses: [email protected] (B.L. Viglianti), [email protected] (J.P. Abraham). 0305-4179/$36.00 # 2013 Elsevier Ltd and ISBI. All rights reserved. http://dx.doi.org/10.1016/j.burns.2013.12.005 Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
2
burns xxx (2014) xxx–xxx
Generally, thermal-based treatments are subdivided into two groups with respect to the targeted tissue temperature. Generally, as well as for discussion here, tissue temperatures above 50 8C are reserved for direct treatment, and the therapy is termed ablation. When the target temperatures are between 40 and 45 8C, the term hyperthermia is used to describe the therapy [1,6]. Ablation therapy relies on the direct cytotoxic effect of temperature elevation. This mechanism of cell death is related to denaturing both functional and structural proteins (intra and extra cellular) [6]. The major extracellular structural protein constituent is collagen of various types, all with similar sensitivities to thermal injury [7,8]. Thermal denaturation of collagen is a high-temperature metric of severe thermal damage and represents an upperbound target process in ablation treatments that, when reached, is a sure sign of cellular death and severe vascular disruption. Hyperthermia-based therapies rely on elevating the tissue temperature to relatively non-cytotoxic levels to alter the local physiological environment and/or cellular functions in a way that enhances other treatments. The details of these changes are extensive and have been reviewed elsewhere [1,6,9,10]. The dominant physiological changes involve improved blood flow and oxygenation, stimulation of immune cell migration, and increased vascular permeability. Independent of the heating method used, standardized metrics are needed to quantify the relationship between thermal exposure and damage. This is particularly important when comparing results from different studies, quantifying tissue-dependent sensitivities to heat, or attempting to repeat studies for the purpose therapeutic implementation. Two methods have come into general use for quantifying the deposited thermal energy. The ablation community often uses the damage index or the 50 8C isothermal contour, whereas the hyperthermia community typically uses cumulative equivalent minutes at 43 8C, or the CEM43 method [6,10,11]. Both the damage index and CEM43 methods are based on the underlying premise that tissue damage follows an irreversible first-order chemical reaction with the rate constant following the Arrhenius relationship. Despite this commonality, the two methods are used differently: one to predict the degree of necrosis and the other to guide treatment duration. These methods have been used for the last quarter century, with some rationalizations between them reported in the published literature [11–16]. Here, the two methods are reconciled in what is believed to be a definitive manner. In particular, a specific case study is carried out to facilitate a highly detailed rationalization. Furthermore, for the seemingly the first time, the CEM43 method is used to predict the depth of skin burns. It will also be shown how cell survival results for disparate thermal histories can be brought together and correlated. The application used here for the demonstration has particular importance for the treatment of burns and the results will be compared with literature information on scald wounds. On the other hand, it is expected that the method can also be applied for other situations, such as the intentional application of heat in medical treatments.
2.
Injury quantification methods
2.1.
CEM43 8C method
Cumulative equivalent minutes of thermal treatment at 43 8C (CEM43 8C) (first proposed by Sapareto and Dewey [11]) is commonly used as a standard in the hyperthermia literature to compare different thermal treatment histories to an equivalent heating time at 43 8C. This procedure is discussed in depth in [6,10]. Although the analysis is based on the assumption that thermal damage follows an irreversible first-order chemical reaction, experimental data have demonstrated that observed damage is approximately linear with temperature over a narrow range. Additionally, the dose response curve has inflection points (‘‘breaks’’); the break is related to increased tolerance to thermal injury that is developed during heating [6,10]. There is insufficient data for human tissue to accurately define the breakpoint; most data show that it varies from 43.5 to 47 8C [6,10]. However, Lepock et al. [16] concluded that 43 8C in cell culture likely represents the upper limit at which thermal tolerance can be induced in human cells. For intentional thermal treatments, tissues are often heated to the lower end of the injury-causing temperature range so that the breakpoint has particular importance. On the other hand, for scald wounds where temperatures usually greatly exceed the breakpoint values, its consideration is much less important. In those circumstances, the bulk of the injury occurs well above 43 8C. Because of the presence of a breakpoint, the calculation of CEM43 has to occur in two steps using Eq. (1) separately above and below the breakpoint. CEM43 C ¼ t½RCEM ð43TÞ
(1)
The symbol t is the time of thermal exposure. The timescaling ratio RCEM is the number of minutes needed to compensate for a 1 8C change in the applied therapeutic temperature, either above or below the breakpoint, and T is temperature in degrees Celsius. The breakpoint of 43.5 8C is chosen here, with an RCEM below the breakpoint of 0.233 and above the breakpoint of 0.428. Eq. (1) can also be used in a differential and/or a discretized form if the thermal history is dynamic and known. Z t N X ½RCEM ð43TðtÞÞ dt ¼ ½RCEM ð43Ti Þ Dti (2) CEM43 C ¼ 0
i¼1
However, the process of integration/summation has to account for temperatures that occur both above and below the breakpoint.
2.2.
Damage index/injury integral method
The second metric used to quantify thermal exposure and cell injury is the damage index V. This metric has been widely adopted by tissue ablation practitioners. Thermal ablation generally occurs at higher temperatures than does hyperthermia. Collagen is in high abundance and is, therefore, assumed to be one of the main proteins that are involved with thermal damage at these higher temperatures. The typical thermal
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
3
burns xxx (2014) xxx–xxx
damage process is protein denaturation that follows a firstorder chemical reaction. The reaction state equation, combined with the temperature-dependent reaction rate, gives Z t Cð0Þ Ae½Ea =RTðtÞ dt ¼ Damage index ¼ VðtÞ ¼ ln CðtÞ 0 X Ea ¼ A exp (3) Dt RTðtÞ The damage index V defined by Eq. (3) is the logarithm of the ratio between the number of undamaged cells C(0) present prior to the start of the treatment to the remaining number of undamaged cells at time t indicated by C(t). For example, a damage index V = 0.1 would indicate that 90% of the cells are still viable at the end of the given treatment period, whereas V = 1 would correspond to 36% of the cells still viable. In Eq. (3), A is the frequency factor (1/s), Ea is the activation energy (J/mol), R is the universal gas constant (8.3143 J/mol-K), T is the temperature in Kelvin, and t is the time (s) [7,8,11,12]. If the temperature–time curve is discretized, the right-hand member of Eq. (3) can be used.
2.3.
Relationship between the two methods
The CEM43 and the Damage Index both originate from Arrhenius’ experimental observations in the 1880s [17,18]. The results and their interrelationship are very well described by [19–22]. Eyring’s introduction of the activation energy concept in the 1930s [20–24], that the reactants must surmount an activation energy barrier in order to form product, explained Arrhenius’ experimental observations and resulted in the theory of absolute reaction rates. When the time-scaling ratio RCEM is derived from the constant-rate region of cell survival curves where the slope is D0(T) and where the surviving fraction is C(t)/C(0), the relationship between CEM43 and V is deceptively simple, that is V¼
3.
CEM43 D0 ð43Þ
(4)
Application to skin burns
With the foregoing as background, attention will now be turned to a case study in which the thermal damage to skin will be quantified by both the already identified dosimetry methods. The situation in question is the heating of the exposed surface of the skin by a heat source which imposes a constant elevated temperature for a prescribed duration. Previous analyses of this situation [25,26] were handicapped by incorrect information from the literature relevant to the evaluation of the cell damage index of Eq. (3). Those investigators used Ea of 6.27 105 J/mole and A = 3.1 1098 1/s as originally presented by Henriques and Moritz in their classic studies of skin burns [27–30]. Although these values have been used for many years by numerous investigators, it has been shown that they actually do not fit the Henriques– Moritz data very well. Diller and Klutke [31] reanalyzed the data for temperatures below 52 8C and provided revised coefficients of Ea of 6.04 105 J/mole and A = 1.30 1095 1/s.
Fig. 1 – Image of the tissue layers used in the computational model.
The present analysis of the problem covered the range of prescribed skin surface temperatures from 60 to 90 8C and exposure times from 10 to 110 s. The adopted tissue model consisted of four layers: epidermis, dermis, subcutaneous tissue, and muscle, as illustrated in Fig. 1. The thicknesses of the various layers used in the simulations are shown in Table 1, and the values of the thermal properties for each layer are listed in Table 2. These properties and layer thicknesses were carefully selected from a comprehensive review of the available literature. The Pennes bioheat equation [32] was used to model thermal transport in the tissue bed. ðrcÞt
@Tt @Tt ¼ Kt 2 þ ðrcÞb vðTcore Tt Þ @t @x
(5)
The bioheat equation takes into account the time-dependent heat transfer due to thermal conduction with k as the thermal conductivity and blood perfusion as v. The quantity rc represents the volumetric heat capacity, and the subscripts t and b respectively refer to tissue and blood. The term (Tcore Tt) is the temperature difference between the incoming blood and the local tissue temperature. Results from the solution of Eq. (5) provided the temperature profiles Tt(x,t) needed for the evaluation of the damage index as a function of location and time. With the use of this same timetemperature data, the CEM43 8C at the basal layer and the depth of thermal injury can also be extracted. The basal-layer location was chosen as the reference for the CEM43 8C calculations because of its consistent use by practitioners to characterize thermal injury [33,34], and it is the location of the stem cells that generate the dermis/epidermis skin. Thermal necrosis was defined as corresponding to V = 1 (i.e., the cell damage process is 63.2% complete). The basis for the selection of this value of V is partly from historical
Table 1 – Thicknesses of tissue layers used in model (mm). Epidermis
Dermis
SubQ
Muscle
0.08
2
10
30
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
4
burns xxx (2014) xxx–xxx
Table 2 – Summary of properties used in numerical simulations. Property
Epidermis
Dermis
SubQ
Muscle
k (W/m 8C) c (kJ/kg 8C) r (kg/m3) v (1/s)
0.22 3.6 1200 0
0.4 3.6 1200 0.00125
0.2 2.5 1000 0.00125
0.45 3.8 1000 0.00125
tradition which related temperatures at the basal layer to complete epidermal necrosis. Furthermore, since the injury parameters used in the model were based on experiments of [33,34], it is appropriate to use that measure. The V = 1 criterion corresponding to local cell death has been widely used (e.g., [35–39]); whereas in other studies, values of V = 0.53, 1.0, and 104 have been used to characterize first-, second-, and third-degree burns, respectively (e.g., [40–44]). Temperature solutions were obtained for 12 individual thermal situations, and a listing of these cases is provided in Table 3. A representative temperature distribution is shown in Fig. 2 which shows temperatures at various tissue depths and at various times after the onset of heating. In this case, the duration of heating was 10 s with the surface temperature maintained constant at a 60 8C. After the initial 10-s exposure, convective heat loss occurs characterized by a convective coefficient of 10 W/m2 8C to a fluid environment at 20 8C. At a later time (20 s), the surface temperature is seen to have decreased and the thermal penetration within the tissue has spread, representing the propagation of the thermal energy into the tissue. The CEM43 8C at the basal location was found numerically using Eq. (2) and the in-vitro parameters (R = 0.233 below 43.5 8C and 0.428 above 43.5 8C). The results of these calculations are shown in Fig. 3. There, values of the log(CEM43 8C) are correlated with the burn injury depth divided by the square root of the time following the onset of the thermal insult. The scaling by the square root of time is encountered in the analytical solution for the thermal wave penetration problem and is a common approach in thermal modeling. It is seen that there is a consistent relationship between the quantities of interest, despite the very wide variation of exposure temperatures and exposure durations used to generate the correlation.
In Fig. 3, an algebraic trendline is included to quantify the correlation, facilitating prediction of the extent of the burn injury if the CEM43 8C at the base of the epidermal layer is known along with the exposure time. While it is generally understood that the CEM43 8C method can be used to relate thermal exposures over a limited range of temperatures, its utilization for higher-temperature cases is novel. The finding that there is a clear relationship between burn depth and CEM43 8C at the basal layer is independent of the temperature range over which CEM43 8C comparisons can be made. It is believed that this finding has not been demonstrated before and is significant because of its simplicity and universality. Another connection between the CEM43 8C and the injury integral is the development of local CEM43 8C thresholds that
Fig. 2 – Tissue temperature results for a skin surface temperature of 60 8C for an exposure time of 10 s.
Table 3 – Summary of conditions used for the calculations. Case number 1 2 3 4 5 6 7 8 9 10 11 12
Exposure temp. (8C)
Exposure duration (s)
60 60 60 70 70 70 80 80 80 90 90 90
10 20 110 10 20 110 10 20 110 10 20 110
Fig. 3 – Relationship between CEM43 8C at the basal layer to the depth of burn injury and the time of exposure. Burn depth values are in mm and exposure time is in seconds.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7 burns xxx (2014) xxx–xxx
5
Fig. 4 – Relationship between % of cells surviving thermal insult and CEM43 8C.
correspond to V = 1. Such an analysis will now be described. The distribution of the CEM43 8C throughout the tissue layers following thermal insult is plotted against the predicted cell survival (with Ea = 6.04 105 J/mole and A = 1.30 1095 1/s, taken from [31]). The outcome of this confluence is shown in Fig. 4. The general trend conveyed by the figure is expected, high cell survival for low CEM43 8C, and cell survival decreasing markedly as CEM43 8C increases. It is seen that there is a significant decrease in cell viability as CEM43 8C approaches and exceeds 100 min. The inset in Fig. 4 shows a subset of the data which extends from CEM43 8C of approximately 100–10,000. This range was selected because it corresponds to a decrease in cell viability from approximately 90% to 10%. In this range, it was possible to correlate local cell survival with local CEM43 8C values. Such a correlation is indicated in the inset of Fig. 4. For CEM43 8C values less than approximately 100, almost all cells survive whereas for CEM43 8C values exceeding approximately 10,000, virtually all cells have been destroyed. Although the data shown in Fig. 4 have not collapsed upon a single curve and there is some variation among the data points, the extent of congruence is remarkable. The high degree of the agreement is made more apparent by comparing the results of Fig. 4 with the results that would have been obtained if the fraction of surviving cells (calculated by the injury integral) were compared with CEM values for isothermal exposures (local tissue temperatures brought to and held fixed at an elevated temperature). Such a comparison is shown in Fig. 5. There, it is envisioned that cells are raised instantaneously and homogeneously to one of the temperatures indicated in the figure and held at that temperature indefinitely. This is contrasted with the situation of Fig. 4 where the skin surface is heated and the heat flows by diffusion to the deeper tissue regions. For the instantaneous/homogenous case, Eqs. (1) and (3) are applied for the duration of the exposure to fixed temperature values. It can be seen from the figure that there is a very wide variation in the relationship between CEM and cell survival under this condition. For the temperatures listed in
the figure, none of the curves are coincident. This finding suggests that for isothermal exposures at these temperatures, there is no unique relationship between CEM values and the accumulated injury. Overlaid on the graph of Fig. 5 are the results from Fig. 4. It is seen that the discrete points which correspond to the skinsurface-heating case are most similar to isothermal exposures in the 50 8C range. This appraisal was made by evaluating the equivalent isothermal temperatures for which the largest amount of cellular damage occurred (from 100% survival to 10% survival). While at first it might be surprising that the results coincided in a very small range of isothermal dose injury models, upon reflection there is sound justification for this. The thermal exposures used in the calculations ranged from 10 to 110 s. For durations of this duration, temperatures of 50 8C are required for thermal necrosis.
Fig. 5 – Relationship between % of cells surviving thermal insult and CEM43 8C for exposures that are instantaneous and isothermal at temperature levels designated in the graph. Also shown on the graph are results from Fig. 4 which are outcomes of the present simulations.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7
6
burns xxx (2014) xxx–xxx
rate, and a correlating equation was developed for the decrease in cell survival from 90% to 10%. Finally, it was shown that the cell survival/CEM43 relationship for the cases investigated here most closely aligns with isothermal exposure of tissue to temperatures of 50 8C.
Conflict of interest statement The authors declare no conflict of interest.
references Fig. 6 – Relationship between local CEM43 8C and % surviving cells for the range 1000 < CEM43 8C < 10,000.
From a clinical treatment standpoint, another way to use the results of this modeling technique is through a relationship of the burn depth to the exposure temperature and the exposure duration. Such a relationship was developed in [25] and is repeated here as Burn depth ¼ 2:9302 þ 0:0473T 0:0317t þ 0:000913Tt
(6)
Where the burn depth is in mm, the time is in seconds, and the temperature in 8C. This equation, or the equation shown in Fig. 3 allow a treating physician to quickly estimate a burn depth based on the skin surface experience. Here, as elsewhere, burn depth was defined as V = 1 however [25] showed that this quantification closely matched the burn injury depths observed by treating physicians in clinical setting. Finally, it is useful to graphically present the correlation from Fig. 4 in an expanded format. That presentation, shown in Fig. 6, relates the percentage of surviving cells to the instantaneous CEM43 8C value. As expected, as the CEM 43 8C increases, the survival rate decreases. The graph helps provide perspective for the results of the prior images by relating the CEM43 8C quantity to a physiologic outcome.
4.
Concluding remarks
The focus of this research has been to unearth and quantify interrelationships between the two established means of classifying thermal injury. Those means, CEM43 8C and the thermal injury index, have been respectively employed by practitioners of the hyperthermic temperature range and those concerned with tissue ablation. Although it is well established that these two metrics stem from a common base, other interrelations between them for a practical situation (for skin burns) have not heretofore been disclosed. The implementation of the research was accomplished by means of numerical simulation. The variations of temperature with time and with sub-surface depth provided the inputs needed for the reconciliation of the two indices. It was demonstrated that values of CEM43 at the basal layer of the skin were highly correlated with the depth of injury calculated from an injury integral. In addition, relationships between local values of CEM43 were connected to the local cell survival
[1] Hong WK. American Association for Cancer Research. Cancer Medicine, 8th ed., Shelton, Connecticut: People’s Medical Pub. House; 2010. [2] Kong G, Braun RD, Dewhirst MW. Characterization of the effect of hyperthermia on nanoparticle extravasation from tumor vasculature. Cancer Research 2001;61(7):3027–32. [3] Ponce AM, Viglianti BL, Yu D, Yarmolenko PS, Michelich CR, Woo J, et al. Magnetic resonance imaging of temperaturesensitive liposome release: drug dose painting and antitumor effects. Journal of the National Cancer Institute 2007;99(1):53–63. [4] Brizel DM, Scully SP, Harrelson JM, Layfield LJ, Dodge RK, Charles HC, et al. Radiation therapy and hyperthermia improve the oxygenation of human soft tissue sarcomas. Cancer Research 1996;56(23):5347–50. [5] Brizel DM, Scully SP, Harrelson JM, Layfield LJ, Bean JM, Prosnitz LR, et al. Tumor oxygenation predicts for the likelihood of distant metastases in human soft tissue sarcoma. Cancer Research 1996;56(5):941–3. [6] Dewhirst MW, Viglianti BL, Lora-Michiels M, Hanson M, Hoopes PJ. Basic principles of thermal dosimetry and thermal thresholds for tissue damage from hyperthermia. International Journal of Hyperthermia 2003;19(3):267–94. [7] Pearce JA, Thomsen S. Kinetic models of laser-tissue fusion processes. Biomedical Sciences Instrumentation 1993;29:355–60. [8] McMurray T, Pearce JA. Thermal damage quantification utilizing tissue birefringence color image analysis. Biomedical Sciences Instrumentation 1993;29:235–42. [9] Dewhirst MW, Lora-Michiels M, Viglianti BL, Dewey WC, Repacholi M. Carcinogenic effects of hyperthermia. International Journal of Hyperthermia 2003;19(3):236–51. [10] Yarmolenko PS, Moon EJ, Landon C, Manzoor A, Hochman DW, Viglianti BL, et al. Thresholds for thermal damage to normal tissues: an update. International Journal of Hyperthermia 2011;27(4):320–43. [11] Sapareto SA, Dewey WC. Thermal dose determination in cancer therapy. International Journal of Radiation Oncology Biology Physics 1984;10(6):787–800. [12] He X, Bhowmick S, Bischof JC. Thermal therapy in urologic systems: a comparison of Arrhenius and thermal isoeffective dose models in predicting hyperthermic injury. Journal of Biomechanical Engineering 2009;131: 71–7450. [13] Prakash P, Ciederich CJ. Considerations for theoretical modeling of thermal ablation with catheter-based ultrasonic sources: implications for treatment, planning, monitoring, and control. International Journal of Hyperthermia 2012;28:69–86. [14] Reddy G, Dreher MR, Rossman C, Wood BJ, Haemmerich D. Cytotoxicity of hepatocellular carcinoma cells to hyperthermic and ablative temperature exposures: in vitro
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
JBUR-4239; No. of Pages 7 burns xxx (2014) xxx–xxx
[15]
[16]
[17]
[18] [19]
[20]
[21] [22]
[23] [24]
[25]
[26]
[27]
[28]
[29]
studies and mathematical modelling. International Journal of Hyperthermia 2013;29:318–23. Pearce JA. Comparative analysis of mathematical models of cell death and thermal damage processes. International Journal of Hyperthermia 2013;29:262–80. Lepock JR. Cellular effects of hyperthermia: relevance to the minimum dose for thermal damage. International Journal of Hyperthermia 2003;19(3):252–66. Arrhenius S. Uber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Sauren On the reaction rate in the inversion of cane sugar by acids Zeitschrift fur Physikalische Chemie 1889;4:226–48. Arrhenius S. Quantitative laws in biological chemistry. London: G. Bell & Sons; 1915: 184. Johnson FH, Eyring H, Stover BJ. The theory of rate processes in biology and medicine. New York: John Wiley & Sons; 1974. Eyring H. The energy of activation for bimolecular reactions involving hydrogen and the halogens, according to quantum mechanics. Journal of the American Chemical Society 1931;53:2537–49. Eyring H. The activated complex in chemical reactions. Journal of Chemical Physics 1935;3(2):107–15. ¨ ber Einfache Gasreaktionen On Eyring H, Polyani M. U simple gas reactions Zeitschrift fur Physikalische Chemie B 1931;12:279–311. Polyani M. Atomic reactions. London: Williams and Norgate; 1932. Pearce JA. Relationship between Arrhenius models of thermal damage and the CEM 43 thermal dose. Energybased Treatment of Tissue and Assessment V, vol. 7181. San Jose, CA, United States: SPIE, P.O. Box 10, Bellingham, WA 98227-0010, United States; 2009. 718104-718101–718104718115. Abraham JP, Hennessey MP, Minkowycz WJ. A simple algebraic model to predict burn depth and injury. International Communications in Heat and Mass Transfer 2011;38:1169–71. Johnson NN, Abraham JP, Helgeson ZI, Minkowycz WJ, Sparrow M. An archive of skin-layer thicknesses and properties and calculations of scald burns with comparisons to experimental observations. Journal of Thermal Science and Engineering Applications 2011;3:011003. Henriques FC. Studies of thermal injury, V. The predictability and significance of thermally induced rate processes leading to irreversible epidermal injury. Archives of Pathology 1947;43:489–502. Henriques FC, Moritz AR. Studies of thermal injury in the conduction of heat to and through skin and the temperatures attained therein: a theoretical and experimental investigation. American Journal of Pathology 1947;23:531–49. Moritz AR. Studies of thermal injury III. The pathology and pathogenesis of cutaneous burns: an experimental
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42] [43]
[44]
study. American Journal of Pathology 1947; 23:915–34. Moritz AR, Henriques FC. Studies in thermal injury II: the relative importance of time and surface temperature in the causation of cutaneous burns. American Journal of Pathology 1947;23:695–720. Diller KR, Klutke GA. Accuracy analysis of the Henriques model for predicting thermal burn injury. Advances in Bioheat and Mass Transfer Volume HTD 268: ASME Heat Transfer Division 1993;117–23. Pennes HH. Analysis of tissue and arterial blood temperatures in resting human forearm. Journal of Applied Physics 1948;1:93–133. Henriques FC, Moritz AR. 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):530–49. Henriques Jr FC. Studies of thermal injury; the predictability and the significance of thermally induced rate processes leading to irreversible epidermal injury. Archives of Pathology 1947;43(5):489–502. Agah R, Pearce JA, Welch AJ, Motamedi M. Rate process model for arterial tissue thermal damage: implications on vessel photocoagulation. Lasers in Surgery and Medicine 1994;15(2):176–84. Rylander MN, Diller KR, Wang S, Aggarwal SJ. Correlation of HSP70 expression and cell viability following thermal stimulation of bovine aortic endothelial cells. Journal of Biomechanical Engineering 2005;127(5):751–7. Stoll AM, Greene LC. Relationship between pain and tissue damage due to thermal radiation. Journal of Applied Physiology 1959;14(3):373–82. Torpea BI, Lee RC. Thermal injury kinetics in electrical trauma. Journal of Biomechanical Engineering 1992;114:241–50. Zhang A, Xu LX. Numerical bioheat transfer in tumor detection and treatment. In: Advances in numerical heat transfer. New York, NY: CRC Press; 2009. Dai W, Wang H, Jordan PM, Mickens RE, Bejan A. A mathematical model for skin burn injury induced by radiation heating. International Journal of Heat and Mass Transfer 2008;51:5497–510. Diller KR, Hayes LJ. Analysis of tissue injury by burning: comparison of in situ and skin flat models. International Journal of Heat and Mass Transfer 1991;34:1393–406. Roselli RJ, Diller KR. Biotransport: principles and applications. New York, NY: Springer; 2011. Rubinsky B. Numerical bioheat transfer. In: Handbook of numerical heat transfer. Hoboken, NJ: John Wiley and Sons; 2006. Sun J, Zhang A, Xu LX. Evaluation of alternative cooling and heating for tumor treatment. International Journal of Heat and Mass Transfer 2008;51:5478–85.
Please cite this article in press as: Viglianti BL, et al. Rationalization of thermal injury quantification methods: Application to skin burns. Burns (2014), http://dx.doi.org/10.1016/j.burns.2013.12.005
7
