The standard method for assessing hyperthermia treatment has been calculation of cumulative equivalent minutes at 43 °C, CEM43 and its variations. This parameter normalises treatment thermal histories rather than predicts treatment results. Arrhenius models have been widely used in analysing higher temperature thermal treatments and successfully employed to predict irreversible thermal alterations in structural proteins. Unfortunately, in many, but not all cases they fail to represent thermally induced damage or cell death at hyperthermic temperatures, 43-50 °C, exhibiting significant over-prediction of the initial 'shoulder' region. The failure arises from the simplifying assumptions used to derive the irreversible reaction format that has been used in thermal damage studies. Several successful multi-parameter fit methods have been employed to model cell survival data. The two-state statistical thermodynamic model was derived from basic thermodynamic principles. The three-state model results from relaxing the assumptions under the Arrhenius formulation that result in an irreversible reaction. In other cell processes studied in vitro the irreversible Arrhenius model holds, and is sufficient to provide an accurate and useful estimate of thermal damage and cell death. It is essential in numerical model work to include multiple thermal damage processes operating in parallel to obtain a clear image of the likely outcome in tissues. Arrhenius and other C(t) models have that capability, while a single value for CEM43, does not.

A numerical model for thermal damage to human arterial tissue is presented, based on protein denaturation kinetics. The model involves determination of coefficients of rate processes A & δE, which are tissue type‐dependent (arterial tissue in this study), and definition of threshold damage. A feedback‐controlled constant surface temperature device was used to induce 80 coagulative lesions of arterial human tissue ranging in temperature from 66°C to 76°C and in duration from 15 to 1,500 seconds. The measured coefficients were determined to be A = 5.6 × 1063 s−1 and δE = 430 KJ mole−1. These numerical values closely approximate the coefficients of the rate process for denaturation of collagen molecules. These and other histological observations strongly suggest collagen to be the primary coagulating component of arterial tissue at the onset of thermal coagulative damage. The ability of this model to predict onset of tissue coagulation during laser coagulation was studied using 10 postmortem human arterial samples exposed to argon laser irradiation. © 1994 Wiley‐Liss, Inc.

The conductance catheter technique could be improved by determining instantaneous parallel conductance (G(P)), which is known to be time varying, and by including a time-varying calibration factor in Baan's equation [alpha(t)]. We have recently proposed solutions to the problems of both time-varying G(P) and time-varying alpha, which we term "admittance" and "Wei's equation," respectively. We validate both our solutions in mice, compared with the currently accepted methods of hypertonic saline (HS) to determine G(P) and Baan's equation calibrated with both stroke volume (SV) and cuvette. We performed simultaneous echocardiography in closed-chest mice (n = 8) as a reference for left ventricular (LV) volume and demonstrate that an off-center position for the miniaturized pressure-volume (PV) catheter in the LV generates end-systolic and diastolic volumes calculated by admittance with less error (P < 0.03) (-2.49 +/- 15.33 microl error) compared with those same parameters calculated by SV calibrated conductance (35.89 +/- 73.22 microl error) and by cuvette calibrated conductance (-7.53 +/- 16.23 microl ES and -29.10 +/- 31.53 microl ED error). To utilize the admittance approach, myocardial permittivity (epsilon(m)) and conductivity (sigma(m)) were calculated in additional mice (n = 7), and those results are used in this calculation. In aortic banded mice (n = 6), increased myocardial permittivity was measured (11,844 +/- 2,700 control, 21,267 +/- 8,005 banded, P < 0.05), demonstrating that muscle properties vary with disease state. Volume error calculated with respect to echo did not significantly change in aortic banded mice (6.74 +/- 13.06 microl, P = not significant). Increased inotropy in response to intravenous dobutamine was detected with greater sensitivity with the admittance technique compared with traditional conductance [4.9 +/- 1.4 to 12.5 +/- 6.6 mmHg/microl Wei's equation (P < 0.05), 3.3 +/- 1.2 to 8.8 +/- 5.1 mmHg/microl using Baan's equation (P = not significant)]. New theory and method for instantaneous G(P) removal, as well as application of Wei's equation, are presented and validated in vivo in mice. We conclude that, for closed-chest mice, admittance (dynamic G(P)) and Wei's equation (dynamic alpha) provide more accurate volumes than traditional conductance, are more sensitive to inotropic changes, eliminate the need for hypertonic saline, and can be accurately extended to aortic banded mice.

Light microscopy using polarized transmission illumination of routinely stained histologic sections shows changes of the native birefringence of certain tissue constituents when heated by laser irradiation or electrosurgical current. The naturally occurring birefringence of cardiac muscle disappears permanently when the muscle is frozen, thawed, and heated to temperatures in excess of 42 degrees C in vitro. This loss of birefringence is produced with temperatures at which other morphologic thermal changes are hard to detect; thus, it is a low-temperature tissue marker which can be used to observe the extent of thermal damage in tissues. Partial loss of the native birefringence of collagen occurs in canine urinary bladder coagulated by laser irradiation and pericardium heated with electrodes. In addition, thermally coagulated collagens have variable birefringence color shifts when compared to the adjacent unaffected collagens in stained histologic sections. The gradual birefringence color changes are seen at tissue temperatures higher than those at which the thermally induced hyalinization (coagulation) of collagen usually occurs (about 60-70 degrees C), but below those at which carbonization is seen (200+ degrees C). Birefringence changes can be measured to test mathematical models of thermal damage necessary for development of dosimetry models in medical applications of laser irradiation.

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