Equivalence of cell survival data for radiation dose and thermal dose in ablative treatments: analysis applied to essential tremor thalamotomy by focused ultrasound and gamma knife

Abstract

Thermal dose and absorbed radiation dose have historically been difficult to compare because different biological mechanisms are at work. Thermal dose denatures proteins and the radiation dose causes DNA damage in order to achieve ablation. The purpose of this paper is to use the proportion of cell survival as a potential common unit by which to measure the biological effect of each procedure.

Survival curves for both thermal and radiation doses have been extracted from previously published data for three different cell types. Fits of these curves were used to convert both thermal and radiation dose into the same quantified biological effect: fraction of surviving cells. They have also been used to generate and compare survival profiles from the only indication for which clinical data are available for both focused ultrasound (FUS) thermal ablation and radiation ablation: essential tremor thalamotomy.

All cell types could be fitted with coefficients of determination greater than 0.992. As an illustration, survival profiles of clinical thalamotomies performed by radiosurgery and FUS are plotted on a same graph for the same metric: fraction of surviving cells.

FUS and Gamma Knife have the potential to be used in combination to deliver a more effective treatment (for example FUS may be used to debulk the main tumor mass, and radiation to treat the surrounding tumor bed). In this case, a model which compares thermal and radiation treatments is valuable in order to adjust the dose between the two.

I. Introduction

Therapies involving the use of ionizing radiation and/or thermal energy have a long history in the treatment of disease, including cancer. Evidence from an Egyptian papyryus suggests that as early as 5000 years ago heat was applied in an attempt to treat breast cancer {Horsman, 2007 #79}. Therapy involving radiation had to wait until the discovery of X-rays in 1895, however within several years of this discovery radiation therapy based on radionuclides and low-energy X-ray generating equipment was used for the treatment of cancer. [1]. More recently there have been parallel developments in the use of heat and ionizing radiation for both diffuse and focal disease, as well as attempts to combine the benefit of the two modalities. A number of techniques have been developed to allow the focal destruction of malignant tissue in humans, including ablation by radiofrequency [3], microwaves[4], lasers, or high-intensity focused ultrasound. Recent advancements in the focal treatment of cancer using ionizing radiation include the development of stereotractic radiosurgery (SRS), stereotactic body radiotherapy (SBRT), and intraoperative radiotherapy (IORT).

From an early date and continuing to the present, investigation of the synergies between heat and ionizing radiation have been a natural avenue for research [insert citations from dewhirst, etc.], and significant evidence in the form of several phase III clinical trials exists to demonstrate that sub-lethal tissue heating followed by radiation can significantly improve outcomes [clinical trial list]. The recent progress in focal ablative therapies such as HIFU and SRS/SBRT may also benefit from combined approaches. However, direct comparison of absorbed dose in ionizing radiation and thermal dose for heating have historically been difficult because of the widely different physical and biological mechanisms in play.

In this work, we compare thermal and ionizing radiation modalities in terms of biological damage to tissue by using equivalent historical in-vitro cell survival data. By doing so, we aim to create a method for translation between measures of thermal and radiation dose. Essential tremor thalamotomy is currently the only indication for which quantitative clinical data are available for both radiation and FUS treatments. In order to illustrate this approach, we thus took into account the beam shaping capabilities of the stereotactic radiosurgery (SRS) and FUS devices available for treatment of essential tremor, in order to allow more direct comparison between FUS and SRS treatments. Our approach could facilitate dosimetry planning in the setting of combined radiosurgery and FUS.

II. Materials and methods

A. Radiation dose vs thermal dose

Radiation dose

Photon-based ionizing radiation (X-rays and γ-rays) are indirectly ionizing; they deposit energy in tissue in a two-step process. In the first step, photolectric and Compton interactions between photons and atoms in tissue result in the transfer of energy to fast electrons ejected from the target atoms. In a second step, atoms in the targeted tissue are ionized as these fast electrons undergo Coulomb interactions with other atoms in the targeted tissue, transferring a fraction of their energy during each interaction [cite Khan]. In traditional radiobiology theory, the biological target of ionizing radition is damage to DNA. In a minority of cases (~33%), DNA is directly ionized, leading to strand breaks. In the majority of cases (~66%), the ions created in irradiated tissue result in the creation of free radicals (most significantly hydroxyl radicals) which subsequently react with and create strand breaks in DNA. The ultimate biological effect of the DNA damage is mitotic death of the cells in the irradiated tissue. At higher, ablative doses there may additional biological mechanisms at play as well, including microvascular damage.

Radiation dose is described in physical terms; the amount of energy absorbed per mass of tissue. This is the definition of “absorbed dose”, and is most commonly described in units of Gray (Gy), where 1 Gy = 1 J/kg of energy absorbed in tissue [20]. The amount of biological damage caused can be related directly to the physical quantity of absorbed dose, and this has become the standard method of prescribing the appropriate amount of radiation to be delivered in any given therapeutic setting.

Biological effect of thermal energy and definition of Thermal Dose

Thermal energy causes protein denaturation within cells and immediate coagulative necrosis [19]. As with ionizing radiation, the extent of biological changes in tissue resulting from thermal exposure is correlated with the amount of energy absorbed in tissue. However, for thermal energy, it is the temperature to which the tissue is raised, and the duration of the heating that seem to play the predominent biological role. Sapareto and Dewey have defined a ‘thermal isoeffective dose’ [21]. This has units of cumulative equivalent minutes at 43°C (CEM 43°C), and allows conversion of any temperature/time (T/t) combination to the equivalent time for which the reference temperature of 43°C must be applied to obtain the same level of thermal damage:

$$CE{M}_{43}={\displaystyle \underset{0}{\overset{t}{\int }}{R}^{43-T\left(t\right)}dt}$$

$$R=\{\begin{array}{cc}0.25& \mathit{\text{if}}T<43°C\\ 0.5& \mathit{\text{if}}T>43°C\end{array}$$

The definition of the thermal isoeffective dose formalizes the idea that two different temperatures applied over different time intervals can have the same biological effect in a given tissue.

Cell survival curves

Traditionally, the most common method for assessing cell survival in thermo- and radiobiology uses survival curves. The principle of survival curve analysis is the same, irrespective of the source of cell damage. The curve depicts the relationship between the cell’s ability to divide and the damage to which it has been subjected. The development of survival curves involves plating a known number of cells (determined using a standard counting method) out into tissue culture dishes following exposure to heat or ionizing radiation, and analyzing their response at a later time point. The surviving fraction is calculated by normalizing the number of cells or colonies seen in treated samples to that seen in controls. This is then plotted on a logarithmic scale against the thermal or radiation dose delivered. A minimum colony size (usually 50 cells) is used as a cutoff for minimal critical mass of cells to survive as a colony, It should be noted, that, while this type of assay is generally assumed to measure cell survival, the reduction in number may also be due in part to cells going into a “dormant” state, and not dividing. Typical survival curves are shown in Figure 1 for radiotherapy and thermal doses. For thermal treatments, the cells were subjected to a variety of temperatures as shown in the figure legend. However, when both temperature and time are taken into account by calculating thermal dose in CEM, the data fall along a common curve.

Figure 1.

An example of a survival curve for radiotherapy exposure (A), extracted from [22], and for heated cells (B), extracted from previously published results [23], with thermal isoeffective dose calculated from the combination of heating duration and temperature

B. Literature Review

An extensive review of the literature was conducted to identify studies reporting cell survival for thermal exposure, with the goal of identifying cell subtypes for which there were matching published reports on cell survival for ionizing radiation. Basically a literature review for both thermal and radiation cell survival was performed and then data were cross referenced. The literature review was conduced using Cornell University’s online library during June and July of 2013. Key words used in this literature review included: cell survival, radiation treatment, thermal treatment, thermal dose, radiation dose, tissue damage, and hyperthermia. Some exclusion criteria included: articles not written in English, studies that only used thermal and radiation treatment in combination, and studies that did not measure cell survival. Table 1 lists the publications selected for thermal and ionizing radiation modalities: Chinese hamster ovary cells (CHO), Chinese hamster lung cells (CHL), and human glioblastoma tumor cells were the only cell-types for which survival data was available in the literature for both treatment modalities.

Table 1.

Review of papers reporting survival of cells exposed to thermal rise or ionizing radiations, matched for cell subtype and dose range.

Reference Article	Type of Tissue Investigated		Treatment Modality	Dose Range
Sensitivity of Human Cells to Mild Hyperthermia [24]	Human Glioblastoma Tumor Cells	U87MG	Heat	0-240 CEM
Thermal Dose Determination in Cancer Therapy [21]	Chinese Hamster Ovary		Heat	0-150 CEM
Cellular Effects of Hyperthermia: Relevance to the minimum dose for thermal damage[25]	Chinese Hamster Lung	V79	Heat	0-150 CEM
Arrhenius Relationships from the Molecule and Cell to the Clinic[26]	Chinese Hamster Ovary		Heat	0-150 CEM
Basic Principles of thermal dosimetry and thermal threshold for tissue damage from hyperthermia [27]	Chinese Hamster Ovary		Heat	0-180 CEM
A Transient Thermotolerant Survival Response Produced by Single Thermal Doses in HeLa Cells [28]	HeLa		Heat	0-480 CEM
Differential Effect of Hyperthermia on Murine Bone Marrow Normal Colony-forming Units and AKR and L1210 Leukemia Stem Cells [29]	Leukemia Cells	L1210, AKR	Heat	0-60 CEM
A Comparison of Cell Killing by Heat and/or X Rays in Chinese Hamster V79 Cells, Friend Erythroleukemia Mouse Cells, and Human Thymocyte MOLT-4 [30]	Chinese Hamster Lung	V79	Radiation	0-16 Gy
Cellular Responses to Combinations of Hyperthermia and Radiation [31]	Chinese Hamster Ovary		Radiation	0-11 Gy
Cross-Resistance to Ionizing Radiation in a Murine Leukemic Cell Line Resistant to cis-Dichlorodiammineplatinum(II): Role of Ku Autoantigen [32]	Leukemia Cells	L1210	Radiation	0-10 Gy
Effect of Hyperthermia on the Radiation Response of two Mammalian Cell Lines [33]	Chinese Hamster Ovary, mouse mammary sarcoma	HA-1, EMT-6	Radiation	0-12 Gy
Effects of propranolol in combination with radiation on apoptosis and survival of gastric cancer cells in vitro [34]	Human gastric adenocarcinoma cells	BGC-823, SGC-7901	Radiation	0-10 Gy
Enhancement of Radiation Damage in Cellular DNA Following Unifilar Substitution with Iododeoxyuridine [35]	Chinese Hamster Lung	V79	Radiation	0-16 Gy
Hyperthermia Radiosensitization in Human Glioma Cells Comparison of Recovery of Polymerase Activity, Survival, and Potentially Lethal Damage Repair [36]	Human Glioblastoma Tumor Cells	U87MG	Radiation	0-12 Gy
Influence of Hyperthermia on Gamma-Ray-Induced Mutation in V79 Cells [37]	Chinese Hamster Lung	V79	Radiation	0-12 Gy
Interaction of Hyperthermia and Radiation in CHO Cells: Recovery Kinetics [38]	Chinese Hamster Ovary		Radiation	0-12 Gy
Long duration mild temperature hyperthermia and brachytherapy [39]	Human Normal fibroblasts, Human radiation resistant melanoma cells, Human Ovarian Carcinoma cells	AG1522, SkMe13, A2780	Radiation	0-10 Gy
Moderate Hyperthermia and Low Dose Irradiation [22]	Chinese Hamster Lung	V79	Radiation	0-14 Gy
Radiosensitivity and Capacity to Recover from Radiation Induced Damage in Pimonisazol-Unlabeled Intratumor Quiescent Cells Depend on p53 Status [40]	Human head and neck squamous carcinoma cells	SAS	Radiation	0-14 Gy
Recovery of Sublethal Radiation Damage and is inhibition by Hyperthermia in normal and transformed mouse cells [41]	Chinese Hamster Lung	V79	Radiation	0-14 Gy
The p65 subunit of nuclear factor-κB is a molecular target for radiation sensitization of human squamous carcinoma cells [42]	Human head and neck squamous carcinoma cells	SCC-35, d6, d12	Radiation	0-11 Gy
Thermal radiosensitization in Chinese hamster and mouse C3H 10T 1/2 cells. The thermotolerance effect [40]	Chinese Hamster Lung, mouse embryo	V79, C3H	Radiation	0-14 Gy
Thermal Sensitivity and Radiosensitization in V79 Cells after BrdUrd or IdUrd Incorporation [43]	Chinese Hamster Lung	V79	Radiation	0-16 Gy
Thermally Enhanced Radioresponse of Cultured Chinese Hamster Cells: Inhibition of Repair of Sublethal Damage and Enhancement of Lethal Damage [44]	Chinese hamster fibroblasts	V79	Radiation	0-11 Gy
Thermal sensitivity and radiosensitization in Chinese hamster V79 cells exposed to 2-aminopurine or 6-thioguanine [45]	Chinese Hamster Lung	V79	Radiation	0-14 Gy

C. Data Extraction and Cell Survival Modeling

Each point of the survival data, as displayed in the reports selected for thermal and ionizing radiation experiments, was manually transferred into Matlab version R2013a (Mathworks, Inc., Natick, MA) for each cell type: Chinese Hamster Ovary (CHO), Chinese Hamster Lung (CHL), and Human Glioblastoma Astrocytoma (GBA). The radiation dose survival profiles for each of the 3 cell types were modeled using the Universal Survival Curve (USC) developed by Park, et al[46]. The USC is one of several derivatives of the linear quadratic model that attempt to take into account low and high dose survival regimes [47–52]:

$$\mathit{\text{lnS}}=\{\begin{array}{ll}-n(a\ast D_r+\beta \ast {D_r}^2)\hfill & for{D}_r\le D_T\hfill \\ -n\left(\frac{1}{D_o}{D}_r-\frac{D_q}{D_o}\right)\hfill & for{D}_r\ge D_T\hfill \end{array}$$

where S is the cell survival, D_r is the radiation dose in Gray, n is the number of fractionations, and α (units of log_e of the cells killed per Gy) and β (units log_e of cells killed per Gy²) are constants that describe the linear and quadratic portions of the curve, respectively. In traditional radiobiology, α and β are also often represented in ratio form (the α/β ratio, units of Gy), which is the dose at which the linear and quadratic components are equal. Tumors and tissue which show an early response to radiation damage tend to have a large α/β ratio, while tissue which shows a late response to radiation damage have a small α/β ratio). D_T is the transition dose, where the curve changes from using the low dose model to the high dose. D_o is a measure of the slope of the linear portion of the curve at high doses and D_q is the x-intercept of the survival line valid for D_r ≤ D_T. β and D_T are calculated from the parameters α, D_o, and D_q to ensure continuity and differentiability at D_T [53]:

$$\beta =\frac{{\left(1-\alpha \ast D_o\right)}^2}{4D_o\ast D_q}$$

$$D_T=\frac{2\ast D_q}{1-\alpha \ast D_o}$$

Thermal dose survival data were fitted with a linear-quadratic equation for all 3 cell types [54,55]):

$$S=e^{-\left(a{D}_t+b{D_t}^2\right)}$$

where S is the cell survival, D_t is the thermal dose in equivalent minutes, and a and b are constants.

D. Evaluation of clinical treatment spot sizes

For sake of illustration, the clinical data from both radiation surgery and thermal ablation have been processed. The only indication which the authors could get access to data sets for both is essential tremor. Thalamotomy data for both FUS and SRS were thus analyzed for predicted cell survival.

Focused Ultrasound

The clinical FUS data used for analysis is from a pilot study for essential tremor patients conducted at the University of Virginia[56]. The study consisted of 15 patients with essential tremor whose condition did not improve with medication. The patients were treated with MR-guided FUS, targeting the ventral intermediate (VIM) nucleus of the thalamus. A series of low-power sonications were delivered to the intended target to validate the geometric accuracy of the setup.

Temperature maps were recorded during treatment using MR thermometry[57]. In this study, the temperature for each voxel was read from the raw data files for each timepoint of the sonication and used to calculate the thermal dose. The thermal dose profile was determined by normalizing the data to the maximum thermal dose in the volume of interest.

Using the calculated thermal profiles and the cell survival-thermal dose relationship for all cell lines (CHO, CHL and GBA), cell survival was calculated for each voxel in the region of interest.

Gamma Knife

The clinical Gamma Knife data is derived from treatment plans for 3 radiosurgical thalamotomies performed at University of Virginia for individuals with essential tremor that have failed to improve with other treatments and are unwilling, or unable, to undergo an invasive procedure [58]. Radiosurgical thalamotomy was achieved using the Leksell Gamma Knife to deliver a maximum dose of 130-140Gy with a 4mm isocenter to the VIM nucleus on the opposite side of the brain from the more severe tremor.

SRS dose distributions were created using the Gamma Knife treatment planning software (Leksell GammaPlan versions 8.0 - 10.1, Elekta AB, Stockholm). The resulting dose distributions were exported in DICOM-RT format. The radiotherapy dose profiles in x and y directions were averaged and then normalized to the maximum administered dose and converted to a percentage. Using the cell survival-radiotherapy dose relationship for CHO, CHL and GBA, the fraction of cells surviving was determined as a function of distance.

I. Results

Cell survival fitting

The resulting cell survival curves, extracted from previous studies, [24,25,29–31,36] are shown in Figure 2 for radiotherapy and thermal dose.

Figure 2.

Fraction of cells surviving as a function of the radiation (A) or thermal (B) dose for (●) CHO, (♦) CHL, and (■) GBA. Data have been extracted from previously published results: (CHO),[31] (CHL),[30] (GBA)[36] (A) and (CHO),[29] (CHL),[25] (GBA)[24] (B).

The thermal dose data was fitted with a linear-quadratic equation using Matlab, and the radiation dose data was fitted with the USC model. Results are summarized in Table 2. The α/β values for the radiation treatment on the 3 types of cells are close to the accepted values.[59–61]. The linear quadratic fit of the curves resulted in an average coefficient of determination of R²=0.995, a maximum of 0.998, and a minimum of 0.992. All R² values are displayed in Table 2. In order to achieve a cell survival fraction of 10^-5 (i.e. a survival of 0.001%), a radiotherapy dose of 17Gy must be applied to CHO cells, 20.5Gy to CHL cells, and 14Gy to GBA cells. To achieve the same percentage of surviving cells a thermal dose of 148.5CEM must be administered to the targeted CHO cells, 178CEM to CHL cells, and 249.5CEM to GBA cells.

Table 2.

Parameters for the Universal Survival Curve (USC) for radiation therapy doses and the linear quadratic exponential fit for thermal doses.

USC fit (radiation dose)	α (1/Gy)	β (1/Gy2)	α/β (Gy)	Dq (Gy)	Do (Gy)	DT (Gy)	R2
CHO	0.043	0.062	0.69	2.93	1.23	6.19	0.993
CHL	0.11	0.026	4.12	5.23	1.33	12.22	0.995
GBA	0.14	0.094	1.53	1.81	1.06	4.28	0.996
Exponential fit (thermal dose)	a (1/CEM)		b (1/CEM2)		a/b (CEM)		R2
CHO	0.0047		0.00049		9.6		0.994
CHL	0.035		0.00017		210		0.992
GBA	0.044		9.1e-6		4800		0.998

Estimated cell survival from clinical MRgFUS and Gamma Knife essential tremor treatments

The dose profiles from the clinical essential tremor data for FUS and SRS are shown in Figure 3A, normalized to the point of maximum delivered dose (3160 CEM for thermal and 130 Gy for SRS). 10% of the maximum dose is delivered to cells at 1.6mm for thermal dose and at 6.9mm for radiotherapy exposures. As seen in the simulated profiles, the thermal dose profile drop off is sharp and by 3mm the dose is at zero. For the radiotherapy dose, the drop off is much more gradual and reaches an average of 4% of the maximum dose at 11 mm.

Figure 3.

Average dose profiles (A) and corresponding survival curves (B) for essential tremor clinical data. The average profiles amongst patients are shown in four directions from the center and the average is highlighted in bold (A). Survival curves for essential tremor clinical data for FUS (solid) and SRS (dashed) are plotted for each cell type available.

The corresponding simulated cell survival curves for the essential tremor clinical data are displayed in Figure 3B. As an example, for GBA cells, the survival curve for the radiotherapy dose clinical data reaches a level of 90% at 28.9mm and 99.5% at 27.78mm. For the thermal dose, 90% survival occurs at a distance of 3.71mm and reaches 99.5% survival at a distance of 6.5mm. The survival curve for radiotherapy dose drops off more gradually than the thermal dose survival curve (Figure 3A).

IV. Discussion

Potential clinical applications of FUS overlap significantly with SRS. FUS is being considered as a substitute modality for radiotherapy for indications such as essential tremor, neuropathic pain, and others. However, the techniques do not need to compete. A more common scenario may be to use FUS in combination with radiotherapy, especially in the treatment of malignant disease. In this setting, FUS may be used to debulk the main tumor mass, allowing for significant and immediate symptomatic relief. This may be followed by radiation to the surrounding tumor bed with the goal of reducing local failure and regional recurrences. Investigators are also looking at the reverse approach, where the tumor and the surrounding tumor bed are first irradiated to damage the ability of the cells to reproduce. This is then followed by FUS to debulk the main tumor.

In either situation, a method of quantifying the biological damage inflicted on both normal and diseased tissue from both modalities, like the one introduced in this paper, would be valuable, and in particular for areas of tissue receiving sub-lethal doses from either modality on its own.

Historically, creating a direct comparison between thermal dose and radiation dose has been considered impractical [18]. This is in part because the concept of absorbed dose for ionizing radiation describes the physics of the situation; i.e. the energy absorbed by a mass of tissue from exposure to ionizing radiation [20]. On the other hand, the formulation of the thermal iso-effective dose, is based on empirically observed effects in heated cells.

However, SRS [62] and FUS surgery [63,64] attempt to achieve a similar biological effect: the ablation of a volume of tissue. SRS, especially when delivered in a single fraction, delivers a dose to tissue that can be considered “ablative” in the sense that the expected surviving fraction of cells is low [65].

Likewise, FUS achieves ablation of a desired region of tissue by heating to a thermal isoeffect dose known to cause coagulative necrosis with a similarly negligible surviving cell fraction [19,66]. A threshold for damage of 240CEM was determined in vivo in dog prostate[67] and in muscle[26] and corresponds to the threshold used in most clinical systems[68]. Normalization to a similar biological endpoint makes feasible a direct comparison of radiation dose and thermal isoeffect. The threshold thermal or radiation dose required to “just” achieve ablation gives us a sort of “calibration” point in the spectrum of biological damage at which to equate the two dose formulations.

Equating the dose fomulations might benefit the planning of combination therapies which take advantage of the synergistic effect of radiotherapy and thermal ablation. Compared to RF ablation alone, RF ablation combined with radiation therapy has been shown to increase the ablation volume in rat tumors[69] and improve survival[70], has shown a low rate of complications in patients with unresectable lung cancer[71–73] and has increased the relapse-free survival rate in prostate adenocarcinoma [74]. This pioneering work could be revisited in an optimal way by taking advantage of the non invasive and conformal treatment capabilities of focused ultrasound and external beam therapy for inducing thermal and radiation effects with 3D planning based on the cell survival formulation proposed here.

Limitations of this study

The intent of this paper was to explore the potential utility of equating thermal dose and radiation dose effects using cell survival as a common unit of measurement. As there is limited data collected with the intent of making such a direct comparison, there are assumptions that impact the uncertainties in the analysis including the in-vitro cell survival data used in the study and the accuracy of survival models at ablative doses.

Limitations of in-vitro cell survival data in this study

Perhaps the most significant limitation of our experiment is that in-vitro studies do not represent clinical reality. By design, in-vitro experiments use cells grown under carefully controlled conditions. The in-vivo situation is obviously much more complex; for example our models do not take into account the heat sink effect of the surrounding tissue vasculature [76], cell-cycle differences [77], or tissue inhomogenities which can distort thermal and radiation dose [78–80]. In addition, the cell lines used to create the thermal dose and radiation dose survival curves in this paper do not correspond with the cell types (i.e. normal brain tissue) irradiated during a FUS thalamotomy or radiosurgery thalamotomy. This was because of the non-existence of published data for our chosen clinical example. The mismatch between in-vitro cell lines and the cells found in human brain tissue creates uncertainties on the specific parameters determined for our model fit. As in-vitro and in-vivo cell survival data is accrued for thermal and radiation doses over a larger range of cell-types, the method presented in this paper can be refined to include better parameter estimates.

Another limitation to our approach is that the mathematical models used for thermal and radiation dose derive from in-vitro cell survival data acquired at sub-ablative doses. Both the thermal dose and ionizing radiation cell survival models have been shown to have weaknesses at high, single-fraction doses. Ideally, experiments should be conducted on the same types of cells, with the same cell survival assay and for SRS-like doses. This is beyond the scope of the present paper.

Limitations of the work

Finally, different tissue and organ types have differential sensitivity to both ionizing and thermal dose. This is also not modeled in the current approach.

V. Conclusion

Radiation- and thermal- based treatments are difficult to compare because of the differences in the physics of the energy deposition and the resulting biological effects. The work presented in this paper is a first attempt at creating a method of equating thermal and radiation doses for ablative treatments by considering “ablation” as a common biological endpoint. It was shown how radiation dose and thermal dose could both be expressed in terms of percentage of surviving cells, and thus be compared with the same quantitative effect on tissues. Much work remains to be done in order to validate the regression equations and dose models against both in-vitro and in-vivo targets of different heterogeneous tissues.

Summary.

Thermal dose and absorbed radiation dose have been extensively investigated separately over the last decades. The combined effects of heat and ionizing radiation, such as thermal radiosensitization, have also been reported, but the individual modalities have not been compared with each other. In this paper, we propose a comparison of thermal and radiation dose by going back to basics and comparing the cell survival ratios.