A Model for Evaluating Therapeutic Response of Combined Cancer Treatment Modalities: Applied to Treatment of Subcutaneously Implanted Brain Tumors (N32 and N29) in Fischer Rats with Pulsed Electric Fields (PEF) and <sup>60</sup> Co-gamma Radiation (RT) (2003)

The aim of the present study is to develop a mathematical model for evaluating therapeutic response of combined treatment modalities. The study was performed in rats of the Fischer-344 strain with rat glioma N32 or N29 tumors implanted subcutaneously on the thigh of the hind leg. Pulsed electric fields, PEF, with 16 exponentially decaying pulses with a maximum electric field strength of 140 V/mm and t(1/e)= 1 ms were first applied to the tumors. Then within 5 min radiation therapy with (60)Co-gamma radiation, RT, was given in daily fractions of 5 Gy. The animals were arranged into one group of controls and 3 groups of different kind of treatments: PEF only, RT only or combination of PEF + RT. At about 4 weeks after inoculation, the tumors were given the treatment sessions during one week. In 2 experimental series with totally 52 rats with N32 tumors, of which 16 were controls, were given 4 sessions of PEF treatments and RT (totally 20 Gy). In a special experimental series with totally 56 rats with N32 tumors, of which 10 were controls, the different groups were given 1, 2, 3 or 4 treatment sessions respectively. Another strain of glioma tumor, N29 with 62 tumors of which 14 were controls was studied in 2 series given 4PEF + 4RT and 2PEF + 4RT respectively. Fitting the data obtained from consecutive measurements of tumor volume (TV) of each individual tumor to an exponential model TV = TV(0). exp[TGR.t] estimated the tumor growth rate (TGR % per day) after the first day of treatment (t = 0). The TGR of N32 tumors treated with the combination of 4PEF + 4RT are significantly decreased compared to the controls (p < 0.0001), compared to RT alone (p < 0.0001) and compared to PEF alone (p < 0.001). The combined treatment of N32 gives significant effect on the tumor growth rate after 2, 3 and 4 treatment session while RT alone seems to be most efficient after one treatment of 5 Gy and PEF alone is most efficient after 2 treatments at 2 consecutive days. The TGR of N29 tumors treated with the combination of 4PEF + 4RT are significantly decreased compared to the controls (p < 0.05) but the combination of 2PEF + 4RT was more effective (p < 0.005). The specific therapeutic effect STE is defined as the difference between the average tumor growth rates of controls and exposed tumors divided by the average tumor growth rate of the controls. With 4PEF treatments alone the average STE value was 0.32 for N32 tumors and 0 for N29; for 4RT alone the STE values were 0.29 and 0.42 respectively, and for combined treatments 4PEF + 4RT 0.67 and 0.17 respectively. For the N29 tumors treated with 2PEF + 4RT the STE value was 0.53. The therapeutic enhancement ratio, TER, value increase with the number of treatment sessions and the TER of the combined treatments is above 1 in two of the N32 series, which indicates a synergistic effect of 4PEF + 4RT. This work demonstrate the use of our model for analyzing the combination PEF + RT, but it can also be used for evaluation the therapeutic effects of combining RT with chemotherapy or immunogenetic therapy.