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Category:Films directed by Sekhar Kammuladata-label=“fig:noise“}](noise.png){width=“0.8\linewidth“}

We assume that the RBE of the G2-HOT cell at the simulation time $t=0$ is known with sufficient precision. Then, we apply the optimization algorithm described in the previous section to the problem of finding the optimal volumetric heating profile, which maximizes the expected RBE of the G2-HOT cell, at $t=0$. In particular, we minimize the integral given in equation and we compare the result with the following analytical solution: $$\label{AnalyticSoln}
\phi_{\textrm{opt},0}(r) = \frac{\sigma_{\textrm{opt}}\left(b-r\right)e^{ -r/b}}{\int_{0}^{b}\sigma_{\textrm{opt}}(s)e^{ -s/b}\mathrm{d}s},$$ where $\sigma_{\textrm{opt}}$ is defined as in.

The results for the volumetric heating profile, $\phi$, of the G2-HOT cell, which maximizes the RBE at $t=0$, are shown in figure \[fig:noise\]. The black curve shows the solution when no noise is present. Moreover, the red and blue curves show the optimal solution in the presence of noise, corresponding to 10% and 50% of the optimum in the absence of noise. As expected, the optimal solution is more concentrated around the target radius, $r=b$. As before, we see that we obtain an increase in RBE when we use the optimal solution in the presence of noise.

Application to the case of a patient treated with [$\mathrm{SBRT}$]{} {#sec:4}
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In this section we discuss an application of the proposed optimisation framework to the problem of volumetric heating of a patient treated with volumetric re-irradiation. In particular, https://saintjohnvianneysocials.com/upload/files/2022/06/aEZsQAqCeGhlUF6mqLqx_07_74d7552d8d84ceb509aed6279db6f5a5_file.pdf

Jul 16, 2010
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