Table 4 Summary of optimization model for MFH
Eq. no. | Parameter | Equation expression | Nomenclature |
|---|---|---|---|
Bagaria and Johnson optimization model, 2005 [136] | |||
20 | Objective function, \(f\) Error function for insufficient and overheating in tumor, \(E_{1}\) Error function for overheating in healthy tissue, \(E_{2}\) | \(f = \sqrt {E_{1} + E_{2} }\) For \(42 \le T_{1\infty } \le 45\) \(E_{1} = 0\) For \(T_{1\infty } < 42\) or \(T_{1\infty } > 45\) \(E_{1} = W_{1} \mathop \sum \nolimits (T_{1\infty } - 42)^{2}\) For \(T_{2\infty } = 37\) \(E_{2} = 0\) For \(T_{2\infty } \ne 37\) \(E_{2} = W_{2} \mathop \sum \nolimits (T_{2\infty } - 37)^{2}\) | \(T_{1\infty }\) steady state temperature of a point in tumor \(T_{2\infty }\) steady state temperature of a point in healthy tissue \(W_{1}\) weight factor for insufficient heating in tumor \(W_{2}\) weight factor for overheating in healthy tissue |
Mital and Tafreshi optimization model, 2012 [145] | |||
21 | Objective function, \(f\) Thermal damage, \(D\) | \(f = \propto_{1} D_{1} - \propto_{2} D_{2}\) \(D\left( {x,y} \right) = \mathop \smallint \limits_{0}^{{t_{f} }} R^{{(43 - T\left( {x,y,t} \right))}} {\text{d}}t\) | \(\propto_{1}\) weight factor for tumor damage \(\propto_{2}\) weight factor for healthy tissue damage \({\text{D}}_{1}\) thermal damage value of tumor \({\text{D}}_{2}\) thermal damage value of healthy tissue \(t_{f}\) period of time \(R\) empirical constant \(T\) temperature at a point at a time \(t\) time |
Salloum, Ma and Zhu optimization model, 2009 [146] | |||
22 | Objective function, \(f\) Error function for deviation of tumor boundary temperature, \(E\) Percentage of tumor volume with \(T \ge T_{n}\), \(R_{1}\) Percentage of tumor boundary with \(T \ge T_{n}\), \(R_{2}\) | \(f = \frac{E}{{R_{1} \cdot R_{2} }}\) \(E = \frac{{\mathop \sum \nolimits \left( {T_{b} - T_{n} } \right)^{2} }}{{\left( {T_{a} - T_{n} } \right)^{2} }}\) \(R_{1} = \frac{{V_{{{\text{tumor}}, T \ge T_{n} }} }}{{V_{{{\text{tumor}},{\text{total}}}} }} \cdot 100\) \(R_{2} = \frac{{S_{{{\text{boundary}}, T \ge T_{n} }} }}{{S_{{{\text{boundary}},{\text{total}}}} }} \cdot 100\) | \(T_{b}\) temperature at tumor boundary \(T_{n}\) cutoff temperature where the value above it is desired for tumor and below it for healthy tissue \(T_{a}\) arterial blood temperature \(V\) volume \(S\) surface area |