Mooibroek J, Lagendijk J J
Department of Radiotherapy, University Hospital Utrecht, The Netherlands.
IEEE Trans Biomed Eng. 1991 May;38(5):490-501. doi: 10.1109/10.81569.
A fast and simple algorithm has been presented for the calculation of time-dependent temperature distributions in inhomogeneous vascularized tissue. Three-dimensional anatomical data of tissues and vessel structures are decomposed into elementary cubic nodes by a special digitizing routine with vessels represented by connected strings of vessel nodes. Vessel cross sections may be irregular shaped and/or tapered. Conductive and convective heat transfer was calculated through use of the heat balance technique on each cubic node resulting in an explicit finite difference computational scheme. Employing a three time level scheme, the Fourier stability criterion is circumvented allowing arbitrary time steps to be defined in the algorithm. Time steps as large as 100 times the Fourier restricted one still result in stable and convergent calculations of the stationary temperature distribution. Vessels with different flows and diameters are incorporated by performing a vessel specific second discretization step in time. Using the new algorithm as a mathematical tool the thermal equilibration length of vessel segments have been established under a broad range of geometrical and flow conditions. Validation followed from comparing transient and stationary temperature distributions derived by the proposed algorithm to those from an accurate cylindrical numerical model. Predicted values for the thermal equilibration lengths are compared to an analytical expression and phantom experiments. The algorithm is incorporated in a thermal model being the main part of our hyperthermia treatment planning system.
提出了一种快速简单的算法，用于计算非均匀血管化组织中随时间变化的温度分布。通过一种特殊的数字化程序，将组织和血管结构的三维解剖数据分解为基本立方节点，血管由相连的血管节点串表示。血管横截面可以是不规则形状和/或锥形。通过在每个立方节点上使用热平衡技术计算传导和对流热传递，从而得到一个显式有限差分计算方案。采用三级时间格式，规避了傅里叶稳定性准则，允许在算法中定义任意时间步长。高达傅里叶限制时间步长100倍的时间步长仍能使稳态温度分布的计算稳定且收敛。通过在时间上执行特定于血管的第二次离散化步骤，纳入了具有不同流量和直径的血管。将新算法作为数学工具，在广泛的几何和流动条件下确定了血管段的热平衡长度。通过将所提出算法得出的瞬态和稳态温度分布与精确圆柱数值模型得出的温度分布进行比较来进行验证。将热平衡长度的预测值与一个解析表达式和体模实验进行比较。该算法被纳入一个热模型，该热模型是我们热疗治疗计划系统的主要部分。
