Hyperthermia with laser heating can be a noninvasive treatment for tumors near the body surface. Thermal damage of tissues depends on temperature levels and time of exposure to high temperatures, thus requiring accurate techniques to measure the temperature in the target region of interest. In this computational work, we couple the laser hyperthermia treatment of cancer to the photoacoustic temperature measurement of internal tissues, by solving a state estimation problem with the Kalman filter. The region of interest is considered to be continuously heated by a laser for the hyperthermia treatment, while another laser is sequentially pulsed over the same heated surface to generate acoustic pressure waves. The observation model is derived from the photoacoustic problem, which is linear with respect to the local internal temperatures of the tissues. The evolution model given by the bioheat transfer problem is also supposed linear and uncertainties are modeled as additive and Gaussian. Therefore, the Kalman filter provides the optimal solution of the state estimation problem considered in this work. Simulated nonintrusive acoustic pressure measurements are used in inverse analyses for two test cases, with different dimensions and locations of a tumor in a two-dimensional region. The simulated tumors are supposed loaded with nanoparticles, in order to enhance the local absorption of the laser energy and to reduce thermal damage to healthy cells. The Kalman filter estimated accurate and stable temperature distributions, even in the tumor region that involved large gradients. Moreover, uncertainties in the Kalman filter estimates were smaller than those resulting from the direct simulation of the photoacoustic thermometry problem.

使用激光加热的热疗可以是一种无创治疗体表附近肿瘤的方法。组织的热损伤取决于温度水平和暴露于高温的时间，因此需要精确的技术来测量感兴趣的目标区域的温度。在这项计算工作中，我们通过使用卡尔曼滤波器解决状态估计问题，将癌症的激光热疗治疗与内部组织的光声温度测量相结合。感兴趣的区域被认为是由激光连续加热以进行热疗，而另一个激光在同一加热表面上顺序脉冲以产生声压波。观察模型源自光声问题，该问题与组织的局部内部温度呈线性关系。由生物传热问题给出的演化模型也被假设为线性的，不确定性被建模为加性和高斯。因此，卡尔曼滤波器提供了本工作中考虑的状态估计问题的最优解。模拟的非侵入性声压测量用于两个测试案例的逆分析，在二维区域中肿瘤的不同尺寸和位置。模拟的肿瘤应该装载有纳米颗粒，以增强对激光能量的局部吸收并减少对健康细胞的热损伤。卡尔曼滤波器估计准确和稳定的温度分布，即使在涉及大梯度的肿瘤区域也是如此。而且，