Department of Radiology, Baylor College of Medicine, Houston, Texas 77030, USA.
Med Phys. 2013 Jul;40(7):071705. doi: 10.1118/1.4808148.
TomoTherapy systems lack real-time, tumor tracking. A possible solution is to use electromagnetic markers; however, eddy-current magnetic fields generated in response to a magnetic source can be comparable to the signal, thus degrading the localization accuracy. Therefore, the tracking system must be designed to account for the eddy fields created along the inner bore conducting surfaces. The aim of this work is to investigate localization accuracy using magnetic field gradients to determine feasibility toward TomoTherapy applications.
Electromagnetic models are used to simulate magnetic fields created by a source and its simultaneous generation of eddy currents within a conducting cylinder. The source position is calculated using a least-squares fit of simulated sensor data using the dipole equation as the model equation. To account for field gradients across the sensor area (≈ 25 cm(2)), an iterative method is used to estimate the magnetic field at the sensor center. Spatial gradients are calculated with two arrays of uniaxial, paired sensors that form a gradiometer array, where the sensors are considered ideal.
Experimental measurements of magnetic fields within the TomoTherapy bore are shown to be 1%-10% less than calculated with the electromagnetic model. Localization results using a 5 × 5 array of gradiometers are, in general, 2-4 times more accurate than a planar array of sensors, depending on the solenoid orientation and position. Simulation results show that the localization accuracy using a gradiometer array is within 1.3 mm over a distance of 20 cm from the array plane. In comparison, localization errors using single array are within 5 mm.
The results indicate that the gradiometer method merits further studies and work due to the accuracy achieved with ideal sensors. Future studies should include realistic sensor models and extensive numerical studies to estimate the expected magnetic tracking accuracy within a TomoTherapy system before proceeding with prototype development.
TomoTherapy 系统缺乏实时肿瘤跟踪功能。一种可能的解决方案是使用电磁标记物；然而，响应磁源产生的涡流磁场可能与信号相当，从而降低定位精度。因此，跟踪系统必须设计为考虑在内孔导电表面上产生的涡流场。这项工作的目的是研究使用磁场梯度进行定位的准确性，以确定其在 TomoTherapy 应用中的可行性。
使用电磁模型模拟源产生的磁场及其在导电圆柱内同时产生的涡流。使用最小二乘法拟合模拟传感器数据，将偶极子方程作为模型方程来计算源位置。为了考虑传感器区域（≈25cm²）内的场梯度，使用迭代方法来估计传感器中心的磁场。使用两个单轴、成对的传感器阵列来计算空间梯度，形成梯度计阵列，其中传感器被认为是理想的。
实验测量表明，TomoTherapy 孔内的磁场比电磁模型计算的低 1%-10%。使用 5×5 个梯度计阵列的定位结果通常比传感器的平面阵列精确 2-4 倍，具体取决于螺线管的方向和位置。模拟结果表明，在距离阵列平面 20cm 的范围内，使用梯度计阵列的定位精度在 1.3mm 以内。相比之下，使用单个阵列的定位误差在 5mm 以内。
结果表明，由于使用理想传感器实现了高精度，梯度计方法值得进一步研究和探索。未来的研究应包括实际传感器模型和广泛的数值研究，以估计在 TomoTherapy 系统中进行原型开发之前的预期磁跟踪精度。
