Pohl Michel, Uesaka Mitsuru, Takahashi Hiroyuki, Demachi Kazuyuki, Chhatkuli Ritu Bhusal
The University of Tokyo, 113-8654 Tokyo, Japan.
Japan Atomic Energy Commission, 100-8914 Tokyo, Japan.
Comput Methods Programs Biomed. 2025 Sep;269:108828. doi: 10.1016/j.cmpb.2025.108828. Epub 2025 May 20.
In lung radiotherapy, infrared cameras can track reflective objects on the chest to estimate tumor motion due to breathing. However, treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL), the conventional online learning approach for training recurrent neural networks (RNNs), is a potential solution that can learn patterns within non-stationary respiratory data but has high complexity. This research assesses the capabilities of resource-efficient online algorithms for RNNs-unbiased online recurrent optimization (UORO), sparse one-step approximation (SnAp-1), and decoupled neural interfaces (DNI)-to forecast respiratory motion during radiotherapy accurately.
We use nine time series lasting from 73 s to 320 s, each containing the three-dimensional (3D) locations of three external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI that compress the influence and immediate Jacobian matrices and accurately update the linear coefficients used in credit assignment estimation, respectively. Data was originally sampled at 10 Hz; we resampled it at 3.33 Hz and 30 Hz to analyze the effect of the sampling rate on performance. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons h≤2.1s (the time interval in advance for which predictions are made) and compare them with RTRL, least mean squares, kernel support vector regression, and linear regression.
RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, although we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root-mean-square errors (nRMSEs) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33 Hz and 10 Hz, respectively. Similarly, UORO had the lowest nRMSE at 30 Hz, equal to 0.086. Linear regression was effective at low horizons, attaining an nRMSE of 0.098 for h=100ms at 10 Hz. DNI's inference time (6.8 ms per time step at 30 Hz, Intel Core i7-13700 CPU) was the lowest among the RNN methods; it was 5 times lower than that of RTRL.
UORO, SnAp-1, and DNI can accurately forecast respiratory movements using little data, which will help improve radiotherapy safety.
在肺部放射治疗中，红外摄像机可追踪胸部的反光物体以估计呼吸引起的肿瘤运动。然而，治疗系统的延迟会影响辐射束的精度。实时递归学习（RTRL）是训练递归神经网络（RNN）的传统在线学习方法，是一种潜在的解决方案，它可以在非平稳呼吸数据中学习模式，但复杂度较高。本研究评估了资源高效的RNN在线算法——无偏在线递归优化（UORO）、稀疏一步近似（SnAp-1）和解耦神经接口（DNI）——在放射治疗期间准确预测呼吸运动的能力。
我们使用了9个时长从73秒到320秒的时间序列，每个序列包含健康受试者胸部三个外部标记的三维（3D）位置。我们为SnAp-1和DNI提出了高效的实现方法，分别压缩影响矩阵和即时雅可比矩阵，并准确更新信用分配估计中使用的线性系数。数据最初以10Hz采样；我们将其重新采样为3.33Hz和30Hz，以分析采样率对性能的影响。我们使用UORO、SnAp-1和DNI预测每个标记的3D位置，预测时域h≤2.1秒（提前进行预测的时间间隔），并将它们与RTRL、最小均方、核支持向量回归和线性回归进行比较。
在线训练的RNN达到了与大多数先前使用更大训练数据库和深度学习的研究相似或更好的准确率，尽管我们仅使用每个序列的第一分钟来预测该序列内的运动。在考虑的时域值上，SnAp-1的归一化均方根误差（nRMSE）最低，在3.33Hz和10Hz时分别为0.335和0.157。同样，UORO在30Hz时的nRMSE最低，为0.086。线性回归在低时域时有效，在10Hz时h = 100ms时的nRMSE为0.098。DNI的推理时间（30Hz时每个时间步长6.8ms，英特尔酷睿i7 - 13700 CPU）在RNN方法中最低；比RTRL低5倍。
UORO、SnAp-1和DNI可以使用少量数据准确预测呼吸运动，这将有助于提高放射治疗的安全性。
