Purpose:

Augmented reality can improve the outcome of hepatic surgeries, assuming an accurate liver model is available to estimate the position of internal structures. While researchers have proposed patient-specific liver simulations, very few have addressed the question of boundary conditions. Resulting mainly from ligaments attached to the liver, they are not visible in preoperative images, yet play a key role in the computation of the deformation.

Method:

We propose to estimate both the location and stiffness of ligaments by using a combination of a statistical atlas, numerical simulation, and Bayesian inference. Ligaments are modeled as polynomial springs connected to a liver finite element model. They are initialized using an anatomical atlas and stiffness properties taken from the literature. These characteristics are then corrected using a reduced-order unscented Kalman filter based on observations taken from the laparoscopic image stream.

Results:

Our approach is evaluated using synthetic data and phantom data. By relying on a simplified representation of the ligaments to speed up computation times, it is not estimating the true characteristics of ligaments. However, results show that our estimation of the boundary conditions still improves the accuracy of the simulation by 75% when compared to typical methods involving Dirichlet boundary conditions.

Conclusion:

By estimating patient-specific boundary conditions, using tracked liver motion from RGB-D data, our approach significantly improves the accuracy of the liver model. The method inherently handles noisy observations, a substantial feature in the context of augmented reality.

中文翻译：

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增强手术期间针对患者特定肝脏模拟的边界条件的估计。

目的：

假设可以使用精确的肝脏模型来估计内部结构的位置，增强现实可以改善肝脏手术的效果。尽管研究人员提出了针对患者的肝模拟，但很少有人讨论边界条件的问题。它们主要由附着在肝脏上的韧带引起，因此在术前图像中不可见，但在变形计算中起着关键作用。

方法：

我们建议通过结合使用统计图集，数值模拟和贝叶斯推断来估计韧带的位置和刚度。韧带建模为连接到肝脏有限元模型的多项式弹簧。使用从文献中获取的解剖图谱和刚度属性对它们进行初始化。然后，基于从腹腔镜图像流中获取的观察结果，使用降阶无味卡尔曼滤波器对这些特征进行校正。

结果：

我们的方法是使用合成数据和幻像数据进行评估的。通过依靠韧带的简化表示来加快计算时间，这并不是在估算韧带的真实特性。但是，结果表明，与涉及Dirichlet边界条件的典型方法相比，我们对边界条件的估计仍将模拟的准确性提高了75％。

结论：

通过使用RGB-D数据跟踪的肝脏运动来估计患者特定的边界条件，我们的方法可以显着提高肝脏模型的准确性。该方法固有地处理嘈杂的观察，这是增强现实环境中的一个重要特征。