Measures of vascular tortuosity—how curved and twisted a vessel is—are associated with a variety of vascular diseases. Consequently, measurements of vessel tortuosity that are accurate and comparable across modality, resolution, and size are greatly needed. Yet in practice, precise and consistent measurements are problematic—mismeasurements, inability to calculate, or contradictory and inconsistent measurements occur within and across studies. Here, we present a new method of measuring vessel tortuosity that ensures improved accuracy. Our method relies on numerical integration of the Frenet-Serret equations. By reconstructing the three-dimensional vessel coordinates from tortuosity measurements, we explain how to identify and use a minimally-sufficient sampling rate based on vessel radius while avoiding errors associated with oversampling and overfitting. Our work identifies a key failing in current practices of filtering asymptotic measurements and highlights inconsistencies and redundancies between existing tortuosity metrics. We demonstrate our method by applying it to manually constructed vessel phantoms with known measures of tortuousity, and 9,000 vessels from medical image data spanning human cerebral, coronary, and pulmonary vascular trees, and the carotid, abdominal, renal, and iliac arteries.

中文翻译：

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通过对Frenet-Serret方程进行高度采样的数值积分来改善血管曲折度的测量。

血管曲折度的度量（血管弯曲和扭曲程度）与多种血管疾病有关。因此，迫切需要在模态，分辨率和尺寸上准确且可比的血管曲折度测量。然而实际上，精确和一致的测量是有问题的–错误的测量，无法计算，或者在研究之内和之间都存在矛盾和不一致的测量。在这里，我们提出了一种测量船只曲折度的新方法，可确保提高准确性。我们的方法依赖于Frenet-Serret方程的数值积分。通过从曲折度测量重建三维血管坐标，我们将说明如何根据容器半径确定和使用最小采样率，同时避免与过度采样和过度拟合相关的错误。我们的工作确定了当前渐近测量过滤方法的一个主要失败之处，并强调了现有曲折度指标之间的不一致和冗余。我们通过将其应用于具有已知曲折度的手动构建的人体模型来证明我们的方法，并从跨越人脑，冠状动脉和肺血管树以及颈动脉，腹部，肾和动脉的医学图像数据中提取了9,000个血管。