Geodesic Length Measurement in Medical Images: Effect of the Discretization by the Camera Chip and Quantitative Assessment of Error Reduction Methods

Abstract

After interventions such as bypass surgeries the vascular function is checked qualitatively and remotely by observing the blood dynamics inside the vessel via Fluorescence Angiography. This state-of-the-art method has to be improved by introducing a quantitatively measured blood flow. Previous approaches show that the measured blood flow cannot be easily calibrated against a gold standard reference. In order to systematically address the possible sources of error, we investigated the error in geodesic length measurement caused by spatial discretization on the camera chip. We used an in-silico vessel segmentation model based on mathematical functions as a ground truth for the length of vessel-like anatomical structures in the continuous space. Discretization errors for the chosen models were determined in a typical magnitude of 6%. Since this length error would propagate to an unacceptable error in blood flow measurement, counteractions need to be developed. Therefore, different methods for the centerline extraction and spatial interpolation have been tested and compared against their performance in reducing the discretization error in length measurement by re-continualization. In conclusion, the discretization error is reduced by the re-continualization of the centerline to an acceptable range. The discretization error is dependent on the complexity of the centerline and this dependency is also reduced. Thereby the centerline extraction by erosion in combination with the piecewise Bézier curve fitting performs best by reducing the error to 2.7% with an acceptable computational time.

CVAR-Seg: An Automated Signal Segmentation Pipeline for Conduction Velocity and Amplitude Restitution

“…Since the pipeline uses bipolar signals, the mean location of the two electrodes is taken as a surrogate for bipole location. Inter-bipole distances between catheters are calculated using the geodesic distance by searching the shortest path on the mesh and subsequent Bézier spline interpolation ( Naber et al, 2020 ). For the electrode distances within a single catheter, the Euclidean distance is chosen, since often the surface mesh is too coarse to compute mesh-based distances, and additionally, the projection onto the mesh results in non-negligible errors.…”

Transit Time Measurement in Indicator Dilution Curves: Overcoming the Missing Ground Truth and Quantifying the Error

“…Now, the findings of this paper allow a quantification and reduction of the absolute statistical error in transit time measurement in dependency of the noise level and sequentially its propagation on the volume flow calculation. Assuming a transit time of four frames and a determined error of 0.25 frames for a sampling rate of 25 fps and a SNR of 8 dB would result in an error in transit time measurement of ∼6%, the error in geodesic measurements (according to Equation 1) would be added to this value (Naber et al, 2020a). This error seems to be acceptable in comparison with the accuracy of the state-of-the-art clinical flow probes (Transonic, 2019).…”

“…The accuracy of the calculation ofV strongly depends on the errors in measuring s, d i , and t. The quantification of these errors and their error propagation is necessary and not sufficiently investigated yet (Cimalla et al, 2008;Weichelt et al, 2013). The accuracy in the measurement of the distance s (geodesic length of the vessel's centerline) is of a magnitude of 3% but shall not be discussed in this paper (Naber et al, 2020a).…”