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

In

**Abstract:**

Afterinterventionssuchasbypasssurgeriesthevascularfunctionischeckedqualitatively 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.

Diffuse reflectance Monte Carlo simulation to assess the transit time error in intraoperative fluorescence angiography.

In

**Abstract:**

The vascular function after interventions as revascularization surgeries is checked intraoperatively and qualita- tively by observing the blood flow dynamic in the vessel via Indocyanine Green (ICG) Fluorescence Angiography. This state-of-the-art technique does not provide the surgeon with objective information whether the revascu- larization is sufficient and should be improved by obtaining a quantitative intraoperative optical blood flow measurement. Previous approaches using ICG Fluorescence Angiography show that the blood flow measure- ment does not match the reference and overestimates the flow. The experiments indicate that the amount of overestimation is linked to the vessels diameter. We have, in previous work, quantified the propagated error on the flow calculation resulting from the error in the measurement of the vessels diameter and length and realized that they cannot be accounted solely for this deviation. The influence of the transit time error is not revealed yet. We propose a model combining the penetration depth of diffusely reflected photons and the flow velocity profile to estimate the error in transit time measurement. The flow is assumed to be laminar. The photons path is obtained from a Monte Carlo simulation. This is used to determine the maximum penetration depth of each diffusely reflected photon and therefore state how the recorded signal is composed of the signals originating from different depths to check the hypothesis that the error is systematically linked to the vessels diameter. A simplified geometry is set as a homogeneous layer structure of vessel wall, blood and vessel wall. The total thickness ranges from 1 mm to 5 mm. The probability density of the depth distribution of the diffusely reflected photons and the parabolic flow profile are convolved to obtain a weighted average of the flow velocity, which is set into relation with the mean flow velocity. The results show a clear dependency of the error in transit time measurement on the vessels diameter which complies qualitatively with literature and confirms the hypothesis.

Spatial gradient based segmentation of vessels and quantitative measurement of the inner diameter and wall thickness from ICG fluorescence angiographies.

In

**Abstract:**

During neurovascular surgery the vascular function can be checked intraoperatively and qualitatively by observing the blood dynamics inside the vessel via Indocyanine Green (ICG) Fluorescence Angiography. This state-of-the- art method provides the surgeon with valuable semi-quantitative information but needs to be improved towards a quantitative assessment of vascular volume flow. The precise measurement of volume flow rely on the assumption that both the inner geometry of the blood vessel and the blood flow velocity can be precisely obtained from Fluorescence Angiography. The correct reconstruction of the inner diameter of the vessel is essential in order to minimize the propagated error in the flow calculation. Although ICG binds specifically on blood plasma proteins the fluorescence light radiates also from outside the inner vessel volume due to multiple scattering in the vessel wall, causing a fading edge intensity contrast. A spatial gradient based segmentation method is proposed to reliably estimate the inner diameter of cerebral vessels from intraoperative Fluorescence Angiography images. As result the minimum of the second deviation of the intensity values perpendicular to the vessels edge was identified as the best feature to assess the inner diameter of artificial vessel phantoms. This method has been applied to cerebrovascular vessel images and the results, since no ground truth is available, comply with literature values.

M. Reiß, **A. Naber**, and W. Nahm.

Simulating a Ground Truth for Transit Time Analysis of Indicator Dilution Curves.

In*Current Directions in Biomedical Engineering*, vol. 6(3) , pp. 268-271, 2020

Simulating a Ground Truth for Transit Time Analysis of Indicator Dilution Curves.

In

**Abstract:**

Transit times of a bolus through an organ can provide valuable information for researchers, technicians and clinicians. Therefore, an indicator is injected and the temporal propagation is monitored at two distinct locations. The tran- sit time extracted from two indicator dilution curves can be used to calculate for example blood flow and thus provide the surgeon with important diagnostic information. However, the performance of methods to determine the transit time Δt can- not be assessed quantitatively due to the lack of a sufficient and trustworthy ground truth derived from in vivo measure- ments. Therefore, we propose a method to obtain an in silico generated dataset of differently subsampled indicator dilution curves with a ground truth of the transit time. This method allows variations on shape, sampling rate and noise while be- ing accurate and easily configurable. COMSOL Multiphysics is used to simulate a laminar flow through a pipe containing blood analogue. The indicator is modelled as a rectangular function of concentration in a segment of the pipe. Afterwards, a flow is applied and the rectangular function will be diluted. Shape varying dilution curves are obtained by discrete-time measurement of the average dye concentration over differ- ent cross-sectional areas of the pipe. One dataset is obtained by duplicating one curve followed by subsampling, delaying and applying noise. Multiple indicator dilution curves were simulated, which are qualitatively matching in vivo measure- ments. The curves temporal resolution, delay and noise level can be chosen according to the requirements of the field of research. Various datasets, each containing two corresponding dilution curves with an existing ground truth transit time, are now available. With additional knowledge or assumptions re- garding the detection-specific transfer function, realistic signal characteristics can be simulated. The accuracy of methods for the assessment of Δt can now be quantitatively compared and their sensitivity to noise evaluated.