A. Naber, **M. Reiß**, and W. Nahm.

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

In*Frontiers in Physiology*, vol. 12, pp. 1-16, 2021

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

In

**Abstract:**

The vascular function of a vessel can be qualitatively and intraoperatively checked by recording the blood dynamics inside the vessel via fluorescence angiography (FA). Although FA is the state of the art in proving the existence of blood flow during interventions such as bypass surgery, it still lacks a quantitative blood flow measurement that could decrease the recurrence rate and postsurgical mortality. Previous approaches show that the measured flow has a significant deviation compared to the gold standard reference (ultrasonic flow meter). In order to systematically address the possible sources of error, we investigated the error in transit time measurement of an indicator. Obtaining in vivo indicator dilution curves with a known ground truth is complex and often not possible. Further, the error in transit time measurement should be quantified and reduced. To tackle both issues, we first computed many diverse indicator dilution curves using an in silico simulation of the indicator’s flow. Second, we post-processed these curves to mimic measured signals. Finally, we fitted mathematical models (parabola, gamma variate, local density random walk, and mono-exponential model) to re-continualize the obtained discrete indicator dilution curves and calculate the time delay of two analytical functions. This re-continualization showed an increase in the temporal accuracy up to a sub-sample accuracy. Thereby, the Local Density Random Walk (LDRW) model performed best using the cross-correlation of the first derivative of both indicator curves with a cutting of the data at 40% of the peak intensity. The error in frames depends on the noise level and is for a signal-to-noise ratio (SNR) of 20dB and a sampling rate of fs = 60 Hz at f−1 · 0.25(±0.18), so this error is smaller than the distance between two consecutive s samples. The accurate determination of the transit time and the quantification of the error allow the calculation of the error propagation onto the flow measurement. Both can assist surgeons as an intraoperative quality check and thereby reduce the recurrence rate and post-surgical mortality.

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.

Verbesserung der Genauigkeit bei der Bestimmung der Zeitdifferenz zwischen zwei Indikatordilutionskurven in quantitativer Fluoreszenzangiographie unter Verwendung mathematischer Modelle.

Institut für Biomedizinische Technik, Karlsruher Institut für Technologie (KIT). Bachelorarbeit. 2020

**Abstract:**

Transit times of a bolus through an organ can provide valuable information for researchers, technicians and clinicians. Current clinical routines for blood flow measurement involve the usage of an ultrasonic flowprobe. Although this clinical flowprobe has an accuracy of ± 10 %, downsides are additional time, equipment and interrupting surgical workflow; rupturing the cerebral vessel due to mechanical stress is possible as well. Thus, quantitative fluorescence angiography would be advantageous as a non-invasive method monitoring the temporal propagation of an injected indicator at two distinct locations for cerebral blood flow evaluation. However, current methods extracting the blood's transit from two discrete-time dilution curves show a low accuracy and thus cannot be used for clinical studies. Therefore, the goal of this thesis is the evaluation of new methods ascertaining the time difference between two indicator dilution curves using four mathematical models. The target is to achieve a relative mean temporal error less than one camera frame. In the first part of the thesis, datasets of two corresponding in silico generated indicator dilution curves with a ground truth of the transit time are created. To obtain one dataset, one dilution curve is duplicated followed by subsampling, delaying and applying noise. In the second part, the two corresponding curves of one dataset are cut and fitted by a mathematical model before ascertaining the time difference using a feature. Overall, 574 combinations of mathematical models, features and methods to cut the discrete-time dilutions curves before fitting were compared for seven different noise levels and two framerates. The evaluation showed the local density random walk (LDRW) model and the gamma-variate model being superior to the monoexponential model and the parabola model. The LDRW model in combination with the feature cross-correlation of the first derivation showed the best results overall after cutting the indicator dilution curves before the rise at the ascending side and after 40 % of the respective peak at the descending side. For a framerate of 25 fps, the regarded noise levels SNR ∈ [20,8] dB showed a mean temporal error of µ ∈ [0.25,0.78] frames, respectively. At a framerate of 60 fps, the mean temporal error using the same SNR levels was evaluated to µ ∈ [0.43,1.41] frames with a mean temporal error less than one frame only for SNR ≥ 12 dB.