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

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 20 dB and a sampling rate of fs = 60 Hz at fs-1·0.25(±0.18), so this error is smaller than the distance between two consecutive 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

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 transit 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 cannot be assessed quantitatively due to the lack of a sufficient and trustworthy ground truth derived from in vivo measurements. 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 being 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 different 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 measurements. 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 regarding 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.

Introducing a Linear Gamma Variate Fit to Measure Pulmonary Perfusion with Electrical Impedance Tomography

The indicator dilution method (IDM) is one approach to measure pulmonary perfusion using Electrical Impedance Tomography (EIT). To be able to calculate perfusion parameters and to increase robustnes, it is necessary to approximate and then to separate the components of the measured signals. The component referring to the passage of the injected bolus through the pixels can be modeled as a gamma variate function, its parameters are often determined using nonlinear optimization algorithms. In this paper, we introduce a linear approach that enables higher robustnes and faster computation, and compare the linear and nonlinear fitting approach on data of an animal study.

Estimation of intracardiac shunts in young children with a novel indicator dilution technology

Clinical evaluation of intracardiac shunts in children is not straightforward. Echocardiography can only diagnose the presence of a shunt but does not estimate the shunt ratio. This can be a critical factor that influences treatment options. In this single-center, prospective, observational, method-comparison study, we validate the ability of a novel monitoring device COstatus to estimate the intracardiac shunt ratio (Qp/Qs) of pulmonary (Qp) to systemic (Qs) blood flow in young children before and after corrective cardiac surgery. The indicator dilution technology COstatus monitor was compared to two other more invasive reference techniques, perivascular ultrasonic flow probes (placed around the pulmonary truncus and ascending aorta) and the oximetric shunt equation (using arterial and venous blood gases). Our study revealed that the COstatus monitor detected intracardiac shunts with high sensitivity and specificity but there was some underestimation of the shunt ratios compared to the reference techniques.

Diameter of inflow as a predictor of radiocephalic fistula flow

Introduction: The optimal method for vascular access surveillance is largely unknown. A previous case–control study suggested a simplified anatomical measure obtained by Doppler ultrasound—the narrowest segment of the circuit or “minimal luminal diameter” may identify patients with a dysfunctional radiocephalic arteriovenous fistula. The relationship between minimal luminal diameter and access flow (Qa) in the radiocephalic arteriovenous fistula has not previously been studied. Methods: Patients undergoing Doppler ultrasound of a radiocephalic arteriovenous fistula over an 8-month period were identified retrospectively. Minimal luminal diameter was identified and demographic and clinical data were collected. Qa was estimated by Doppler estimation of brachial artery flow. The relationship between minimal luminal diameter and Qa was examined by correlation and using different levels of minimal luminal diameter as a simplified measure to detect or exclude low Qa (<600 mL/min). Results: A total of 81 Doppler ultrasound scans were performed. In all, 26 scans demonstrated brachial artery flow <600 mL/min. Simple logistic regression indicated a weak statistical relationship between the minimal luminal diameter and Qa (R2 = 0.27, p < 0.01). Minimal luminal diameter performed poorly as a marker of low Qa with low specificity, however, showed high negative predictive value for ruling out low Qa at a minimal luminal diameter of 3.2 mm or higher (94%). Qa estimated by brachial artery flow correlated well with Qa estimated by indicator dilution (R2 = 0.83, p < 0.01) without significant mean difference or proportional bias. Conclusion: Minimal luminal diameter correlates weakly with Qa. Low minimal luminal diameter values should not be used in isolation to determine low Qa for a radiocephalic arteriovenous fistula. Conversely, minimal luminal diameter >3.2 mm largely excludes a low-flow radiocephalic arteriovenous fistula in this cohort. Brachial artery flow is a reasonable measure of Qa in comparison with indicator dilution.

The effects of hypercapnia on cortical capillary transit time heterogeneity (CTH) in anesthetized mice

Capillary flow patterns are highly heterogeneous in the resting brain. During hyperemia, capillary transit-time heterogeneity (CTH) decreases, in proportion to blood's mean transit time (MTT) in passive, compliant microvascular networks. Previously, we found that functional activation reduces the CTH:MTT ratio, suggesting that additional homogenization takes place through active neurocapillary coupling mechanisms. Here, we examine changes in the CTH:MTT ratio during hypercapnic hyperemia in anesthetized mice (C57Bl/6NTac), expecting that homogenization is smaller than during functional hyperemia. We used an indicator-dilution technique and multiple capillary scans by two-photon microscopy to estimate CTH and MTT. During hypercapnia, MTT and CTH decreased as derived from indicator-dilution between artery and vein, as well as between arterioles and venules. The CTH:MTT ratio, however, increased. The same tendency was observed in the estimates from capillary scans. The parallel reductions of MTT and CTH are consistent with previous data. We speculate that the relative increase in CTH compared to MTT during hypercapnia represents either or both capillary constrictions and blood passage through functional thoroughfare channels. Intriguingly, hemodynamic responses to hypercapnia declined with cortical depth, opposite previous reports of hemodynamic responses to functional activation. Our findings support the role of CTH in cerebral flow-metabolism coupling during hyperemia.