Precision blood flow measurements in vascular networks with conservation constraints

摘要

In-vivo blood flow measurement, either catheter based or derived from medical images, has become increasingly used for clinical decision making. Most methods focus on a single vascular segment, catheter or simulations, due to mechanical and computational complexity. Accuracy of blood flow measurements in vascular segments are improved by considering the constraint of blood flow conservation across the whole network. Image derived blood flow measurements for individual vessels are made with a variety of techniques including ultrasound, MR, 2D DSA, and 4D-DSA. Time resolved DSA (4D) volumes are derived from 3D-DSA acquisitions and offer one such environment to measure the blood flow and respective measurement uncertainty in a vascular network automatically without user intervention. Vessel segmentation in the static DSA volume allows a mathematical description of the vessel connectivity and flow propagation direction. By constraining the allowable values of flow afforded by the measurement uncertainty and enforcing flow conservation at each junction, a reduction in the effective number of degrees of freedom in the vascular network can be made. This refines the overall measurement uncertainty in each vessel segment and provides a more robust measure of flow. Evaluations are performed with a simulated vascular network and with arterial segments in canine subjects and human renal 4D-DSA datasets. Results show a 30% reduction in flow uncertainty from a renal arterial case and a 2.5-fold improvement in flow uncertainty in some canine vessels. This method of flow uncertainty reduction may provide a more quantitative approach to treatment planning and evaluation in interventional radiology. Purpose: Estimation of blood flow in specific vessel segments can help diagnose the impact of vascular pathology including stenosis, aneurysms, AVMs, etc. Moreover, the success of an interventional procedure can be established by increased precision of flow measurements. Small blood flow changes correlated with cardiovascular disease can be better determined if measurement uncertainty is reduced. Methods: Temporally resolved 3D volumes are made utilizing 4D-DSA waveforms located at the vessel centerline.1 The pulsatility of waveforms are isolated and processed to isolate the principal wave component and determine its temporal shift at different centerline locations, thus providing a velocity measurement.2 An ensemble of measurements from pairs of centerline locations provide blood flow measurement and uncertainty within each vessel using the Fourier Flow technique. The vessel connections in the vascular network can be defined in terms of a directed adjacency matrix, indicating the direction of flow. A Markov Chain Monte Carlo (MCMC) is a Bayesian approach to fit a model to data. With the MCMC, a very efficient sampling of the degrees of freedom is made to estimate the posterior distribution of vascular flow in each segment. The MCMC is used to determine the best fit configuration of blood flow within the vasculaturc while using the adjacency matrix to enforce flow conservation at each junction. This effectively reduces the degrees of freedom to a smaller independent set. of vessels while leveraging the measurement and uncertainty of flow in all vessels. This implementation is first performed on a simulated dataset with flow measurement and error for a vascular network to demonstrate its efficacy and later on canine carotid and human renal arterial networks in-vivo. Results: 4D-DSA acquisitions of renal arterial contrast injections are vessel segmented and flow measurements are made using the Fourier Flow technique. There are N branches in the vascular network with J junctions, resulting in N-J terminal branches and degrees of freedom. The flow measurements show flow non-conservation since each measurement is independent. For the simulated vessel network with 31 total vessel segments and a 10% measurement uncertainty, we find a reduction in overall uncertainty by a factor of 1.63. For the canine bifurcation arterial system, the flow measurement RMS uncertainty is 17% before the flow conservation fit. After the fit, the R.MS uncertainty reduces to 10%. In the renal case with 15 segments and 7 terminal branches, the RMS uncertainty is reduced by a factor of 30%. In other cases where there is poor flow measurement in one branch, the flow conservation fit can recover the flow with improved measurement uncertainty due to the connecting branches with acceptable flow measurements. Conclusion: A full vascular network can be imaged and temporally resolved with 4D-DSA using C-Arm angiographic methods. The vascular network connections can be quantified and combined with segment, flow measurements to arrive at refined flow values that both conserve flow and reduce flow measurement uncertainty. This method may help toward a more quantitative approach to treatment planning and evaluation in interventional radiology.