Cerebral Blood Flow Measurement Using MRI: Mathematical Regularization and Phantom Evaluation.

Abstract

Strokes have been the third most prevalent cause of death in developed countries and the second most prevalent cause of mortality worldwide. Ischemic strokes are by far the most common type of strokes. Verifying the extent and severity of brain damage may be the most challenging problem in the diagnosis and treatment of stroke. Magnetic resonance imaging provides important indicators, such as cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transition time (MTT), for tissues at the risk for acute strokes. These perfusion-related parameters can be estimated using MR techniques, specifically as dynamic susceptibility contrast (DSC).

The DSC technique measures the change in MR signal during the passage of a non-diffusible tracer through the brain tissue. The signal change can be related to the blood flow through a mathematical convolution model, originally suggested by Meier and Zierler, based on indicator-dilution theory. There have been many attempts to find a deconvolution algorithm that overcomes the many limitations, especially, the instability issue of this ill-posed problem. We have suggested a new approach based on the framework of Tikhonov regularization which we will refer to that as "Generalized Tikhonov". Using computer simulations, this method proved promising for blood flow estimation in the presence of the major sources of error: noise, tracer delay and dispersion. In comparison to the standard Tikhonov regularization, our method showed less sensitivity to the changes in regularization parameters that determine the extent of the regularization.

To investigate the model we have designed a perfusion phantom which is very similar to actual tissues in terms of perfusion-related parameters such as blood volume, blood flow and the flow transition time. The signal to noise ratio, due to the similarity of the flow volume, is similar to that in actual perfusion measurements. The phantom has the capability of including or excluding the tracer delay and dispersion depending on the desired nature of experiments. Flow at every point of the phantom can be calculated using finite element methods. The perfusion phantom was used to verify the accuracy of the Generalized Tikhonov method and to compare it to the conventional methods.