# Spin Dephasing in Krogh's Capillary Model of the Myocardium

## TL;DR

This paper investigates how the microscopic structure of myocardium, modeled by Krogh's capillary model, influences spin dephasing, combining mathematical analysis with experimental measurements to relate capillary radius to signal decay.

## Contribution

It provides a mathematical framework linking capillary radius to spin dephasing and validates it through experimental signal decay measurements.

## Key findings

- Dephasing relates to capillary radius and tissue structure.
- Mathematical model describes dephasing via Bloch-Torrey equation.
- Experimental data supports the model's predictions.

## Abstract

The relation between the parameters of the microscopic structure of the myocardium and the spin dephasing is analyzed. The microscopic structure of the myocardium is described in terms of Krogh's capillary model. In this model the myocardium is reduced to a single capillary which is surrounded by a concentric tissue cylinder. In the tissue cylinder the dephasing and diffusion process occurs. Mathematically the dephasing process is described by the Bloch-Torrey-equation. Experimentally the Signal-time-decay was measured using a PRESS-sequence and a gradient-echo-sequence. Using the methods provided in this work, the relation between the capillary radius and the measured free induction decay can be given.