Purpose: This study aimed to propose a mathematical model to describe motion blur in hepatobiliary-phase magnetic resonance images.
Methods: Simulated images were constructed based on the mathematical model of motion blur, and this model was then validated by comparing the simulated images with the magnetic resonance images obtained using a dynamic phantom. The mathematical model employed a convolution integral that combined the stationary-state signal distribution and the probability density distribution of the positional shifts during acquisition. The stationary signal distribution was obtained from the magnetic resonance images of a bottle phantom, and the probability density distribution was derived from sinusoidal motion mimicking respiratory movement. Both visual and quantitative evaluations were performed between the simulated images based on the mathematical model and the magnetic resonance images acquired using the dynamic phantom.
Results: The simulated and acquired magnetic resonance images exhibited similar shapes. The difference in the lengths of the respective high-intensity regions was 0.7 mm.
Conclusion: The proposed mathematical model effectively represents motion blur in magnetic resonance images.
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