Closed-form solution of the convolution integral in the magnetic resonance dispersion model for quantitative assessment of angiogenesis

Prostate cancer (PCa) diagnosis and treatment is still limited due to the lack of reliable imaging methods for cancer localization. Based on the fundamental role played by angiogenesis in cancer growth and development, several dynamic contrast enhanced (DCE) imaging methods have been developed to probe tumor angiogenic vasculature. In DCE magnetic resonance imaging (MRI), pharmacokinetic modeling allows estimating quantitative parameters related to the physiology underlying tumor angiogenesis. In particular, novel magnetic resonance dispersion imaging (MRDI) enables quantitative assessment of the microvascular architecture and leakage, by describing the intravascular dispersion kinetics of an extravascular contrast agent with a dispersion model. According to this model, the tissue contrast concentration at each voxel is given by the convolution between the intravascular concentration, described as a Brownian motion process according to the convective-dispersion equation, with the interstitium impulse response, represented by a mono-exponential decay, and describing the contrast leakage in the extravascular space. In this work, an improved formulation of the MRDI method is obtained by providing an analytical solution for the convolution integral present in the dispersion model. The performance of the proposed method was evaluated by means of dedicated simulations in terms of estimation accuracy, precision, and computation time. Moreover, a preliminary clinical validation was carried out in five patients with proven PCa. The proposed method allows for a reduction by about 40% of computation time without any significant change in estimation accuracy and precision, and in the clinical performance.