The relaxation in blood vessel networks depends on susceptibility and diffusion effects around vessels. In 1994, Yablonskiy and Haacke developed a geometrical model of vessels and analyzed the gradient echo signal for negligible diffusion. Many approximative methods were developed generalizing this model in the limits of small and large diffusion effects. Important methods like vessel size or architectural imaging are based on these works. Here, we provide an exact solution of the Bloch-Torrey-equation in the model of Yablonskiy and Haacke for arbitrary diffusion effects that allows a validation of previously developed methods.