(eng): This paper describes a publicly available MATLAB toolbox called SpinDoctor that can be used 1) to solve the Bloch-Torrey partial differential equation in order to simulate the diffusion magnetic resonance imaging signal. 2) to solve a diffusion partial differential equation to obtain directly the apparent diffusion coefficient. 3) to compare the simulated apparent diffusion coefficient with a short-time approximation formula. The partial differential equations are solved by P1 finite elements combined with built-in MATLAB routines for solving ordinary differential equations. The finite element mesh generation is performed using an external package called Tetgen.