Abstract. Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI)technique that employs diffusion-encoding gradients to sensitize the signal to the diffusion of water molecules. DWI allows the noninvasive and quantitative probing of opaque structures such as fibrous soft tissues. Model-based DWI post-processing algorithms, such as diffusion tensor imaging (DTI), solve an inverse problem to estimate from a series of DWI data a set of model parameters representing the diffusion process and the environment of the water molecules. DWI models connect the model parameters (e.g., fiber orientations for fibrous soft tissues) with the experimental parameters (e.g., strengths and directions of the 3-D diffusion-encoding gradients). For spinal cord injuries and skeletal muscle characterization, the fiber orientations within the imaged region can be approximately known a priori using localizer images. Then, we propose and implement a model-based robust optimization framework for two axisymmetric diffusion models, producing robust DWI protocols with respect to the approximate knowledge of the fiber orientations within the images, thereby reducing the uncertainty in the parameter estimates caused by experimental noise. Our goal is to improve the yield of quantitative DWI diagnostics used in clinical and preclinical trials by minimizing the experimental uncertainty.1. Introduction 1.1. Background Model-based diffusion-weighted imaging (DWI) methods, such as DTI [1,2] and QUAQ [3,4], are a subset of quantitative magnetic resonance imaging (MRI) techniques, which are used to infer important structural information within biological tissues. DWI is based on its sensitivity to the diffusive movement of water molecules [5], which in turn is representative of the molecular environment. The sensitization to diffusion is achieved by applying a pair of pulsed diffusionencoding gradients [5]. While for standard MRI the imaging is done by collecting points in k-space, the Fourier reciprocal space of spin locations, DWI protocols involve acquiring a series of DWI images that sample q-space, the Fourier reciprocal space of spin displacements, by using one different set of diffusion-encoding gradient pulses per image [2,3]. The 3-D vector q is related to the diffusion-encoding gradient vector (g) via q := γδg/2π, where γ is the gyromagnetic ratio (γ/2π = 42.576 MHz T −1 ) and δ is the gradient pulse duration. The b-factor is often used