Modeling dendrite density from magnetic resonance diffusion measurements Sune N. Jespersen, a, ⁎ Christopher D. Kroenke, b Leif Østergaard, a Joseph J.H. Ackerman, b,c,d and Dmitriy A. Yablonskiy b,e a Center of Functionally Integrative Neuroscience, Aarhus University Hospital–Århus Sygehus, Nørrebrogade 44, Building 30, 8000 Århus C, Denmark b Department of Radiology, Washington University, St. Louis, Missouri 63110, USA c Department of Chemistry, Washington University, St. Louis, Missouri 63110, USA d Department of Internal Medicine, Washington University, St. Louis, Missouri 63110, USA e Department of Physics, Washington University, St. Louis, Missouri 63110, USA Received 15 September 2006; accepted 29 October 2006 Available online 22 December 2006 Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (D L ) and perpendicular (D T ) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion- weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an estimate of dendrite density from noninvasive MR diffusion measurements, a parameter likely to be of value for understanding normal as well as abnormal brain development and function. © 2006 Elsevier Inc. All rights reserved. Keywords: Diffusion; Neural tissue; Cytoarchitectonics; Spherical harmonics Introduction Although diffusion-weighted imaging is by now a well- established clinical tool, especially in the diagnosis of acute stroke (Moseley et al., 1990), its detailed biophysical underpinnings remain only partially understood. In stroke, for example, the origin of the observed acute decrease in the apparent diffusion coefficient (ADC) has received no satisfactory explanation so far, but more fundamentally, a detailed theory of the relation between the diffusion signal and the underlying tissue structure at the cellular level in a given type and state of tissue is still lacking. During the typical diffusion experiment, with a diffusion time Δ of 20–80 ms, the average water molecule probes a length scale on the order of 5 to 20 μm, making diffusion sensitive to a wide range of microstructural and physiological parameters in the tissue. The ultimate goal of a MR diffusion theory is to relate these microstructural and physiological parameters quantitatively to the diffusion-weighted MR signal. However, deducing the values of these parameters from the MR signal constitutes a complex inverse problem requiring careful modeling of the diffusion signal over a wide range of diffusion times and diffusion weightings (b-factors). Despite these challenges, the efforts will undoubtedly be worth- while. Indeed, the prospect of noninvasively measuring quantita- tive cytoarchitectural parameters, for example neuron density, dendrite density and neuropil volume fraction, can be anticipated to have a significant impact on a broad range of research areas such as brain mapping (Schleicher et al., 1999), postnatal ontogeny (Amunts et al., 1997), comparative neuroanatomy (Sherwood et al., 2004; Zilles et al., 1986), and be of great value in the study of microstructural changes underlying various pathologies, such as schizophrenia (Colon, 1972), Alzheimer’ s disease (Stark et al., 2005), and alcoholism (Tang et al., 2004). In addition, histologic studies of neurodegenerative changes during aging have indicated a loss of neurons and dendrites (Stark and Pakkenberg, 2004), and a means to noninvasively characterize these variables in vivo would shed considerable light on the aging nervous system. Here, we develop a simple, analytical model based on three fundamental experimental observations: first, the diffusion signal from gray matter and white matter is not monoexponential (Assaf and Cohen, 1998; Buckley et al., 1999; Le Bihan et al., 1991; Mulkern et al., 1999; Niendorf et al., 1996), suggesting compartmentalization of water. Second, the time independence of the ADC (Clark et al., 2001; Le Bihan et al., 1993; Moonen et al., www.elsevier.com/locate/ynimg NeuroImage 34 (2007) 1473 – 1486 ⁎ Corresponding author. Fax: +45 89494400. E-mail address: sune@pet.auh.dk (S.N. Jespersen). Available online on ScienceDirect (www.sciencedirect.com). 1053-8119/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2006.10.037