A fully probabilistic framework is presented for estimating local probability density functions on parameters of interest in a model of diffusion. This technique is applied to the estimation of parameters in the diffusion tensor model, and also to a simple partial volume model of diffusion. In both cases the parameters of interest include parameters defining local fiber direction. A technique is then presented for using these density functions to estimate global connectivity (i.e., the probability of the existence of a connection through the data field, between any two distant points), allowing for the quantification of belief in tractography results. This technique is then applied to the estimation of the cortical connectivity of the human thalamus. The resulting connectivity distributions correspond well with predictions from invasive tracer methods in nonhuman primate. Key words: diffusion-weighted MRI; probability density functions Uncertainty and its representation have an important role to play in any situation where the goal is to infer useful information from noisy data. In diffusion-weighted MRI (DW-MRI) scientists attempt to infer information about, for example, diffusion anisotropy or underlying fiber tract direction, by fitting models of the diffusion and measurement processes to DW-MRI data (e.g., Refs. 1,2). In this scheme there is uncertainty caused both by the noise and artifacts present in any MR scan, but also by the incomplete modeling of the diffusion signal. That is, the true diffusion signal is more complicated than we choose to model. This additional complexity in the diffusion signal appears as residuals when we fit a simple model to the data, causing additional uncertainty in the model parameters. All of the uncertainty in these parameters may be represented in the form of probability density functions (pdfs). This article is essentially divided into two parts, dealing separately with uncertainty at the local and global levels. In the first part, we describe a technique for estimating the pdfs on all parameters in any local model of diffusion. We will show results derived from two simple models of the diffusion process within a voxel: The diffusion tensor model which assumes a local 3D Gaussian diffusion profile, and a simple partial volume model of local diffusion, which assumes that a fraction of diffusion is along a single dominant direction, and that the remainder is isotropic. We will then make suggestions for the extension to more complete models of the diffusion process which are able to account for one, or more, distribution of fiber directions within the voxel. In all of these models, the use of Bayesian techniques allows for the application of prior constraints on parameters in the model where such constraints are sensible. For example, in the fitting of the diffusion tensor model, the eigenvalues of the diffusion tensor are constrained to be positive.The distributions on parameters in a diffusion model are of great significance when making inference on the basis of these param...

A fundamental issue in neuroscience is the relation between structure and function. However, gross landmarks do not correspond well to microstructural borders and cytoarchitecture cannot be visualized in a living brain used for functional studies. Here, we used diffusion-weighted and functional MRI to test structurefunction relations directly. Distinct neocortical regions were defined as volumes having similar connectivity profiles and borders identified where connectivity changed. Without using prior information, we found an abrupt profile change where the border between supplementary motor area (SMA) and pre-SMA is expected. Consistent with this anatomical assignment, putative SMA and pre-SMA connected to motor and prefrontal regions, respectively. Excellent spatial correlations were found between volumes defined by using connectivity alone and volumes activated during tasks designed to involve SMA or pre-SMA selectively. This finding demonstrates a strong relationship between structure and function in medial frontal cortex and offers a strategy for testing such correspondences elsewhere in the brain.S ince early attempts to parcellate human and nonhuman cortex into structurally distinct subdivisions, the hypothesis that structural borders correspond to functional borders has been widely held (1-3). However, this hypothesis has been tested only rarely. Structural features such as sulci and gyri are commonly used to define anatomical regions in functional imaging, neurophysiology, and lesion studies, yet they have only a limited correspondence to more fine-grained structural organization such as cytoarchitecture (4-6). Microstructural borders based, for example, on measurements of cyto-, myelo-, or receptor architecture (7-9), can only be defined post mortem, and the methodological demands of such studies preclude investigation of the regional functional specializations in the same animals. Detailed testing of the relationship between these anatomicallybased measures and function based on comparisons between subjects is limited by the apparently substantial interindividual variations in microstructural anatomical boundaries (4-6).A structural feature that has not previously been used to define areal boundaries in the human neocortex is connectivity to other brain regions. Whereas features such as cytoarchitecture, myeloarchitecture, and receptor distributions distinguish the processing capabilities of a region, connectional anatomy constrains the nature of the information available to a region and the influence that it can exert over other regions in a distributed network. Therefore, not only does structural variation reflect functional organization, but local structural organization also determines local functional specialization. Data on brain connectivity in macaque monkeys show that cytoarchitectonically and functionally distinct regions of prefrontal cortex have distinct connectivity ''fingerprints'' (10). Differences in connectivity that parallel differences in cytoarchitecture have been used to define su...

This study determined the difference in rate of degradation between pure polymers of lactic acid (pla), glycolic acid (PGA), and various ratios of copolymers of these two substances. Fast-cured and slow-cured polyglycolide was compared with copolymers of glycolide/lactide intermixed in ratios of 75:25, 50:50, and 25:75, as well as pure polylactide. A total of 420 rats were implanted with carbon-14 and tritium-labeled polymers in bone and soft tissue. At intervals of 1, 2, 3, 5, 7, 9, and 11 months, groups of five animals with the implants in bone and five with the implants in the abdominal wall were sacrificed. The implant area as well as tissue from the liver, spleen, kidney, lung and some muscle tissue was analyzed for radioactivity along with the urine and feces collected throughout the experiment. Half-lives of the different polymers and copolymers were calculated from the radioactivity present in the implant area for each time interval. Half-life of the polymers and copolymers decreased from 5 months for 100% PGA to 1 week with 50:50 PGA:PLA copolymer and rapidly increased to 6.1 months for 100% PLA. Fast-cured PGA had a half-life in tissue of 0.85 months. No difference in rate of degradation was seen in soft tissue or bone. No significant radioactivity was detected in urine, feces, or tissue samples. From this study, it is concluded that control of degradation rate of the implant could best be attained by varying the composition of PLA and PGA between 75% and 100% PLA along with a corresponding 25% to 0% PGA. This would provide a half-life range of the implant of from 2 weeks to 6 months.

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