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A novel tensor distribution model for the diffusion-weighted MR signal.

ABSTRACT: Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms.

SUBMITTER: Jian B

PROVIDER: S-EPMC2576290 | biostudies-literature | 2007 Aug

REPOSITORIES: biostudies-literature

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A novel tensor distribution model for the diffusion-weighted MR signal.

Jian Bing B Vemuri Baba C BC Ozarslan Evren E Carney Paul R PR Mareci Thomas H TH

NeuroImage 20070503 1

Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized ...[more]

PMID: 17570683

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Project description:PurposeTo quantitatively compare the potential of various diffusion parameters obtained from monoexponential, biexponential, and stretched exponential diffusion-weighted imaging models and diffusion kurtosis imaging in the grading of gliomas.Materials and methodsThis study was approved by the local ethics committee, and written informed consent was obtained from all subjects. Both diffusion-weighted imaging and diffusion kurtosis imaging were performed in 69 patients with pathologically proven gliomas by using a 3-T magnetic resonance (MR) imaging unit. An isotropic apparent diffusion coefficient (ADC), true ADC, pseudo-ADC, and perfusion fraction were calculated from diffusion-weighted images by using a biexponential model. A water molecular diffusion heterogeneity index and distributed diffusion coefficient were calculated from diffusion-weighted images by using a stretched exponential model. Mean diffusivity, fractional anisotropy, and mean kurtosis were calculated from diffusion kurtosis images. All values were compared between high-grade and low-grade gliomas by using a Mann-Whitney U test. Receiver operating characteristic and Spearman rank correlation analysis were used for statistical evaluations.ResultsADC, true ADC, perfusion fraction, water molecular diffusion heterogeneity index, distributed diffusion coefficient, and mean diffusivity values were significantly lower in high-grade gliomas than in low-grade gliomas (U = 109, 56, 129, 6, 206, and 229, respectively; P < .05). Pseudo-ADC and mean kurtosis values were significantly higher in high-grade gliomas than in low-grade gliomas (U = 98 and 8, respectively; P < .05). Both water molecular diffusion heterogeneity index (area under the receiver operating characteristic curve [AUC] = 0.993) and mean kurtosis (AUC = 0.991) had significantly greater AUC values than ADC (AUC = 0.866), mean diffusivity (AUC = 0.722), and fractional anisotropy (AUC = 0.500) in the differentiation of low-grade and high-grade gliomas (P < .05).ConclusionWater molecular diffusion heterogeneity index and mean kurtosis values may provide additional information and improve the grading of gliomas compared with conventional diffusion parameters.

Project description:Quantitative diffusion-weighted MR imaging (DW-MRI) of the body enables characterization of the tissue microenvironment by measuring variations in the mobility of water molecules. The diffusion signal decay model parameters are increasingly used to evaluate various diseases of abdominal organs such as the liver and spleen. However, previous signal decay models (i.e., mono-exponential, bi-exponential intra-voxel incoherent motion (IVIM) and stretched exponential models) only provide insight into the average of the distribution of the signal decay rather than explicitly describe the entire range of diffusion scales. In this work, we propose a probability distribution model of incoherent motion that uses a mixture of Gamma distributions to fully characterize the multi-scale nature of diffusion within a voxel. Further, we improve the robustness of the distribution parameter estimates by integrating spatial homogeneity prior into the probability distribution model of incoherent motion (SPIM) and by using the fusion bootstrap solver (FBM) to estimate the model parameters. We evaluated the improvement in quantitative DW-MRI analysis achieved with the SPIM model in terms of accuracy, precision and reproducibility of parameter estimation in both simulated data and in 68 abdominal in-vivo DW-MRIs. Our results show that the SPIM model not only substantially reduced parameter estimation errors by up to 26%; it also significantly improved the robustness of the parameter estimates (paired Student's t-test, p < 0.0001) by reducing the coefficient of variation (CV) of estimated parameters compared to those produced by previous models. In addition, the SPIM model improves the parameter estimates reproducibility for both intra- (up to 47%) and inter-session (up to 30%) estimates compared to those generated by previous models. Thus, the SPIM model has the potential to improve accuracy, precision and robustness of quantitative abdominal DW-MRI analysis for clinical applications.

Project description:Purpose To assess the repeatability of apparent diffusion coefficient (ADC) estimates in extracranial soft-tissue diffusion-weighted magnetic resonance imaging across a wide range of imaging protocols and patient populations. Materials and Methods Nine prospective patient studies and one prospective volunteer study, performed between 2006 and 2016 with research ethics committee approval and written informed consent from each subject, were included in this single-institution study. A total of 141 tumors and healthy organs were imaged twice (interval between repeated examinations, 45 minutes to 10 days, depending the on study) to assess the repeatability of median and mean ADC estimates. The Levene test was used to determine whether ADC repeatability differed between studies. The Pearson linear correlation coefficient was used to assess correlation between coefficient of variation (CoV) and the year the study started, study size, and volumes of tumors and healthy organs. The repeatability of ADC estimates from small, medium, and large tumors and healthy organs was assessed irrespective of study, and the Levene test was used to determine whether ADC repeatability differed between these groups. Results CoV aggregated across all studies was 4.1% (range for each study, 1.7%-6.5%). No correlation was observed between CoV and the year the study started or study size. CoV was weakly correlated with volume (r = -0.5, P = .1). Repeatability was significantly different between small, medium, and large tumors (P < .05), with the lowest CoV (2.6%) for large tumors. There was a significant difference in repeatability between studies-a difference that did not persist after the study with the largest tumors was excluded. Conclusion ADC is a robust imaging metric with excellent repeatability in extracranial soft tissues across a wide range of tumor sites, sizes, patient populations, and imaging protocol variations. Online supplemental material is available for this article.

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A novel tensor distribution model for the diffusion-weighted MR signal.

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A novel tensor distribution model for the diffusion-weighted MR signal.

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