G. Larry Bretthorst

Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI

The study of lung emphysema dates back to the beginning of the 17th century. Nevertheless, a number of important questions remain unanswered because a quantitative localized characterization of emphysema requires knowledge of lung structure at the alveolar level in the intact living lung. This information is not available from traditional imaging modalities and pulmonary function tests. Herein, we report the first in vivo measurements of lung geometrical parameters at the alveolar level obtained with 3He diffusion MRI in healthy human subjects and patients with severe emphysema. We also provide the first experimental data demonstrating that 3He gas diffusivity in the acinus of human lung is highly anisotropic. A theory of anisotropic diffusion is presented. Our results clearly demonstrate substantial differences between healthy and emphysematous lung at the acinar level and may provide new insights into emphysema progression. The technique offers promise as a clinical tool for early diagnosis of emphysema.

Statistical model for diffusion attenuated MR signal.

A general statistical model that can describe a rather large number of experimental results related to the structure of the diffusion‐attenuated MR signal in biological systems is introduced. The theoretical framework relies on a phenomenological model that introduces a distribution function for tissue apparent diffusion coefficients (ADC). It is shown that at least two parameters—the position of distribution maxima (ADC) and the distribution width (σ)—are needed to describe the MR signal in most regions of a human brain. A substantial distribution width, on the order of 36% of the ADC, was found for practically all brain regions examined. This method of modeling the MR diffusion measurement allows determination of an intrinsic tissue‐specific ADC for a given diffusion time independent of the strength of diffusion sensitizing gradients. The model accounts for the previously found biexponential behavior of the diffusion‐attenuated MR signal in CNS. Magn Reson Med 50:664–669, 2003.

Equilibrium Water Exchange Between the Intra- and Extracellular Spaces of Mammalian Brain

This report describes the measurement of water preexchange lifetimes and intra/extracellular content in intact, functioning mammalian brain. Intra‐ and extracellular water magnetic resonance (MR) signals from rat brain in vivo were quantitatively resolved in the longitudinal relaxation domain following administration of an MR relaxation agent into the extracellular space. The estimated intracellular water content fraction was 81% ± 8%, and the intra‐ to extracellular exchange rate constant was 1.81 ± 0.89 s–1 (mean ± SD, N = 9), corresponding to an intracellular water preexchange lifetime of ∼550 ms. These results provide a temporal framework for anticipating the water exchange regime (fast, intermediate, or slow) underlying a variety of compartment‐sensitive measurements. The method also supplies a means by which to evaluate membrane water permeability and intra/extracellular water content serially in intact tissue. The data are obtained in an imaging mode that permits detection of regional variations in these parameters. Magn Reson Med 50:493–499, 2003.

Bayesian analysis. I. Parameter estimation using quadrature NMR models

Abstract In the analysis of magnetic resonance data, a great deal of prior information is available which is ordinarily not used. For example, considering high-resolution NMR spectroscopy, one knows in general terms what functional form the signal will take (e.g., sum of exponentially decaying sinusoids) and that, for quadrature measurements, it will be the same in both channels except for a 90° phase shift. When prior information is incorporated into the analysis of time-domain data, the frequencies, decay rate constants, and amplitudes may be estimated much more precisely than by direct use of discrete Fourier transforms. Here, Bayesian probability theory is used to estimate parameters using quadrature models of NMR data. The calculation results in an interpretation of the quadrature model fitting that allows one to understand on an intuitive level what frequencies and decay rates will be estimated and why.

Microstructural changes of the baboon cerebral cortex during gestational development reflected in magnetic resonance imaging diffusion anisotropy.

Cerebral cortical development involves complex changes in cellular architecture and connectivity that occur at regionally varying rates. Using diffusion tensor magnetic resonance imaging (DTI) to analyze cortical microstructure, previous studies have shown that cortical maturation is associated with a progressive decline in water diffusion anisotropy. We applied high-resolution DTI to fixed postmortem fetal baboon brains and characterized regional changes in diffusion anisotropy using surface-based visualization methods. Anisotropy values vary within the thickness of the cortical sheet, being higher in superficial layers. At a regional level, anisotropy at embryonic day 90 (E90; 0.5 term; gestation lasts 185 d in this species) is low in allocortical and periallocortical regions near the frontotemporal junction and is uniformly high throughout isocortex. At E125 (0.66 term), regions having relatively low anisotropy (greater maturity) include cortex in and near the Sylvian fissure and the precentral gyrus. By E146 (0.8 term), cortical anisotropy values are uniformly low and show less regional variation. Expansion of cortical surface area does not occur uniformly in all regions. Measured using surface-based methods, cortical expansion over E125–E146 was larger in parietal, medial occipital, and lateral frontal regions than in inferior temporal, lateral occipital, and orbitofrontal regions. However, the overall correlation between the degree of cortical expansion and cortical anisotropy is modest. These results extend our understanding of cortical development revealed by histologic methods. The approach presented here can be applied in vivo to the study of normal brain development and its disruption in human infants and experimental animal models.

Bayesian analysis. III. Applications to NMR signal detection, model selection, and parameter estimation☆

Abstract The two preceding articles developed the application of Bayesian probability theory to the problems of parameter estimation, signal detection, and model selection on quadrature NMR data in some generality. Here those procedures are used to analyze free induction decay data, when the models are sinusoidal. The exact relationship between Bayesian probability theory and the discrete Fourier-transform power spectrum is derived, and it is shown that the discrete Fourier-transform power spectrum is an optimal frequency estimator for a wide class of problems. Signal detection and model selection problems are then examined, and examples are given that demonstrate the ability of Bayesian probability theory to determine the best model of a process even when more complex models fit the data better.

Bayesian analysis. II. Signal detection and model selection

In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockhams razor: theorize about possible models, compare these to experiment, and select the simplest model that “best” fits the data.

Diffusion MR imaging characteristics of the developing primate brain

Diffusion-based magnetic resonance imaging holds the potential to non-invasively demonstrate cellular-scale structural properties of brain. This method was applied to fixed baboon brains ranging from 90 to 185 days gestational age to characterize the changes in diffusion properties associated with brain development. Within each image voxel, a probability-theory-based approach was employed to choose, from a group of analytic equations, the one that best expressed water displacements. The resulting expressions contain eight or fewer adjustable parameters, indicating that relatively simple expressions are sufficient to obtain a complete description of the diffusion MRI signal in developing brain. The measured diffusion parameters changed systematically with gestational age, reflecting the rich underlying microstructural changes that take place during this developmental period. These changes closely parallel those of live, developing human brain. The information obtained from this primate model of cerebral microstructure is directly applicable to studies of human development.

Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals.

We recently proposed that the observed apparent negative dispersion in bone can arise from the interference between fast wave and slow wave modes, each exhibiting positive dispersion [Marutyan et al., J. Acoust. Soc. Am. 120, EL55-EL61 (2006)]. In the current study, we applied Bayesian probability theory to solve the inverse problem: extracting the underlying properties of bone. Simulated mixed mode signals were analyzed using Bayesian probability. The calculations were implemented using the Markov chain Monte Carlo with simulated annealing to draw samples from the marginal posterior probability for each parameter.

An Introduction to Parameter Estimation Using Bayesian Probability Theory

Bayesian probability theory does not define a probability as a frequency of occurrence; rather it defines it as a reasonable degree of belief. Because it does not define a probability as a frequency of occurrence, it is possible to assign probabilities to propositions such as “The probability that the frequency had value ω when the data were taken,” or “The probability that hypothesis x is a better description of the data than hypothesis y.” Problems of the first type are parameter estimation problems, they implicitly assume the correct model. Problems of the second type are more general, they are model selections problems and do not assume the model. Both types of problems are straight forward applications of the rules of Bayesian probability theory. This paper is a tutorial on parameter estimation. The basic rules for manipulating and assigning probabilities are given and an example, the estimation of a single stationary sinusoidal frequency, is worked in detail. This example is sufficiently complex as to illustrate all of the points of principle that must be faced in more realistic problems, yet sufficiently simple that anyone with a background in calculus can follow it. Additionally, the model selection problem is discussed and it is shown that parameter estimation calculation is essentially the first step in the more general model selection calculation.