Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

/pdf/quantifying-brain-microstructure-with-diffusion-mri-theory-m9l3apoxqz.pdf

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI.

TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times

SANDI: a compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI.

Purpose
To determine the intracellular water preexchange lifetime, τi, the “average residence time” of water, in the intracellular milieu of neurons and astrocytes. The preexchange lifetime is important for modeling a variety of MR data sets, including relaxation, diffusion-sensitive, and dynamic contrast–enhanced data sets.

Methods
Herein, τi in neurons and astrocytes is determined in a microbead-adherent, cultured cell system. In concert with thin-slice selection, rapid flow of extracellular media suppresses extracellular signal, allowing determination of the transcytolemmal-exchange-dominated, intracellular T1. With this knowledge, and that of the intracellular T1 in the absence of exchange, τi can be derived.

Results
Under normal culture conditions, τi for neurons is 0.75 ± 0.05 s versus 0.57 ± 0.03 s for astrocytes. Both neuronal and astrocytic τis decrease within 30 min after the onset of oxygen-glucose deprivation, with the astrocytic τi showing a substantially greater decrease than the neuronal τi.

Conclusions
Given an approximate intra- to extracellular volume ratio of 4:1 in the brain, these data imply that, under normal physiological conditions, an MR experimental characteristic time of less than 0.012 s is required for a nonexchanging, two-compartment (intra- and extracellular) model to be valid for MR studies. This characteristic time shortens significantly (i.e., 0.004 s) under injury conditions. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

/pdf/intracellular-water-preexchange-lifetime-in-neurons-and-5bfoiajeiu.pdf

Intracellular water preexchange lifetime in neurons and astrocytes.

Preclinical imaging is critical in the development of translational strategies to detect diseases and monitor response to therapy. The National Cancer Institute Co-Clinical Imaging Resource Program was launched, in part, to develop best practices in preclinical imaging. In this context, the objective of this work was to develop a 1-hour, multiparametric magnetic resonance image-acquisition pipeline with triple-negative breast cancer patient-derived xenografts (PDXs). The 1-hour, image-acquisition pipeline includes T1- and T2-weighted scans, quantitative T1, T2, and apparent diffusion coefficient (ADC) parameter maps, and dynamic contrast-enhanced (DCE) time-course images. Quality-control measures used phantoms. The triple-negative breast cancer PDXs used for this study averaged 174 ± 73 μL in volume, with region of interest-averaged T1, T2, and ADC values of 1.9 ± 0.2 seconds, 62 ± 3 milliseconds, and 0.71 ± 0.06 μm2/ms (mean ± SD), respectively. Specific focus was on assessing the within-subject test-retest coefficient-of-variation (CVWS) for each of the magnetic resonance imaging metrics. Determination of PDX volume via manually drawn regions of interest is highly robust, with ∼1% CVWS. Determination of T2 is also robust with a ∼3% CVWS. Measurements of T1 and ADC are less robust with CVWS values in the 6%-11% range. Preliminary DCE test-retest time-course determinations, as quantified by area under the curve and Ktrans from 2-compartment exchange (extended Tofts) modeling, suggest that DCE is the least robust protocol, with ∼30%-40% CVWS.

/pdf/test-retest-performance-of-a-1-hour-multiparametric-mr-image-2lcqbqvmwl.pdf

Test-Retest Performance of a 1-Hour Multiparametric MR Image Acquisition Pipeline With Orthotopic Triple-Negative Breast Cancer Patient-Derived Tumor Xenografts.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/cmr.a.21467

Magnetic resonance data modeling: The Bayesian analysis toolbox

This study aims to develop a constrained local arterial input function (cL-AIF) to improve quantitative analysis of dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) data by accounting for the contrast-agent bolus amplitude error in the voxel-specific AIF Bayesian probability theory-based parameter estimation and model selection were used to compare tracer kinetic modeling employing either the measured remote-AIF (R-AIF, ie, the traditional approach) or an inferred cL-AIF against both in silico DCE-MRI data and clinical, cervical cancer DCE-MRI data When the data model included the cL-AIF, tracer kinetic parameters were correctly estimated from in silico data under contrast-to-noise conditions typical of clinical DCE-MRI experiments Considering the clinical cervical cancer data, Bayesian model selection was performed for all tumor voxels of the 16 patients (35,602 voxels in total) Among those voxels, a tracer kinetic model that employed the voxel-specific cL-AIF was preferred (ie, had a higher posterior probability) in 80 % of the voxels compared to the direct use of a single R-AIF Maps of spatial variation in voxel-specific AIF bolus amplitude and arrival time for heterogeneous tissues, such as cervical cancer, are accessible with the cL-AIF approach The cL-AIF method, which estimates unique local-AIF amplitude and arrival time for each voxel within the tissue of interest, provides better modeling of DCE-MRI data than the use of a single, measured R-AIF The Bayesian-based data analysis described herein affords estimates of uncertainties for each model parameter, via posterior probability density functions, and voxel-wise comparison across methods/models, via model selection in data modeling

/pdf/modeling-dynamic-contrast-enhanced-mri-data-with-a-4eytd9ezjo.pdf

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF

We recently described rapid quantitative pharmacodynamic imaging, a novel method for estimating sensitivity of a biological system to a drug. We tested its accuracy in simulated biological signals with varying receptor sensitivity and varying levels of random noise, and presented initial proof-of-concept data from functional MRI (fMRI) studies in primate brain. However, the initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters, an approach that was computationally efficient but returned parameters only from a small, discrete set of values chosen a priori. Here we revisit the simulation testing using a Bayesian method to estimate the PKPD parameters. This improved accuracy compared to our previous method, and noise without intentional signal was never interpreted as signal. We also reanalyze the fMRI proof-of-concept data. The success with the simulated data, and with the limited fMRI data, is a necessary first step toward further testing of rapid quantitative pharmacodynamic imaging.

/pdf/rapid-quantitative-pharmacodynamic-imaging-with-bayesian-4srvviudfc.pdf

G. Larry Bretthorst

Papers

Intracellular water preexchange lifetime in neurons and astrocytes.

Test-Retest Performance of a 1-Hour Multiparametric MR Image Acquisition Pipeline With Orthotopic Triple-Negative Breast Cancer Patient-Derived Tumor Xenografts.

Magnetic resonance data modeling: The Bayesian analysis toolbox

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF

Rapid Quantitative Pharmacodynamic Imaging with Bayesian Estimation