Our goal is to understand structure-function relationships in tissues from a physical perspective. There is a unifying interest in understanding the role of water in different physiological processes, in particular, water-mediated interactions with biomolecules that allow cartilage to bear load or that play a role in nerve excitability. We also use nuclear magnetic resonance (NMR) measurements of water mobility in tissues to probe tissue microstructure and architectural organization.

Diffusion Tensor Magnetic Resonance Imaging of the Brain
Pierpaoli, Horkay; in collaboration with Pajevic, Barnett, Aldroubi, Shrager, Miranda, Cohen, Jones
We are continuing to develop Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) as a means to probe tissue microstructure and to assess and diagnose neurological and developmental disorders. DT-MRI measures a diffusion tensor of water on a pixel-by-pixel basis within tissue, both noninvasively and in vivo. It relates an effective diffusion tensor to the measured MR spin echo signal, estimating an effective diffusion tensor, D, in each pixel from a set of diffusion-weighted MR images and then calculating and displaying information derived from D, including local fiber-tract orientation, the mean-squared distance that water molecules diffuse in any given direction, the orientationally averaged mean diffusivity, and other intrinsic scalar invariant quantities that are independent of the laboratory coordinate system. These scalar parameters behave like quantitative histological or physiological “stains,” yet they are “developed” without requiring exogenous contrast agents or dyes.

One example, the orientationally averaged diffusivity (or Trace[D]), has been the most successful imaging parameter proposed to date to identify ischemic tissue regions in the brain during and following an acute stroke. Moreover, we have shown that DT-MRI is effective in identifying white matter degeneration (Wallerian degeneration) associated with chronic stroke. Studies with kittens have also shown that DT-MRI is useful for following early developmental changes occurring in cortical gray and white matter. Such changes cannot be detected with other imaging methods. Developed by Sinisa Pajevic and Carlo Pierpaoli, a method to encode nerve fiber orientation in the brain by using color has allowed us to identify the main association, projection, and commissural white matter pathways in the human brain and even differentiate anatomical white matter pathways that have similar structure and composition but different spatial orientations. It has also allowed us to perform detailed studies of the brain’s structural anatomy; previously, such studies could be performed only by using laborious, invasive histological methods. To assess anatomical connectivity between different functional regions in the brain, we have recently proposed and demonstrated a way to use DT-MRI data to trace out nerve fiber tract trajectories, which we call “fiber tractography.” In this application, we compute the trajectory of a nerve fiber tract by continuously following the direction along which the apparent diffusivity is a maximum.

The development of DT-MRI also requires new mathematical, statistical, and image-processing concepts and constructs for analyzing the multi-dimensional data produced by the recently developed imaging method. Akram Aldroubi and Sinisa Pajevic have established a general mathematical framework for obtaining a continuous, smooth approximation to the discrete, noisy, measured diffusion tensor field data. The framework allows us to reduce the noise in our data and enables us to follow fibers more reliably. We have also derived the form of the parametric distribution governing the statistical variability of diffusion tensor data and have developed nonparametric (bootstrap) methods for determining features of the data’s statistical distribution from experimental DT-MRI data. These developments are allowing us to apply powerful statistical hypothesis tests to address a wide variety of important biological and clinical questions that previously could be tackled only by using ad hoc methods. We are also developing novel image processing methods to enable us to perform quantitative longitudinal or multi-center DT-MRI studies. Gustavo Rohde has been developing methods to warp and register multi-dimensional DT-MRI data sets. To ensure that the DT-MRI acquisitions obtained with different scanners and at different sites are quantitative and of high quality, Ferenc Horkay is developing new polymeric phantoms with which we can calibrate DT-MRI measurement systems. Collectively, these developments are enhancing the utility and broadening the scope of applications of DT-MRI in medicine and biology. Finally, fundamental connections have been established between DT-MRI and a widely used methodology for studying material microstructure and morphology called q-space MRI. We will continue to explore these connections in the coming years.

Physical-Chemical Aspects of Cell and Tissue Excitability
Horkay, Basser; in collaboration with Tasaki
Excitability of cells and tissues is an essential physiological function that allows organisms to sense their environment and respond to it. The primary goal of our work is to explain key physical-chemical features of cell and tissue excitability, many aspects of which are still poorly understood. Widely accepted theories of nerve excitability fail to explain several anomalous phenomena that we have both observed and shown to be necessary for excitation to occur. These phenomena include volume and temperature changes of the superficial protoplasmic layer of nerve axons, which coincide with the action potential waveform. These changes also coincide with a phase transition that occurs in nerve cells, fibers, and synapses and that is caused by the exchange of divalent cations, such as calcium, with monovalent cations, such as sodium and potassium. Our previous experiments with perfused axons clearly implicate divalent/monovalent cation exchange as a mechanism by which nerve fibers can be excited in an “all or none” manner. To understand the physical-chemical basis of these temperature and volumetric changes, particularly how divalent/monovalent cation exchange can induce such changes in biomolecular assemblies, we are studying these processes in synthetic “biomimetic” anionic polymer gels under quasi-physiological solution conditions. An advantage of studying the behavior of these gel model systems is that, unlike in the case of living tissue, their structure, composition, and interactions among their components can be carefully controlled. In particular, in synthetic polyacrylate gels, Ferenc Horkay has observed that minute changes in the concentration of divalent cations in the surrounding liquid can induce significant changes in chain stiffness in the gel, even if ion binding is weak and completely reversible. Various physical-chemical and polymer physics-based techniques, including neutron scattering, osmotic swelling, and mechanical loading, provide complementary information with which to study these biologically relevant phenomena over a wide range of length scales. These basic studies are leading to a deeper understanding of the physical mechanisms underlying nerve excitation.

Functional Properties of Extracellular Matrix
Horkay, Basser; in collaboration with Amis
The collagen network plays a critical role in determining functional properties of cartilage and other extracellular matrices. The collagen network exerts a retractive stress on the osmotically active proteoglycans that are trapped within it in much the same way that a balloon’s elastic membrane exerts hydrostatic pressure on the gas contained within it. Until recently, however, it was not possible to measure the retractive stress of the collagen network independently of other constituents within the extracellular matrix. Previously, we devised a new methodology to determine this structural property of the collagen network, a methodology that involves (1) modeling the cartilage tissue matrix as a composite material consisting of two distinct phases: a collagen network and a proteoglycan (PG) solution trapped within it; (2) applying various known levels of equilibrium osmotic stress; and (3) using physical-chemical principles and independent experiments to determine useful “pressure-volume” relations for both the PG and collagen phases independently. In pilot studies, we used this approach to determine pressure-volume curves for the collagen network and the PG phases in native and in trypsin-treated normal human cartilage specimen as well as in cartilage specimens from osteoarthritic (OA) joints. In both normal and trypsin-treated specimens, collagen network stiffness appeared unchanged, whereas collagen network stiffness decreased in the OA specimen. Our findings highlight the critical role of the collagen network in limiting normal cartilage hydration and in ensuring a high PG concentration in the matrix, both of which are essential for effective load bearing in cartilage but are lost in OA. The data also suggest that the loss of collagen network stiffness, and not the loss or modification of PGs, may be the incipient event leading to the subsequent disintegration of cartilage observed in OA.

More recently, Ferenc Horkay has developed a prototype instrument to study osmotic properties of extremely thin tissue sections. The instrument will permit us to obtain a profile of the functional properties of cartilage as a function of depth from the joint’s articular surface. Horkay is also developing novel spectroscopic methods (both light scattering and neutron scattering) to investigate interactions between water, ions, and extracellular matrix constituents in various tissue specimens.