Richard D. Rabbitt

Deformable templates using large deformation kinematics

A general automatic approach is presented for accommodating local shape variation when mapping a two-dimensional (2-D) or three-dimensional (3-D) template image into alignment with a topologically similar target image. Local shape variability is accommodated by applying a vector-field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth (globally positive definite Jacobian). Smoothness is guaranteed without specifically penalizing large-magnitude deformations of small subvolumes by constraining the transformation on the basis of a Stokesian limit of the fluid-dynamical Navier-Stokes equations. This differs fundamentally from quadratic penalty methods, such as those based on linearized elasticity or thin-plate splines, in that stress restraining the motion relaxes over time allowing large-magnitude deformations. Kinematic nonlinearities are inherently necessary to maintain continuity of structures during large-magnitude deformations, and are included in all results. After initial global registration, final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem. Automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular. Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.

3D brain mapping using a deformable neuroanatomy

This paper presents two different mathematical methods that can be used separately or in conjunction to accommodate shape variabilities between normal human neuroanatomies. Both methods use a digitized textbook to represent the complex structure of a typical normal neuroanatomy. Probabilistic transformations on the textbook coordinate system are defined to accommodate shape differences between the textbook and images of other normal neuroanatomies. The transformations are constrained to be consistent with the physical properties of deformable elastic solids in the first method and those of viscous fluids in the second. Results presented in this paper demonstrate how a single deformable textbook can be used to accommodate normal shape variability.

Electric impedance spectroscopy using microchannels with integrated metal electrodes

Microelectric impedance measurement systems containing microchannels with integrated gold electrodes were fabricated to enable EI measurements of femtoliter (10/sup -15/) volumes of liquid or gas. The microinstruments were characterized using samples of air, partially deionized water, and saline solutions with various ionic concentrations over the frequency range of 100 Hz to 2 MHz. Resulting spectral patterns varied systemically as a function of ionic concentration. In addition to industrial sensing applications, this technology may prove to be beneficial in monitoring microsystems utilizing on-chip fluid chemistry, measuring the dielectric dispersion of polymer solutions, and determining the electrical properties of isolated biological materials.

Intracellular calcium transients evoked by pulsed infrared radiation in neonatal cardiomyocytes

Non‐technical summary  We have investigated the mechanisms underlying the response of cells to pulsed infrared radiation (IR, ∼1862 nm) using the neonatal rat ventricular cardiomyocyte as a model. Fluorescence monitoring of the intracellular free calcium (Ca2+) demonstrated that infrared irradiation induced rapid (millisecond time scale) intracellular Ca2+ transients in the cells. The results showed that the Ca2+ transients were sufficient to elicit contractile responses from the cardiomyocytes and could be ‘paced’ or entrained to the pulsing frequency of the IR. Pharmacological results strongly implicate mitochondria as the primary intracellular organelles contributing to the IR‐evoked Ca2+ cycling.

Substrate curvature influences the direction of nerve outgrowth

Nerve outgrowth in the developing nervous system utilizes a variety of attractive and repulsive molecules found in the extracellular environment. In addition, physical cues may play an important regulatory role in determining directional outgrowth of nervous tissue. Here, by culturing nerve cells on filamentous surfaces and measuring directional growth, we tested the hypothesis that substrate curvature is sufficient to influence the directional outgrowth of nerve cells. We found that the mean direction of neurite outgrowth aligned with the direction of minimum principle curvature, and the spatial variance in outgrowth direction was directly related to the maximum principle curvature. As substrate size approached the size of an axon, adherent neurons extended processes that followed the direction of the long axis of the substrate similar to what occurs during development along pioneering axons and radial glial fibers. A simple Boltzmann model describing the interplay between adhesion and bending stiffness of the nerve process was found to be in close agreement with the data suggesting that cell stiffness and substrate curvature can act together in a manner that is sufficient to direct nerve outgrowth in the absence of contrasting molecular cues. The study highlights the potential importance of cellular level geometry as a fidelity-enhancing cue in the developing and regenerating nervous system.

Directional coding of three-dimensional movements by the vestibular semicircular canals.

Abstract. A morphologically descriptive mathematical model was developed to study the role of labyrinthine geometry in determining sensitivities of each semicircular canal to angular motion stimuli in three-dimensional (3D) space. For this, equations describing viscous flow of the endolymph and poro-elastic response of the cupulae were coupled together and solved within a 3D reconstructed geometry. Results predict the existence of prime rotational directions about which the labyrinth resolves 3D angular movements into separate vectorial components. The components are predicted to be transmitted to the brain separately, one coded by each canal nerve. Prime directions predicted by the model are non-orthogonal, distinct from the anatomical canal planes, and distinct from the directions of rotation which elicit maximal responses of individual canal nerves. They occur for each canal along the intersection of the two null planes defined by its sister canals. Hence, rotation about a prime direction excites only one canal nerve. This contrasts the situation for rotations about anatomical canal planes, or about maximal response directions, where the model predicts activation of multiple canal nerves. The prime directions are sensitive to labyrinthine morphology and, hence, are predicted to vary between species and, to a lesser extent, vary between individual animals. Prime directions were estimated in the present work using a mathematical model, but could be determined experimentally based on the directional sensitivities of individual canal nerves. The model also predicts the existence of dominant eigenmodes and time constants associated with rotation in each of the prime directions. Results may have implications regarding the central representation of angular head movements in space as well as the neuronal mappings between three-canal afferent inputs and motor outputs.

Infrared photostimulation of the crista ampullaris

Non‐technical summary  It has been shown previously that application of short pulses of optical energy at infrared wavelengths can evoke action potentials in neurons and mechanical contraction in cardiac muscle cells. Optical stimuli are particularly attractive because of the ability to deliver focused energy through tissue without physical contact or electrical charge injection. Here we demonstrate efficacy of pulsed infrared radiation to stimulate balance organs of the inner ear, specifically to modulate the pattern of neural signals transmitted from the angular motion sensing semicircular canals to the brain. The ability to control action potentials demonstrates the potential of pulsed optical stimuli for basic science investigations and future therapeutic applications.

Strain Measurement in Coronary Arteries Using Intravascular Ultrasound and Deformable Images

Atherosclerotic plaque rupture is responsible for the majority of myocardial infarctions and acute coronary syndromes. Rupture is initiated by mechanical failure of the plaque cap, and thus study of the deformation of the plaque in the artery can elucidate the events that lead to myocardial infarction. Intravascular ultrasound (IVUS) provides high resolution in vitro and in vivo cross-sectional images of blood vessels. To extract the deformation field from sequences of IVUS images, a registration process must be performed to correlate material points between image pairs. The objective of this study was to determine the efficacy of an image registration technique termed Warping to determine strains in plaques and coronary arteries from paired IVUS images representing two different states of deformation. The Warping technique uses pointwise differences in pixel intensities between image pairs to generate a distributed body force that acts to deform a finite element model. The strain distribution estimated by image-based Warping showed excellent agreement with a known forward finite element solution, representing the gold standard, from which the displaced image was created. The Warping technique had a low sensitivity to changes in material parameters or material model and had a low dependency on the noise present in the images. The Warping analysis was also able to produce accurate strain distributions when the constitutive model used for the Warping analysis and the forward analysis was different. The results of this study demonstrate that Warping in conjunction with in vivo IVUS imaging will determine the change in the strain distribution resulting from physiological loading and may be useful as a diagnostic tool for predicting the likelihood of plaque rupture through the determination of the relative stiffness of the plaque constituents.

Three-dimensional biomechanical model of benign paroxysmal positional vertigo

A morphologically descriptive 3-canal mathematical model was developed to quantify the biomechanical origins of gravity-dependent semicircular canal responses under pathological conditions of canalithiasis and cupulolithiasis—conditions associated with the vestibular disorder benign paroxysmal positional vertigo (BPPV). The model describes the influence of displaced calcium carbonate debris (particles) located within the labyrinth on the time-dependent responses of the ampullary organs. The particles were modeled as spheres free to move in the canal lumen (canalithiasis) or adhered to a cupula (cupulolithiasis). The model predicts canal responses to the diagnostic Dix–Hallpike maneuver, and to a modified Epley canalith repositioning (CRP) treatment. Results for canalithiasis predict activation latencies and response magnitudes consistent with clinical observations during the Dix–Hallpike maneuver. The magnitude of the response evoked by the Dix–Hallpike test was primarily due to the total weight of the particles while the latency to peak response was due to the time required for the stone to move from the ampulla to the posterior apex of the canal. Results further illustrate the effectiveness of the Epley CRP in repositioning the particles and relieving the symptoms of the canalithiasis type of BPPV.

Mapping of hyperelastic deformable templates using the finite element method

In the current work we integrate well established techniques from finite deformation continuum mechanics with concepts from pattern recognition and image processing to develop a new finite element (FE) tool that combines image-based data with mechanics. Results track the deformation of material continua in the presence of unknown forces and/or material properties by using image-based data to provide the additional required information. The deformation field is determined from a variational problem that combines both the mechanics and models of the imaging sensors. A nonlinear FE approach is used to approximate the solution of the coupled problem. Results can be applied to (1) track the motion of deforming material and/or, (2) morphological warping of template images or patterns. 2D example results are provided for problems of the second type. One of the present examples was motivated primarily by a problem in medical imaging--mapping intersubject geometrical differences in human anatomical structures--with specific results given for the mapping 2D slices of the human distal femur based on X-ray computed tomographic images.