KEYWORDS: Tissues, Reconstruction algorithms, Solids, 3D modeling, Data modeling, Elastography, In vivo imaging, Chemical elements, Algorithm development, Protactinium
Implementing constitutive relations that accurately describe the mechanical behavior of biological tissues in vivo
is integral to the success of any model-based elastographic reconstruction technique, and the diagnostic value of
the recovered images. Recently, poroelastic theory has been used to model tissue and other materials comprised
of two distinct phases. Current linearly elastic techniques are not capable of fully describing the complex
mechanical behavior of fluid-saturated tissues because they consider only a single solid phase, neglecting the
influence of extracellular fluid. In an attempt to model the deformation of biological tissues more effectively
in vivo by employing constitutive relations which are more representative of tissue structure and physiology,
a three-dimensional (3D) finite element reconstruction algorithm has been developed based on the equations
of dynamic poroelasticity. The algorithm operates on a single domain of O(103) nodes. The performance of
the algorithm was tested using simulated data. The results suggest that the technique is capable of recovering
accurate distributions of the underlying mechanical properties of the solid matrix as well as the time-harmonic
pressure field resulting from tissue vibration.
Hydrocephalus occurs due to a blockage in the transmission of cerebrospinal fluid (CSF) in either the ventricles or
subarachnoid space. Characteristics of this condition include increased intracranial pressure, which can result in
neurologic deterioration [1]. Magnetic resonance elastography (MRE) is an imaging technique that estimates the
mechanical properties of tissue in vivo. While some investigations of brain tissue have been performed using MRE
[2,3,4,5], the effects due to changes in interstitial pressure and fluid content on the mechanical properties of the brain
remain unknown. The purpose of this work is to assess the potential of MRE to differentiate between the reconstructed
properties of normal and hydrocephalic brains. MRE data was acquired in 18 female feline subjects, 12 of which
received kaolin injections resulting in an acute form of hydrocephalus. In each animal, four MRE scans were performed
during the process including one pre-injection and three post-injection scans. The elastic parameters were obtained using
a subzone-based reconstruction algorithm that solves Navier's equations for linearly elastic materials [6]. The remaining
cats were used as controls, injected with saline instead of kaolin. To determine the state of hydrocephalus, ventricular
volume was estimated from segmenting anatomical images. The mean ventricular volume of hydrocephalic cats
significantly increased (P ⪅ 0.0001) between the first and second scans. The mean volume was not observed to increase
(P ⪆ 0.5) for the control cats. Also, there was an observable increase in the recorded elastic shear modulus of brain tissue
in the normal and hydrocephalic acquisitions. Results suggest that MRE is able to detect changes in the mechanical
properties of brain tissue resulting from kaolin-induced hydrocephalus, indicating the need for further study.
KEYWORDS: Tissues, Brain, Cancer, In vivo imaging, Magnetic resonance elastography, Atmospheric modeling, Elastography, Animal model studies, Actuators, Pathology
It is well known that many pathologic processes, like cancer, result in increased tissue
stiffness but the biologic mechanisms which cause pathologies to be stiffer than normal tissues
are largely unknown. Increased collagen density has been presumed to be largely responsible
because it has been shown to cause variations in normal tissue stiffness. However, other effects
such as increased tissue pressure are also thought to be significant. We examined the effects of
tissue pressure on shear modulus measured using MR elastography (MRE) by comparing the
shear modulus in the pre-mortem, edematous and post-mortem porcine brain and found that the
measured shear modulus increases with tissue pressure as expected. The slope of a linear fit to
this preliminary data varied from 0.3 kPa/mmHg to 0.1 kPa/mmHg. These results represent the
first in vivo demonstration of tissue pressure affecting intrinsic mechanical properties and have
several implications. First, if the linear relationship described is correct, tissue pressure could
contribute significantly (~20%) to the increase in stiffness observed in cancer. Second, tissue
pressure effects must be considered when in vitro mechanical properties are extrapolated to in
vivo settings. Moreover, MRE might provide a means to characterize pathologic conditions
associated with increased or decreased tissue pressure, such as edema and ischemia, in a diverse
set of diseases including cancer, diabetes, stroke, and transplant rejection.
KEYWORDS: Tissues, Motion estimation, Scanners, Magnetic resonance imaging, Signal to noise ratio, Motion measurement, Magnetic resonance elastography, Phase measurement, Cancer, Medical imaging
A significant effort has been expended to measure the accuracy of the shear modulus estimates. Conversely, very little effort has been expended to establish the reproducibility of the
method in a clinical context. Previously we established the reproducibility in phantoms to be
3% for repeated measurements without moving the phantom and 5% when the phantom was moved,however, the clinical reproducibility has not been demonstrated. The reproducibility of the method was estimated by scanning subjects' heels repeatedly on a GE 1.5T scanner using previously described methods. Three subjects were scanned three times on different days (termed non-consecutive) and three subjects were scanned three times in the same session without changing the position of the foot (termed consecutive). The average difference between mean values within the field of view for the non-consecutive group was 7.75% ± 3.76% and for the consecutive group it was 5.30% ± 4.16%. These values represent remarkably good reproducibility considering the 20% variation in shear modulus observed within individual heels and the several hundred percent changes observed between normal and pathologic tissues. The variation in repeated examinations was caused by four factors: positioning error between examinations accounted for 4.8%, computational noise 3.0%, and the combination of MR noise and patient motion during the examination, 5.3%. Each of these sources of variation can be reduced in relatively straightforward ways if necessary but the current level of reproducibility is sufficient for most current applications.
KEYWORDS: Solids, Tissues, Finite element methods, Magnetic resonance elastography, Chemical elements, 3D modeling, Numerical analysis, Elastography, Fluid dynamics, Soil science
Magnetic Resonance Elastography (MRE) has emerged as a noninvasive, quantitative physical means of examining
the elastic properties of biological tissues. While it is common to assume simplified elasticity models for
purposes of MRE image reconstruction, it is well-accepted that many soft tissues display complex time-dependent
behavior not described by linear elasticity. Understanding how the mechanical properties of biological materials
change with the frequency of the applied stresses and strains is paramount to the reconstructive imaging
techniques used in steady-state MRE. Alternative continuum models, such as consolidation theory, offer the
ability to model tissue and other materials comprised of two distinct phases, generally consisting of an elastic
solid phase and an infiltrating fluid. For these materials, the time-dependent response under a given load is a
function not only of the elastic properties of the solid matrix, but also of the rate at which fluid can flow through
the matrix under a pressure gradient. To better study the behavior of the dynamic poroelasticity equations, a
three-dimensional finite element model was constructed. Confined, time-harmonic excitation of simulated soil
and tissue-like columns was performed to determined material deformation and pore pressure distributions, as
well as to identify the influence of the key model parameters under loading conditions and frequencies relevant
in steady-state MRE. The results show that the finite element implementation is able to represent the analytical
behavior with errors on the order of 1% over a broad range of frequencies. Further, differences between poroelastic
and elastic responses in the column can be significant over the frequency range relevant to MRE depending
on the value of hydraulic conductivity assumed for the medium.
KEYWORDS: Tissues, Computing systems, Motion measurement, Actuators, Magnetic resonance imaging, Anisotropy, In vivo imaging, Signal generators, Elastography, Magnetic resonance elastography
MR elastography (MRE) images the intrinsic mechanical properties of soft tissues; e.g., the shear modulus, μ. The μ of the plantar soft tissues is important in understanding the mechanisms whereby the forces induced during normal motion produce ulcers that lead to amputation in diabetic feet. We compared the compliance of the heel fat pad to compressive forces and to shearing forces. The design of prosthetics to protect the foot depends on the proper understanding of the mechanisms inducing damage.
In the heel fat pads of six normal subjects, between 25 and 65 years of age, the μ for deformation perpendicular to the direction of weight bearing is similar but not identical to that determined for deformation along the weight bearing axis. The average difference between μ along the weight bearing axis and μ perpendicular to the weight bearing axis, is well correlated with age (Correlation Coefficient = 0.789). The p-value for the data being random was 0.0347 indicating that the observed difference is not likely to be random. The p-value for control points is 0.8989, indicating a random process.
The results are suggestive that the high compressive forces imposed during walking damage the heel fat pads over time resulting in softening to compression preferentially over shearing. It is important to validate the observed effect with larger numbers of subjects, and better controls including measures of activity, and to understand if diseases like diabetes increase the observed damage.
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