A numerical framework for interstitial fluid pressure imaging in poroelastic MRE

Effect of interstitial fluid pressure on shear wave elastography: an experimental and computational study

Objective. An elevated interstitial fluid pressure (IFP) can lead to strain-induced stiffening of poroelastic biological tissues. As shear wave elastography (SWE) measures functional tissue stiffness based on the propagation speed of acoustically induced shear waves, the shear wave velocity (SWV) can be used as an indirect measurement of the IFP. The underlying biomechanical principle for this stiffening behavior with pressurization is however not well understood, and we therefore studied how IFP affects SWV through SWE experiments and numerical modeling.Approach. For model set-up and verification, SWE experiments were performed while dynamically modulating IFP in a chicken breast. To identify the confounding factors of the SWV-IFP relationship, we manipulated the material model (linear poroelastic versus porohyperelastic), deformation assumptions (geometric linearity versus nonlinearity), and boundary conditions (constrained versus unconstrained) in a finite element model mimicking the SWE experiments.Main results. The experiments demonstrated a statistically significant positive correlation between the SWV and IFP. The model was able to reproduce a similar SWV-IFP relationship by considering an unconstrained porohyperelastic tissue. Material nonlinearity was identified as the primary factor contributing to this relationship, whereas geometric nonlinearity played a smaller role. The experiments also highlighted the importance of the dynamic nature of the pressurization procedure, as indicated by a different observed SWV-IFP for pressure buildup and relaxation, but its clinical relevance needs to be further investigated.Significance. The developed model provides an adaptable framework for SWE of poroelastic tissues and paves the way towards non-invasive measurements of IFP.

Hydraulic conductivity of human cancer tissue: A hybrid study

Background

Elevated tumor tissue interstitial fluid pressure (IFP) is an adverse biomechanical biomarker that predicts poor therapy response and an aggressive phenotype. Advances in functional imaging have opened the prospect of measuring IFP non-invasively. Image-based estimation of the IFP requires knowledge of the tissue hydraulic conductivity (K), a measure for the ease of bulk flow through the interstitium. However, data on the magnitude of K in human cancer tissue are not available.

Methods

We measured the hydraulic conductivity of tumor tissue using modified Ussing chambers in surgical resection specimens. The effect of the tumor microenvironment (TME) on K was investigated by quantifying the collagen content, cell density, and fibroblast density of the tested samples using quantitative immune histochemistry. Also, we developed a computational fluid dynamics (CFD) model to evaluate the role of K on interstitial fluid flow and drug transport in solid tumors.

Results

The results show that the hydraulic conductivity of human tumor tissues is very limited, ranging from approximately 10-15 to 10-14 m2/Pa∙s. Moreover, K values varied significantly between tumor types and between different samples from the same tumor. A significant inverse correlation was found between collagen fiber density and hydraulic conductivity values. However, no correlation was detected between K and cancer cell or fibroblast densities. The computational model demonstrated the impact of K on the interstitial fluid flow and the drug concentration profile: higher K values led to a lower IFP and deeper drug penetration.

Conclusions

Human tumor tissue is characterized by a very limited hydraulic conductivity, representing a barrier to effective drug transport. The results of this study can inform the development of realistic computational models, facilitate non-invasive IFP estimation, and contribute to stromal targeting anticancer therapies.

Transversely-isotropic brain in vivo MR elastography with anisotropic damping

Measuring tissue parameters from increasingly sophisticated mechanical property models may uncover new contrast mechanisms with clinical utility. Building on previous work on in vivo brain MR elastography (MRE) with a transversely-isotropic with isotropic damping (TI-ID) model, we explore a new transversely-isotropic with anisotropic damping (TI-AD) model that involves six independent parameters describing direction-dependent behavior for both stiffness and damping. The direction of mechanical anisotropy is determined by diffusion tensor imaging and we fit three complex-valued moduli distributions across the full brain volume to minimize differences between measured and modeled displacements. We demonstrate spatially accurate property reconstruction in an idealized shell phantom simulation, as well as an ensemble of 20 realistic, randomly-generated simulated brains. We characterize the simulated precisions of all six parameters across major white matter tracts to be high, suggesting that they can be measured independently with acceptable accuracy from MRE data. Finally, we present in vivo anisotropic damping MRE reconstruction data. We perform t-tests on eight repeated MRE brain exams on a single-subject, and find that the three damping parameters are statistically distinct for most tracts, lobes and the whole brain. We also show that population variations in a 17-subject cohort exceed single-subject measurement repeatability for most tracts, lobes and whole brain, for all six parameters. These results suggest that the TI-AD model offers new information that may support differential diagnosis of brain diseases.

Interstitial fluid pressure as an emerging biomarker in solid tumors

The physical microenvironment of cancer is characterized by elevated stiffness and tissue pressure, the main component of which is the interstitial fluid pressure (IFP). Elevated IFP is an established negative predictive and prognostic parameter, directly affecting malignant behavior and therapy response. As such, measurement of the IFP would allow to develop strategies aimed at engineering the physical microenvironment of cancer. Traditionally, IFP measurement required the use of invasive methods. Recent progress in dynamic and functional imaging methods such as dynamic contrast enhanced (DCE) magnetic resonance imaging and elastography, combined with numerical models and simulation, allows to comprehensively assess the biomechanical landscape of cancer, and may help to overcome physical barriers to drug delivery and immune cell infiltration. Here, we provide a comprehensive overview of the origin of elevated IFP, and its role in the malignant phenotype. Also, we review the methods used to measure IFP using invasive and imaging based methods, and highlight remaining obstacles and potential areas of progress in order to implement IFP measurement in clinical practice.

Noninvasive Detection of Intracranial Hypertension by Novel Ultrasound Time-Harmonic Elastography

OBJECTIVE

A method for measuring intracranial pressure (ICP) noninvasively has long been sought after in neurology and neurosurgery. Treatment failure in individuals presenting with unspecific symptoms such as headache, gait disturbance, or visual impairment occurring in response to increased ICP can lead to irreversible brain injury, progressive disability, and death. Guidelines for diagnostic ICP measurement recommend intracranial placement of pressure tip catheters or lumbar puncture (LP) despite their invasiveness and possible complications. As ICP fluctuations are closely associated with changes in brain stiffness, ultrasound elastography could be a valid method to detect ICP noninvasively and with short examination times.

MATERIALS AND METHODS

In this pilot study, we have investigated the use of time-harmonic shear waves, introduced into the brain by an external shaker, and measured in real-time by transtemporal ultrasound, for deducing a noninvasive imaging marker sensitive to elevated ICP. To this end, we developed cerebral ultrasound time-harmonic elastography for the noninvasive quantification of shear wave speed (SWS) as a surrogate marker of cerebral stiffness in a short examination time of a few minutes.

RESULTS

We found that SWS in patients enrolled for LP with confirmed intracranial hypertension was 1.81 ± 0.10 m/s, distinguishing them from healthy volunteers with excellent diagnostic accuracy (1.55 ± 0.08 m/s; P < 0.001; area under the curve, 0.99). Interestingly, values in symptomatic patients decreased to normal stiffness immediately after LP (1.56 ± 0.06 m/s, P < 0.001). Moreover, invasively measured opening pressure correlated with SWS measured before LP and liquid volume drained through the spinal tap with the SWS difference between the 2 measurements.

CONCLUSIONS

Collectively, our results suggest a tight link between cerebral stiffness and ICP and demonstrate that intracranial hypertension can be detected noninvasively within short examination times, opening avenues for diagnostic applications of cerebral ultrasound time-harmonic elastography in neurology and emergency medicine.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

Strain Tensor Imaging: Cardiac-induced brain tissue deformation in humans quantified with high-field MRI

The cardiac cycle induces blood volume pulsations in the cerebral microvasculature that cause subtle deformation of the surrounding tissue. These tissue deformations are highly relevant as a potential source of information on the brain's microvasculature as well as of tissue condition. Besides, cyclic brain tissue deformations may be a driving force in clearance of brain waste products. We have developed a high-field magnetic resonance imaging (MRI) technique to capture these tissue deformations with full brain coverage and sufficient signal-to-noise to derive the cardiac-induced strain tensor on a voxel by voxel basis, that could not be assessed non-invasively before. We acquired the strain tensor with 3 mm isotropic resolution in 9 subjects with repeated measurements for 8 subjects. The strain tensor yielded both positive and negative eigenvalues (principle strains), reflecting the Poison effect in tissue. The principle strain associated with expansion followed the known funnel shaped brain motion pattern pointing towards the foramen magnum. Furthermore, we evaluate two scalar quantities from the strain tensor: the volumetric strain and octahedral shear strain. These quantities showed consistent patterns between subjects, and yielded repeatable results: the peak systolic volumetric strain (relative to end-diastolic strain) was 4.19⋅10^-4 ± 0.78⋅10^-4 and 3.98⋅10^-4 ± 0.44⋅10^-4 (mean ± standard deviation for first and second measurement, respectively), and the peak octahedral shear strain was 2.16⋅10^-3 ± 0.31⋅10^-3 and 2.31⋅10^-3 ± 0.38⋅10^-3, for the first and second measurement, respectively. The volumetric strain was typically highest in the cortex and lowest in the periventricular white matter, while anisotropy was highest in the subcortical white matter and basal ganglia. This technique thus reveals new, regional information on the brain's cardiac-induced deformation characteristics, and has the potential to advance our understanding of the role of microvascular pulsations in health and disease.

Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

MR elastography: Principles, guidelines, and terminology

Magnetic resonance elastography (MRE) is a phase contrast-based MRI technique that can measure displacement due to propagating mechanical waves, from which material properties such as shear modulus can be calculated. Magnetic resonance elastography can be thought of as quantitative, noninvasive palpation. It is increasing in clinical importance, has become widespread in the diagnosis and staging of liver fibrosis, and additional clinical applications are being explored. However, publications have reported MRE results using many different parameters, acquisition techniques, processing methods, and varied nomenclature. The diversity of terminology can lead to confusion (particularly among clinicians) about the meaning of and interpretation of MRE results. This paper was written by the MRE Guidelines Committee, a group formalized at the first meeting of the ISMRM MRE Study Group, to clarify and move toward standardization of MRE nomenclature. The purpose of this paper is to (1) explain MRE terminology and concepts to those not familiar with them, (2) define "good practices" for practitioners of MRE, and (3) identify opportunities to standardize terminology, to avoid confusion.

Separation of fluid and solid shear wave fields and quantification of coupling density by magnetic resonance poroelastography

PURPOSE

Biological soft tissues often have a porous architecture comprising fluid and solid compartments. Upon displacement through physiological or externally induced motion, the relative motion of these compartments depends on poroelastic parameters, such as coupling density ( ρ 12 ) and tissue porosity. This study introduces inversion recovery MR elastography (IR-MRE) (1) to quantify porosity defined as fluid volume over total volume, (2) to separate externally induced shear strain fields of fluid and solid compartments, and (3) to quantify coupling density assuming a biphasic behavior of in vivo brain tissue.

THEORY AND METHODS

Porosity was measured in eight tofu phantoms and gray matter (GM) and white matter (WM) of 21 healthy volunteers. Porosity of tofu was compared to values obtained by fluid draining and microscopy. Solid and fluid shear-strain amplitudes and ρ 12 were estimated both in phantoms and in in vivo brain.

RESULTS

T₁ -based measurement of tofu porosity agreed well with reference values (R = 0.99, P < .01). Brain tissue porosity was 0.14 ± 0.02 in GM and 0.05 ± 0.01 in WM (P < .001). Fluid shear strain was found to be phase-locked with solid shear strain but had lower amplitudes in both tofu phantoms and brain tissue (P < .05). In accordance with theory, tofu and brain ρ 12 were negative.

CONCLUSION

IR-MRE allowed for the first time separation of shear strain fields of solid and fluid compartments for measuring coupling density according to the biphasic theory of poroelasticity. Thus, IR-MRE opens horizons for poroelastography-derived imaging markers that can be used in basic research and diagnostic applications.

Nonlinear Inversion MR Elastography With Low-Frequency Actuation

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

Towards noninvasive estimation of tumour pressure by utilising MR elastography and nonlinear biomechanical models: a simulation and phantom study

The solid and fluid pressures of tumours are often elevated relative to surrounding tissue. This increased pressure is known to correlate with decreased treatment efficacy and potentially with tumour aggressiveness and therefore, accurate noninvasive estimates of tumour pressure would be of great value. We present a proof-of-concept method to infer the total tumour pressure, that is the sum of the fluid and solid parts, by examining stiffness in the peritumoural tissue with MR elastography and utilising nonlinear biomechanical models. The pressure from the tumour deforms the surrounding tissue leading to changes in stiffness. Understanding and accounting for these biases in stiffness has the potential to enable estimation of total tumour pressure. Simulations are used to validate the method with varying pressure levels, tumour shape, tumour size, and noise levels. Results show excellent matching in low noise cases and still correlate well with higher noise. Percent error remains near or below 10% for higher pressures in all noise level cases. Reconstructed pressures were also calculated from experiments with a catheter balloon embedded in a plastisol phantom at multiple inflation levels. Here the reconstructed pressures generally match the increases in pressure measured during the experiments. Percent errors between average reconstructed and measured pressures at four inflation states are 17.9%, 52%, 23.2%, and 0.9%. Future work will apply this method to in vivo data, potentially providing an important biomarker for cancer diagnosis and treatment.

Dilatational and shear waves in poro-vioscoelastic media

Dynamic elastography methods are being developed for quantitatively and noninvasively mapping the viscoelastic properties of biological tissue that are often altered by disease and injury, as well as response to treatment. This involves inducing mechanical wave motion that also can be affected by the multiphase porous nature of the tissue, whether it be consideration of blood perfusion in the vascular network found in many regions of interest, or consideration of air movement in the complex bronchial tree within the lungs. Elastographic mapping requires reconstructing material properties based on interpretation of the measured wave motion. Reconstruction methods that explicitly incorporate poroelastic behavior are an active area of development. In the present article the equivalence of two theoretical approaches to modeling poroelastic behavior is demonstrated specifically in the frequency domain using parameter values that span the range expected in vivo for analysis of blood and air-infused regions. The two methods are known as (1) the mixture or biphasic formulation and (2) the poroelastic approach. The case of acoustic wave propagation in the lungs is specifically addressed by comparison of analytical predictions to recently reported experimental measurements. Establishing and validating this equivalence of theoretical approaches not only strengthens our fundamental understanding of the relevant physics, but also may lead to improved numerical methods for simulation and elastography reconstruction.

A Poroelasticity Theory Approach to Study the Mechanisms Leading to Elevated Interstitial Fluid Pressure in Solid Tumours

Although the mechanisms responsible for elevated interstitial fluid pressure (IFP) in tumours remain obscure, it seems clear that high IFP represents a barrier to drug delivery (since the resulting adverse pressure gradient implies a reduction in the driving force for transvascular exchange of both fluid and macromolecules). R. Jain and co-workers studied this problem, and although the conclusions drawn from their idealized mathematical models offered useful insights into the causes of elevated IFP, they by no means gave a definitive explanation for this phenomenon. In this paper, we use poroelasticity theory to also develop a macroscopic mathematical model to describe the time evolution of a solid tumour, but focus our attention on the mechanisms responsible for the rise of the IFP, from that for a healthy interstitium to that measured in malignant tumours. In particular, we discuss a number of possible time scales suggested by our mathematical model and propose a tumour-dependent time scale that leads to results in agreement with experimental observations. We apply our mathematical model to simulate the effect of "vascular normalization" (as proposed by Jain in Nat Med 7:987-989, 2001) on the IFP profile and discuss and contrast our conclusions with those of previous work in the literature.