An analytical poroelastic model for ultrasound elastography imaging of tumors

Ultrasonic High-Resolution Imaging and Acoustic Tweezers Using Ultrahigh Frequency Transducer: Integrative Single-Cell Analysis

Ultrasound imaging is a highly valuable tool in imaging human tissues due to its non-invasive and easily accessible nature. Despite advances in the field of ultrasound research, conventional transducers with frequencies lower than 20 MHz face limitations in resolution for cellular applications. To address this challenge, we employed ultrahigh frequency (UHF) transducers and demonstrated their potential applications in the field of biomedical engineering, specifically for cell imaging and acoustic tweezers. The lateral resolution achieved with a 110 MHz UHF transducer was 20 μm, and 6.5 μm with a 410 MHz transducer, which is capable of imaging single cells. The results of our experiments demonstrated the successful imaging of a single PC-3 cell and a 15 μm bead using an acoustic scanning microscope equipped with UHF transducers. Additionally, the dual-mode multifunctional UHF transducer was used to trap and manipulate single cells and beads, highlighting its potential for single-cell studies in areas such as cell deformability and mechanotransduction.

Estimation of Mechanical and Transport Parameters in Cancers Using Short Time Poroelastography

Mechanical and transport properties of cancers such as Young's modulus (YM), Poisson's ratio (PR), and vascular permeability (VP) have great clinical importance in cancer diagnosis, prognosis, and treatment. However, non-invasive estimation of these parameters in vivo is challenged by many practical factors. Elasticity imaging methods, such as "poroelastography", require prolonged data acquisition, which can limit their clinical applicability. In this paper, we investigate a new method to perform poroelastography experiments, which results in shorter temporal acquisition windows. This method is referred to as "short-time poroelastography" (STPE). Finite element (FE) and ultrasound simulations demonstrate that, using STPE, it is possible to accurately estimate YM, PR (within 10% error) using windows of observation (WoOs) of length as short as 1 underlying strain Time Constant (TC). The error was found to be almost negligible (< 3%) when using WoOs longer than 2 strain TCs. In the case of VP estimation, WoOs of at least 2 strain TCs are required to obtain an error < 8% (in simulations). The stricter requirement for the estimation of VP with respect to YM and PR is due its reliance on the transient strain behavior while YM and PR depend on the steady state strain values only. In vivo experimental data are used as a proof-of-principle of the potential applicability of the proposed methodology in vivo. The use of STPE may provide a means to efficiently perform poroelastography experiments without compromising the accuracy of the estimated tissue properties.

Thermal therapy induced fluid pressure and stress reductions in a solid tumor

This paper presents an investigation on the interstitial fluid pressure and stress reductions in a vascularized solid tumor using a thermal therapy approach. The solid tumor is modeled as a fluid infiltrated poroelastic medium with a pressure source subjected to spatial heating. The distributions of temperature, interstitial fluid pressure, strains and stresses in a spherical tumor are obtained using a thermoporoelasticity theory in which the extracellular solid matrix and the interstitial fluid have different coefficient of thermal expansion (CTE). The numerical results for a solid tumor subjected to uniform spatial heating indicate that the CTE of the solid matrix of the tumor plays a crucial role in the reductions in the fluid pressure and effective stresses caused by the thermal therapy. The pore pressure and effective stresses are reduced when the CTE of the solid matrix is higher than that of the interstitial fluid. The reductions in fluid pressure and stresses may become significant depending on the difference between the CTEs of the solid matrix and interstitial fluid. The reductions reach the maximum at the tumor center and decrease with increasing radial distance from the tumor center. Finally, the thermally induced fluid flow is directed from the surface towards the center thereby potentially improving the microcirculation in the solid tumor.

Oscillatory interstitial fluid pressure and velocity in a solid tumor with partial surface fluid leakage

This work investigates the interstitial fluid flow characteristics in a solid tumor with partial fluid leakage at the tumor surface subjected to oscillatory microvascular pressure. Solutions of the pore fluid pressure and velocity in a spherical tumor are obtained using the poroelasticity theory for small strains. It is found that partial fluid leakage at the tumor surface reduces the pore pressure drop and decreases the fluid velocity near the surface compared with those in a tumor with a fully leaking surface. Both the pore pressure and the fluid velocity decrease dramatically with an increase in the vascular frequency. The pore pressure at a vascular frequency of 1 Hz is two orders of magnitude smaller than the amplitude of the vascular pressure, and the fluid velocity at the same frequency is one order of magnitude smaller than that produced by the steady constant vascular pressure. The pore pressure amplitude may reach that of the vascular pressure under the steady state vascular pressure condition.

Multiscale modeling of solid stress and tumor cell invasion in response to dynamic mechanical microenvironment

Mathematical models can provide a quantitatively sophisticated description of tumor cell (TC) behaviors under mechanical microenvironment and help us better understand the role of specific biophysical factors based on their influences on the TC behaviors. To this end, we propose an off-lattice cell-based multiscale mathematical model to describe the dynamic growth-induced solid stress during tumor progression and investigate the influence of the mechanical microenvironment on TC invasion. At the cellular level, cell-cell and cell-matrix interactive forces depend on the mechanical properties of the cells and the cancer-associated fibroblasts in the stroma, respectively. The constitutive relationship between the interactive forces and cell migrations obeys the Hooke's law and damping effects. At the tissue level, the integrated growth-induced forces caused by proliferating cells within the simulation region are balanced by the external forces applied by the surrounding host tissues. Then, the cell movements are calculated according to the Newton's second law of motion, and the morphology of TC invasion is updated. The simulation results reveal the continuous changes of the macroscopic mechanical forces due to the interactions among the structural components and the microscopic environmental factors. Moreover, the simulation results demonstrate the adverse effect of the stiffness of tumor tissue on tumor growth and invasion. A decrease in the stiffness of tumor and matrix can promote TCs to proliferate at a much faster rate and invade into the surrounding healthy tissue more easily, whereas an increase in the stiffness can lead to an aggressive morphology of tumor invasion. We envision that the proposed model can be served as a quantitative theoretical platform to study the underlying biophysical role of the mechanical microenvironmental factors during tumor invasion and metastasis.

Estimation of mechanical parameters in cancers by empirical orthogonal function analysis of poroelastography data

Ultrasound poroelastography is a non-invasive imaging modality that has been shown to be capable of estimating mechanical parameters such as Young's modulus (YM), Poisson's ratio (PR) and vascular permeability (VP) in cancers. However, experimental poroelastographic data are inherently noisy because of the requirement of relatively long temporal data acquisitions often in hand-held mode conditions. In this paper, we propose a new method, which allows accurate estimation of YM and PR from denoised steady state axial and lateral strains by empirical orthogonal function (EOF) analysis of poroelastographic data. The method also allows estimation of VP from the time constant (TC) of the first expansion coefficient (EC) of the temporal axial strain, which has larger dynamic range and lower noise in comparison to the actual temporal axial strain curve. We validated our technique through finite element (FE) and ultrasound simulations and tested the in vivo feasibility in experimental data obtained from a cancer animal model. The percent relative errors (PRE) in the estimation of YM, PR and VP using the EOF analysis as applied to ultrasound simulation data were 3.27%, 3.10%, 14.22%, respectively (at SNR of 20 dB). Based on the high level of accuracy by EOF analysis, the proposed technique may become a useful signal processing technique for applications focusing on the estimation of the mechanical behavior of cancers.

A Robust Method to Estimate the Time Constant of Elastographic Parameters

Novel viscoelastic and poroelastic elastography techniques rely on the accurate estimation of the temporal behavior of the axial or lateral strains and related parameters. From the temporal curve of the elastographic parameter of interest, the time constant (TC) is estimated using analytical models and curve-fitting techniques such as Levenberg-Marquardt (LM), Nelder-Mead (NM), and trust-region reflective (TR). In this paper, we propose a new technique named variable projection (VP) to estimate accurately and robustly the TC and steady-state value of the elastographic parameter of interest from its temporal curve. As a testing platform, the method is used with a novel analytical model, which can be used for both poroelastic and viscoelastic tissues and in most practical experimental conditions of clinical interest. Finite element and ultrasound simulations and experimental results demonstrate that VP is robust to noise and capable of estimating the TC of the elastographic parameter with accuracy higher than that of typically employed curve-fitting techniques. The results also demonstrate that the performance of VP is not affected by an incorrect initial TC guess. For example, in simulations, VP can estimate the TC of axial strain and effective Poisson's ratio accurately for initial guesses ranging from 0.001 to infinite times of the true TC value even in fairly noisy conditions (30-dB signal to noise ratio). In experiments, VP always estimates the axial strain TC reliably, whereas the LM, NM, and TR methods fail to converge or converge to wrong solutions in most of the cases.

An analytical poroelastic model of a non-homogeneous medium under creep compression for ultrasound poroelastography applications - Part II

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical parameters. Specifically, in this derivation, the inclusion is assumed to have significantly higher interstitial permeability than the background. The formulations of the effective Poisson's ratio (EPR) and fluid pressure in the inclusion and in the background are derived for the case of a sample subjected to a creep compression. The developed analytical expressions are validated using finite element models (FEM). Statistical comparison between the results obtained from the developed model and the results from FEM demonstrates accuracy of the proposed theoretical model higher than 99.4%. The model presented in this paper complements the one reported in the companion paper (Part I), which refers to the case of an inclusion having less interstitial permeability than the background.

An analytical poroelastic model of a non-homogeneous medium under creep compression for ultrasound poroelastography applications - Part I

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical properties. Specifically, in this paper, the inclusion is considered to be less permeable than the background. The cylindrical sample is compressed using a constant pressure within two frictionless plates and is allowed to expand in an unconfined way along the radial direction. Analytical expressions for the effective Poisson's ratio (EPR) and fluid pressure inside and outside the inclusion are derived and analyzed. The theoretical results are validated using finite element models (FEM). Statistical analysis shows excellent agreement between the results obtained from the developed model and the results from FEM. Thus the developed theoretical model can be used in medical imaging modalities such as ultrasound poroelastography to extract the mechanical parameters of tissues and/or to better understand the impact of the different mechanical parameters on the estimated displacements, strains, stresses and fluid pressure inside a tumor and in the surrounding tissue.