Nonlinear Tissue Properties Research Articles

Ultrasound Imaging of Nonlinear Media Response Using a Pressure-Dependent Nonlinearity Index

It has been shown that within the range of acoustic pressures used in ultrasound imaging, waveforms are distorted during propagation in tissue due to the physically nonlinear behavior of the tissue. This distortion leads to changes in the spectrum of the received ultrasound echoes, causing the transfer of signal energy from the fundamental frequency to higher harmonics. Interestingly, adipose tissue exhibits up to 50 % stronger nonlinear behavior compared to other soft tissues. The tissue nonlinearity parameter B/A is typically measured ex vivo using an ultrasound method in transmission mode, which requires extensive receiving systems. Currently, there is no improved ultrasound method for measuring the B/A nonlinearity parameter in vivo, which could be used in assessing the degree of fatty liver disease. We propose a new, simple approach to estimating nonlinear tissue properties. The proposed method involves transmitting ultrasound waves at significantly different acoustic pressures, recording echoes only in the fundamental frequency band at various depths, and introducing a nonlinearity index (NLI) based on specific echo amplitude ratios. The NLI at a given depth is calculated using the ratio of two dimensionless parameters. The first parameter is a predetermined constant obtained by dividing the total echo values from transmitting a signal at higher sound pressure by those from a signal at lower sound pressure, summed over a small tissue sample volume located near the transducer. The second parameter is calculated at a fixed distance from the transducer, determined by dividing the total echo values from transmitting a signal at higher sound pressure by those from a signal at lower pressure, summed over a small tissue volume of the tissue at that distance from the transducer. The reliability of the proposed measurements for assessing tissue nonlinearity has been substantiated through experimental confirmation of the existing correlations between the values of NLI and B/A in water, sunflower oil, and animal liver tissue samples with oil-enriched regions. The NLI was more than 15 % higher in sunflower oil than in water. The NLI in bovine liver sample below the area with injected oil (mimicking “steatosis”) was more than 35 % higher than in regions without oil. This method represents a promising modality for the nonlinear characterization of tissue regions in vivo, particularly for diagnosing fatty liver disease.

Geometry of adipocyte packing in subcutaneous tissue contributes to nonlinear tissue properties captured through a Gaussian process surrogate model.

Subcutaneous tissue mechanical response is governed by the geometry and mechanical properties at the microscale and drives physiological and clinical processes such as drug delivery. Even though adipocyte packing is known to change with age, disease, and from one individual to another, the link between the geometry of the packing and the overall mechanical response of adipose tissue remains poorly understood. Here we create 1200 periodic representative volume elements (RVEs) that sample the possible space of Laguerre packings describing adipose tissue. RVE mechanics are modeled under tri-axial loading. Equilibrium configuration of RVEs is solved by minimizing an energetic potential that includes volume change contributions from adipocyte expansion, and area change contributions from collagen foam stretching. The resulting mechanical response across all RVE samples is interpolated with the aid of a Gaussian process (GP), revealing how the microscale geometry dictates the overall RVE mechanics. For example, increase in adipocyte size and increase in sphericity lead to adipose tissue softening. We showcase the use of the homogenized model in finite element simulations of drug injection by implementing a Blatz-Ko model, informed by the GP, as a custom material in the popular open-source package FEBio. These simulations show how microscale geometry can lead to vastly different injection dynamics even if the constituent parameters are held constant, highlighting the importance of characterizing individual's adipose tissue structure in the development of personalized therapies.

Measured Hyperelastic Properties of Cervical Tissue with Shear-Wave Elastography.

The nonlinear mechanical behaviour of cervical tissue causes unpredictable changes in measured elastograms when pressure is applied. These uncontrolled variables prevent the reliable measurement of tissue elasticity in a clinical setting. Measuring the nonlinear properties of tissue is difficult due to the need for both shear modulus and strain to be taken simultaneously. A simulation-based method is proposed in this paper to resolve this. This study describes the nonlinear behaviour of cervical tissue using the hyperelastic material models of Demiray–Fung and Veronda–Westmann. Elastograms from 33 low-risk patients between 18 and 22 weeks gestation were obtained. The average measured properties of the hyperelastic material models are: Demiray–Fung— = 2.07 (1.65–2.58) kPa, = 6.74 (4.07–19.55); Veronda–Westmann— = 4.12 (3.24–5.04) kPa, = 4.86 (2.86–14.28). The Demiray–Fung and Veronda–Westmann models performed similarly in fitting to the elastograms with an average root mean square deviation of 0.41 and 0.47 ms, respectively. The use of hyperelastic material models to calibrate shear-wave speed measurements improved the consistency of measurements. This method could be applied in a large-scale clinical setting but requires updated models and higher data resolution.

Biomechanical Evaluations of Ocular Injury Risk for Blast Loading.

Ocular trauma is one of the most common types of combat injuries resulting from the exposure of military personnel with improvised explosive devices. The injury mechanism associated with the primary blast wave is poorly understood. We employed a three-dimensional computational model, which included the main internal ocular structures of the eye, spatially varying thickness of the cornea-scleral shell, and nonlinear tissue properties, to calculate the intraocular pressure and stress state of the eye wall and internal ocular structure caused by the blast. The intraocular pressure and stress magnitudes were applied to estimate the injury risk using existing models for blunt impact and blast loading. The simulation results demonstrated that blast loading can induce significant stresses in the different components of the eyes that correlate with observed primary blast injuries in animal studies. Different injury models produced widely different injury risk predictions, which highlights the need for experimental studies evaluating mechanical and functional damage to the ocular structures caused by the blast loading.

Mechanical strength of aneurysmatic and dissected human thoracic aortas at different shear loading modes

Rupture of aneurysms and acute dissection of the thoracic aorta are life-threatening events which affect tens of thousands of people per year. The underlying mechanisms remain unclear and the aortic wall is known to lose its structural integrity, which in turn affects its mechanical response to the loading conditions. Hence, research on such aortic diseases is an important area in biomechanics. The present study investigates the mechanical properties of aneurysmatic and dissected human thoracic aortas via triaxial shear and uniaxial tensile testing with a focus on the former. In particular, ultimate stress values from triaxial shear tests in different orientations regarding the aorta׳s orthotropic microstructure, and from uniaxial tensile tests in radial, circumferential and longitudinal directions were determined. In total, 16 human thoracic aortas were investigated from which it is evident that the aortic media has much stronger resistance to rupture under ‘out-of-plane’ than under ‘in-plane’ shear loadings. Under different shear loadings the aortic tissues revealed anisotropic failure properties with higher ultimate shear stresses and amounts of shear in the longitudinal than in the circumferential direction. Furthermore, the aortic media decreased its tensile strength as follows: circumferential direction >longitudinaldirection> radial direction. Anisotropic and nonlinear tissue properties are apparent from the experimental data. The results clearly showed interspecimen differences influenced by the anamnesis of the donors such as aortic diseases or connective tissue disorders, e.g., dissected specimens exhibited on average a markedly lower mechanical strength than aneurysmatic specimens. The rupture data based on the combination of triaxial shear and uniaxial extension testing are unique and build a good basis for developing a 3D failure criterion of diseased human thoracic aortic media. This is a step forward to more realistic modeling of mechanically induced tissue failure i.e. rupture of aneurysms or progression of aortic dissections.

Mitigation of impedance changes due to electroporation therapy using bursts of high-frequency bipolar pulses.

BackgroundFor electroporation-based therapies, accurate modeling of the electric field distribution within the target tissue is important for predicting the treatment volume. In response to conventional, unipolar pulses, the electrical impedance of a tissue varies as a function of the local electric field, leading to a redistribution of the field. These dynamic impedance changes, which depend on the tissue type and the applied electric field, need to be quantified a priori, making mathematical modeling complicated. Here, it is shown that the impedance changes during high-frequency, bipolar electroporation therapy are reduced, and the electric field distribution can be approximated using the analytical solution to Laplace's equation that is valid for a homogeneous medium of constant conductivity.MethodsTwo methods were used to examine the agreement between the analytical solution to Laplace's equation and the electric fields generated by 100 µs unipolar pulses and bursts of 1 µs bipolar pulses. First, pulses were applied to potato tuber tissue while an infrared camera was used to monitor the temperature distribution in real-time as a corollary to the electric field distribution. The analytical solution was overlaid on the thermal images for a qualitative assessment of the electric fields. Second, potato ablations were performed and the lesion size was measured along the x- and y-axes. These values were compared to the analytical solution to quantify its ability to predict treatment outcomes. To analyze the dynamic impedance changes due to electroporation at different frequencies, electrical impedance measurements (1 Hz to 1 MHz) were made before and after the treatment of potato tissue.ResultsFor high-frequency bipolar burst treatment, the thermal images closely mirrored the constant electric field contours. The potato tissue lesions differed from the analytical solution by 39.7 ± 1.3 % (x-axis) and 6.87 ± 6.26 % (y-axis) for conventional unipolar pulses, and 15.46 ± 1.37 % (x-axis) and 3.63 ± 5.9 % (y-axis) for high- frequency bipolar pulses.ConclusionsThe electric field distributions due to high-frequency, bipolar electroporation pulses can be closely approximated with the homogeneous analytical solution. This paves way for modeling fields without prior characterization of non-linear tissue properties, and thereby simplifying electroporation procedures.

Harmonic Imaging Using Multitone Nonlinear Coding

We present a new method that uses nonlinear properties of tissue to improve contrast-to-noise ratio. In our novel method, the acoustic source is activated with two tone-bursts (2.2 and 4.4 MHz), with specially designed polarization of the individual tone-burst. This new approach is called multitone nonlinear coding (MNC) because the choice of polarization of both tones (and their amplitudes), allowing optimization of the receiving properties, depends on the nonlinear properties of tissue. The calculations were done for two tone-bursts propagating in the tissue-like glossy medium with absorption of 7 Np/m · MHz. The method was experimentally verified by scanning the incident pulses propagating in soft tissue and by scanning the thread phantom immersed in water. The concept of the virtual fields was introduced to explain abilities and properties of pulse inversion and MNC and to compare the two methods. Comparison of the spatial field distribution obtained using MNC with the conventional harmonic imaging approach, in which the second harmonic is used to reconstruct the image, is presented. It was shown that, for the same peak pressure amplitude, the resulting mechanical index was about 40% lower for MNC, lateral resolution was 10% to 30% better and, what seems to be the most encouraging, the signal gain was up to eight times higher than pulse inversion. (E-mail: anowicki@ippt.gov.pl)

Anisotropic Mechanical Properties of Tissue Components in Human Atherosclerotic Plaques

Knowledge of the biomechanical properties of human atherosclerotic plaques is of essential importance for developing more insights in the pathophysiology of the cardiovascular system and for better predicting the outcome of interventional treatments such as balloon angioplasty. Available data are mainly based on uniaxial tests, and most of the studies investigate the mechanical response of fibrous plaque caps only. However, stress distributions during, for example, balloon angioplasty are strongly influenced by all components of atherosclerotic lesions. A total number of 107 samples from nine human high-grade stenotic iliac arteries were tested; associated anamnesis of donors reported. Magnetic resonance imaging was employed to test the usability of the harvested arteries. Histological analyses has served to characterize the different tissue types. Prepared strips of 7 different tissue types underwent cyclic quasistatic uniaxial tension tests in axial and circumferential directions; ultimate tensile stresses and stretches were documented. Experimental data of individual samples indicated anisotropic and highly nonlinear tissue properties as well as considerable interspecimen differences. The calcification showed, however a linear property, with about the same stiffness as observed for the adventitia in high stress regions. The stress and stretch values at calcification fracture are smaller (179 +/- 56 kPa and 1.02 +/- 0.005) than for each of the other tissue components. Of all intimal tissues investigated, the lowest fracture stress occurred in the circumferential direction of the fibrous cap (254.8 +/- 79.8 kPa at stretch 1.182 +/- 0.1). The adventitia demonstrated the highest and the nondiseased media the lowest mechanical strength on average.

Observation of nonlinear shear wave propagation using magnetic resonance elastography.

MR elastography (MRE) is an MRI modality that is increasingly being used to image tissue elasticity throughout the body. One MRE technique that has received a great deal of attention is based on visualizing shear waves, which reveal stiffness by virtue of their local wavelength. However, the shape of propagating shear waves can also provide valuable information about the nonlinear stress-strain behavior of tissue. Here an experiment is proposed that allows the observation of nonlinear wave propagation based on spatial-temporal phase contrast images. A theoretical description of the wave propagation was developed that reflects typical MRE excitation, which involves excitation modes both parallel and perpendicular to B0. Based on this model, it is shown that both odd and even higher harmonics are produced with their amplitudes dependent on the details of the actuator, imaging geometry, and the nonlinear tissue properties. With appropriate motion encoding, harmonic vibrations arising from nonlinear tissue response can be detected. The effect is demonstrated on an agarose gel phantom using a sinusoidal shear vibration of 150 Hz, and clearly shows the presence of harmonics at 600 and 750 Hz. Using an estimate of the strain energy of the phantom, we were able to determine the nonlinear tissue properties.

Bio-acoustic thermal lensing and nonlinear propagation in focused ultrasound surgery using large focal spots: a parametric study

It is well known that the acoustic properties of soft tissue have a dependence on tissue temperature. This is of particular interest in focused ultrasound surgery since the mechanism of action of focused ultrasound surgery is to kill targeted tissue by inducing localized heating by ultrasound absorption, and hence cautery of that tissue. However, the act of localized heating induces a change in the acoustic properties of the targeted tissue and tissue surrounding it. This phenomenon distorts the incoming acoustic wavefront, and has been termed the thermal lens effect for this reason. Furthermore, nonlinear effects in acoustic propagation become non-negligible at the ultrasound intensities required for therapeutic action.This paper examines the importance of the thermal lens effect and nonlinear tissue properties by simulating a variety of clinically applicable phased array transducer configurations that have not yet been appropriately analysed using a full three-dimensional nonlinear treatment of acoustic propagation. The significance of the thermal lens effect is characterized by comparing the simulation of coupled acoustic and thermal propagation with an uncoupled treatment; neglecting thermal lensing typically produces a movement of 1 to 2 mm in the predicted position of the focus towards the transducer.The results also show that the classical methods of acoustic propagation can produce grossly erroneous results under certain clinically relevant transducer configurations and that an acoustic field scan with a hydrophone may not accurately predict therapeutic effect.