Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Contactless Remote Induction of Shear Waves in Soft Tissues Using a Transcranial Magnetic Stimulation Device

This study presents the first observation of shear wave induced remotely within soft tissues. It was performed through the combination of a transcranial magnetic stimulation device and a permanent magnet. A physical model based on Maxwell and Navier equations was developed. Experiments were performed on a cryogel phantom and a chicken breast sample. Using an ultrafast ultrasound scanner, shear waves of respective amplitude of 5 and 0.5 micrometers were observed. Experimental and numerical results were in good agreement. This study constitutes the framework of an alternative shear wave elastography method

Dynamic Behavior in Piezoresponse Force Microscopy

Frequency dependent dynamic behavior in Piezoresponse Force Microscopy (PFM) implemented on a beam-deflection atomic force microscope (AFM) is analyzed using a combination of modeling and experimental measurements. The PFM signal comprises contributions from local electrostatic forces acting on the tip, distributed forces acting on the cantilever, and three components of the electromechanical response vector. These interactions result in the bending and torsion of the cantilever, detected as vertical and lateral PFM signals. The relative magnitudes of these contributions depend on geometric parameters of the system, the stiffness and frictional forces of tip-surface junction, and operation frequencies. The dynamic signal formation mechanism in PFM is analyzed and conditions for optimal PFM imaging are formulated. The experimental approach for probing cantilever dynamics using frequency-bias spectroscopy and deconvolution of electromechanical and electrostatic contrast is implemented.Comment: 65 pages, 15 figures, high quality version available upon reques

Quantitative Gewebecharakterisierung mittels mechanischer Kenngrößen in präklinischen Kleintiermodellen

The biomechanical properties of the brain play an important role in vital functioning and disease development. Over the last decade, cerebral magnetic resonance elastography (MRE) has emerged as a valuable imaging technique, revealing important characteristics of tissue biomechanics in disease and health. However, state-of-the-art mouse brain MRE is limited by time-consuming multi-shot acquisition techniques and noise-sensitive single-frequency image reconstruction methods. Therefore, the purpose of this PhD project was the development of multifrequency mouse brain MRE based on a single-shot acquisition technique and noise-robust tomoelastography post-processing for high-resolution stiffness mapping. The feasibility of the method was demonstrated using three in vivo studies. In the first study, shear wave speed (SWS) as a surrogate of stiffness in different areas of the brain was measured. In the second study, the effect of body temperature on biophysical parameters of murine brain tissue was investigated in the normothermic to hypothermic range. Tomoelastography was combined with arterial spin labelling and diffusion-weighted imaging in order to determine the relationship between tissue stiffness, perfusion and diffusion. In the third study, mechanical brain alterations were continuously monitored during the critical phase of death in a mouse model of hypoxia. In ten animals, we quantified regional dependent SWS of 2.9 ± 0.2 m/s, 4.9 ± 0.5 m/s, 4.8 ± 0.8 m/s and 3.5 ± 0.3 m/s for the corpus callosum, hippocampus, diencephalon and cortex. In a group of six animals, we found that SWS decreased from hypothermia (28 ± 0.5 °C) to normothermia (38 ± 0.5 °C) by 6.2%, 10.1% and 7.4% in the whole brain, cortex and hippocampus, respectively. These SWS decreases were correlated with changes in water diffusion (30% increase) and blood perfusion (60% to 90% increase). Furthermore, in fourteen animals, brain death led to a 6% increase of SWS in the whole brain and 9% in the hippocampus when compared to in vivo values. Our novel multifrequency MRE method with tomoelastography processing provides mouse brain stiffness maps within shorter scan times and with greater detail resolution than a conventional MRE. Short scan times, in the order of only 40 seconds, open new horizons for continuous stiffness monitoring during different pathological processes in vivo. Clinical relevant biophysical processes in the brain, such as hypothermia and hypoxia, and the critical phase of brain death were monitored and investigated for the first time. The results show that stiffness varies across sub-regions in the murine brain, is inversely correlated with water diffusion and blood perfusion, and increases in hypoxia towards brain death. The new method contributes to the growing understanding of mechanical signatures of brain tissues and is potentially of great value for future studies of in vivo brain mechanical properties in health and disease.Die biomechanischen Eigenschaften von zerebralem Gewebe beeinflussen zahlreiche physiologische Prozesse im Gehirn. Die zerebrale Magnetresonanz-Elastographie (MRE) erwies sich dabei innerhalb des letzten Jahrzehnts als wertvolles nicht-invasives Bildgebungsverfahren und offenbarte wichtige biomechanische Merkmale im gesunden als auch kranken Gewebe. Die moderne MRE des Maushirns ist jedoch durch zeitaufwändige Multi-Shot-Bildaufnahemetechniken und rauschempfindliche monofrequente Bildrekonstruktionsmethoden begrenzt. Das Ziel dieser Promotion war die Entwicklung eines hochauflösenden Elastographie-Verfahrens mittels multifrequenter Maushirn-MRE auf der Grundlage von Einzelbildaufnahmetechniken und anschließender Tomoelastographie-Postprozessierung zur Minderung der Rauschempfindlichkeit. Die Durchführbarkeit der Methode wurde mit drei in-vivo-Studien nachgewiesen. In der ersten Studie wurden verschiedene Bereiche des Gehirns bezüglich der Scherwellengeschwindigkeit (SWS) als Surrogat der Steifigkeit vermessen. Die zweite Studie untersuchte den Einfluss der Körpertemperatur auf biophysikalische Parameter des murinen Hirngewebes im normothermen bis hypothermen Bereich. Die Tomoelastographie wurde mit arterieller Spin-Markierung und diffusionsgewichteter Bildgebung kombiniert, um mögliche Zusammenhänge zwischen Gewebesteifigkeit, Perfusion und Diffusion zu analysieren. Im Rahmen der dritten Studie wurden anhand eines hypoxischen Mausmodells die biomechanischen Veränderungen des Gehirns während der kritischen Phase des Todes kontinuierlich aufgenommen und überwacht. Für zehn Tiere wurden lokale SWS von 2,9 ± 0,2 m/s für das Corpus callosum, 4,9 ± 0,5 m/s für den Hippocampus, 4,8 ± 0,8 m/s für das Zwischenhirn und 3,5 ± 0,3 m/s für den Cortex cerebri quantifiziert. Anhand von sechs vermessenen Tieren konnte im gesamten Gehirn, Kortex und Hippocampus eine Abnahme der SWS von Hypo- (28 ± 0.5 °C) zu Normothermie (38 ± 0.5 °C) jeweils um 6,2%, 10,1% bzw. 7,4% festgestellt werden. Diese Abnahme der SWS korrelierte mit Veränderungen der Wasserdiffusion (30% Zunahme) und der Perfusion (60% bis 90% Zunahme). Darüber hinaus führte der Hirntod bei vierzehn Tieren zu einem Anstieg der SWS um 6% im gesamten Gehirn und 9% im Hippocampus gegenüber den in-vivo-Werten. Das implementierte neuartige Multifrequenz-MRE-Verfahren liefert innerhalb stark verkürzter Messzeiten Steifigkeitskarten vom Maushirn mit größerer Detailauflösung als bisherige MRE Methoden. Erstmals konnten somit klinisch relevante biophysikalische Prozesse im Gehirn wie die Hypothermie, die Hypoxie und die kritische Phase des Hirntodes beobachtet und untersucht werden. Die Ergebnisse zeigen, dass die Steifigkeit in den verschiedenen Subregionen des Gehirns der Maus variiert, mit der Wasserdiffusion und der Perfusion invers korreliert und durch Hypoxie im Rahmen des Hirntodes zunimmt. Die neuen Entwicklungen tragen zum wachsenden Verständnis der biomechanischen Eigenschaften des Hirngewebes bei

Realignment-enhanced coherent anti-Stokes Raman scattering (CARS) and three-dimensional imaging in anisotropic fluids

We apply coherent anti-Stokes Raman Scattering (CARS) microscopy to characterize director structures in liquid crystals.Comment: 14 pages, 11 figure

Shear Wave Propagation in Soft Tissue with Ultrasound Vibrometry

Studies have found that shear moduli, having the dynamic range of several orders of magnitude for various biological tissues, are highly correlated with the pathological statues of human tissue such as livers. Shear moduli can be investigated by measuring the attenuation and velocity of the shear wave propagation in a tissue region. Many efforts have been made to measure shear wave propagations induced by different types of force, which include the motion force of human organs, external applied force, and ultrasound radiation force. In the past 15 years, ultrasound radiation force has been successfully used to induce tissue motion for imaging tissue elasticity. Vibroacoustography (VA) uses bifocal beams to remotely induce vibration in a tissue region and detect the vibration using a hydrophone. The vibration center is sequentially moved in the tissue region to form a two-dimensional image. Acoustic Radiation Force Imaging (ARFI) uses focused ultrasound to apply localized radiation force to small volumes of tissue for short durations and the resulting tissue displacements are mapped using ultrasonic correlation based methods. Supersonic shear image remotely vibrates tissue and sequentially moves vibration center along the beam axis to create intense shear plan wave that is imaged at a high frame rate (5000 frames per second). These image methods provide measurements of tissue elasticity, but not the viscosity. Because of the dispersive property of biological tissue, the induced tissue displacement and the shear wave propagation are frequency dependent. Tissue shear property can be modeled by several models including Kelvin-Voigt (Voigt) model, Maxwell model, and Zener model. The Voigt model effectively describes the creep behavior of tissue, The Maxwell model effectively describes the relaxation process, and the Zener model effectively describes both creep and relaxation but it requires one extra parameter. The Voigt model is often used by many researchers because of its simplicity and the effectiveness of modeling soft tissue. The Voigt model consists of a purely viscous damper and a purely elastic spring connected in parallel. For Voigt tissue, the tissue motion at a very low frequency largely depends on the elasticity, while the motion at a very high frequency largely depends on the viscosity. In general, the tissue motion depends on both elasticity and viscosity, and estimates of elasticity by ignoring viscosity are biased or erroneous. In 1951, Dr. Oestreicher published his work to solve the wave equation for the Voigt soft tissue with harmonic motions. With assumptions of isotropic tissue and plane wave, he derived equations that relate the shear wave attenuation and speed to the elasticity and viscosity of soft tissue. However, Oestreicher’s method was not realized for applications until the half century later. In the past ten years, Oestreicher’s method was utilized to quantitatively measure both tissue elasticity and viscosity. Ultrasound vibrometry has been developed to noninvasively and quantitatively measure tissue shear moduli. It induces shear waves using ultrasound radiation force and estimates the shear moduli using shear wave phase velocities at several frequencies by measuring the phase shifts of the propagating shear wave over a short distance using pulse echo ultrasound. Applications of the ultrasound vibrometry were conducted for viscoelasticities of liver, bovine and porcine striated muscles, blood vessels, and hearts. A recent in vivo liver study shows that the ultrasound vibrometry can be implemented on a clinical ultrasound scanner of using an array transducer. One potential application of ultrasound vibrometry is to characterize shear moduli of livers. The shear moduli of liver are highly correlated with liver pathology status. Recently, the shear viscoelasticity of liver tissue has been investigated by several research groups. Most of these studies applied ultrasound radiation force in liver tissue regions, measured the phase velocities of shear wave in a limited frequency range, and inversely solved the Voigt model with an assumption that liver local tissue is isotropic without considering boundary conditions. Because of the boundary conditions, shear wave propagations are impacted by the limited physical dimensions of tissue. Studies shows that considerations of boundary conditions should be taken for characterizing tissue that have limited physical dimensions such as heart, blood vessels, and liver, when ultrasound vibrometry is used