Este proyecto fue adjudicado, pero renunciado por el investigador principal

Overview: Mechanical wave propagation physics is related to traumatic brain injury mechanisms. For instance, nonlinear shear waves can form in the brain progressively with propagation, amplifying the acceleration locally. This phenomenon is compatible with axonal brain injury in which the lesions are localized far from the impact region. Within the brain, not only shear waves propagate. Especially when considering the brain is full of folds and surfaces, including the gray-white matter interface, which can be seen in Fig. 1. The abundance of interfaces or surfaces makes us hypothesize that surface waves might be crucial for describing the biomechanics of traumatic brain injury. The surface waves are named after the nature of the interface. A wave propagating in a solid-vacuum interface is known as a Rayleigh wave, a wave propagating in a solid-fluid interface is known as a Scholte wave, and a wave propagating in a solid-solid interface is known as a Stoneley wave. This last might propagate within an interface formed by two types of soft tissue. An example of this is the interfaces formed by the white and gray matter in the brain (see Fig. 1). Surface waves, although confined to a surface, can penetrate up to a wavelength. In the context of soft tissues, the typical frequencies of elastic waves that propagate are in the range of 10 to 300 Hz. At these frequencies, the wavelengths are on the order Figure 1: Section of a temporal
of centimeters, creating the necessity of studying these waves at brain lobe. Image obtained from depth. Surface waves are not explored sufficiently in incompressible soft the visible human project [1]. solids yet. We recently measured Scholte waves at depth in these materials. However, we are not aware of measurements of Stoneley waves at depth in incompressible soft solids like brain matter or gelatin. The lack
of this experimental evidence is due to the challenges of measuring deformation in opaque materials without disrupting the medium. Thus, the general objective of this proposal is to detect, describe and characterize the propagation of Stoneley waves in interfaces formed by two incompressible tissue-mimicking materials using Ultrafast Ultrasound elastography-related techniques.

Methodology: Advanced ultrasound imaging techniques implemented on a highly customized ultrasound imaging platform designed for high frame-rate imaging will be used to characterize fundamental Stoneley wave physics propagating at the interfaces between two soft solids. We first will perform experiments in flats and simple interfaces to obtain the parameter space (shear modulus, density, and prestress) in which planar Stoneley waves exist. Then, we will explore the effects of the bonding condition between the two mediums on the dispersion relation. Third, we will investigate the interaction of the shape of the interface on the wave propagation, and lastly, we will intend to propagate Stonely waves into 3D inclusions. These observations will be achieved with a number of steps that integrate advancements in ultrasound imaging, algorithms that measure the deformation, and modeling. Custom two-dimensional and three-dimensional imaging sequences, designed for displacement tracking, will be implemented for a dedicated Linear and Matrix array transducer that has 128 or 1024 elements and can reach a spatial resolution of 200microns at a very high framerate in the order of 10000 frames per second (2D or 3D frames respectively).

Expected results: The results of this proposal will elucidate the conditions that the two soft solids need to propagate Stoneley waves. These conditions refer to the combination of mechanical properties of the materials, such as shear modulus and density, and the prestress field needed. We expect to establish the effect that the bonding condition between the two soft solids has on the nature of the Stoneley wave. In particular, we will monitor how the Stoneley wave speed and dispersion change with different bonding conditions. We believe this phenomenology has implications in imaging technology, tumor diagnosis, and brain injury biomechanics.

One goal is to enhance the methods being currently developed by Espı́ndola (Physics), Krause (Physiology), and Xavier (Biomedical Engineering) for reconstructing capillary networks with ultrasound. The super-resolution is needed for early detection diseases such as cognitive decline, cancer, or liver fibrosis. They perfuse lipid-encapsulated microbubbles as contrast agents and then localize the bubbles in the ultrasound images with the singular value filter. However, that method leaves a non-negligible percentage of bubbles undetected. Here we propose to complement the singular value filter for the detection and tracking of microbubbles with the sophisticated and mathematically sound Mumford-Shah method for image contour detection, which stems from the conceptually-insightful and numerically-robust perspective of the minimization of energies. In the reconstruction of the capillary network from ultrasound, it is impossible to directly distinguish the microbubbles, or even the blood vessels, in each frame separately, due to the attentuation and degradation in this imaging technique. It is essential to take into account the dynamic nature of the problem, distinguishing the slowly-varying signals emitted by the tissue from those emitted by the microbubbles, which flow rapidly, behave nonlinearly, and have a much shorter coherence length. We therefore propose to regard the collection of two-dimensional frames as a single three-dimensional image, where a moving bubble becomes a tubular neighbourhood of a filament, which the Mumford-Shah model is expected to recover. From these filaments, bubbles can be detected and tracked, and the vertical inclinations of theses filaments will yield the microbubbles velocities. From the velocity profiles it is possible to estimate the shear wall stresses (their ‘tangential elastic rigidities’) of the blood vessels, and anomalies in these stresses are commonly good indicators of the presence of specific diseases.
A fortunate encounter between mathematics and mechanics led to the observation that the problem of
finding the path that the propagation of a crack will follow inside a structure upon loading could be solved with the mathematical theory (the analysis of free-discontinuity problems) developed for the apparently unrelated image segmentation Mumford-Shah model. The variational fracture theory initiated by Francfort and Marigo is by now (20 years after) very well established. The second goal of this proposal is to further develop the ongoing collaboration between Song (Pharmaceutics), Siegel (Pharmaceutics), Sánchez (Numerical analysis), Calderer (Applied mathematics), and the PI on the study of the debonding of polymer gels from rigid substrates (relevant in the design of the synthetic polymers coating the metallic parts of pacemakers and other medical prostheses) from this variational fracture theory perspective.
The third main goal is to apply the mathematical analysis of free-discontinuity problems to the modelling of the evolution of the cavity in the block caving technique in underground rock mining. This has been pursued by Ortega, Lecaros, and coworkers from the side of applied mathematics in academia, in collaboration with Gaete from the Geomechanics Research Department at El Teniente, research group to which Gutiérrez and the PI have joined in the last months. We propose to study the seismic activity induced by the fracture of the rock mass due to gravity, following the works in the last decade within the variational fracture theory that incorporate the inertia effects. The final aim is to optimize the injection of water jets for the aminoration of the seismic events near the operation sites.
The three research lines are applications of the phase-field regularization by Ambrosio and Tortorelli of the Mumford-Shah free-discontinuity model, a different variant being required in each of the three contexts. The first stage of the implementation is of mathematical modelling and high-level numerical simulation abilities, in which the intuition and first-hand knowledge from the members of the research team that are experts in vascular function, ultrasound imaging, polymer chemistry, and mining geomechanics is translated into particular mathematical concepts and concrete computational methods. This is followed by a stage of calibration and validation, where the full interplay with experiments is required. The product of a robust and validated computational method will constitute then an advancement in the capabilities, available resources, and understanding in each of the applied disciplines.

During the last decades, compelling evidence shows how the context in which early life takes place impinges risk or protection for later development of non-communicable chronic diseases. In this regard, impaired fetal growth, as occur in the fetal growth restriction (FGR), leads to a higher risk for later cardiovascular diseases, an effect that would be mediated by accelerated aging at molecular, structural, and functional levels. FGR remains a leading cause of perinatal morbidity and mortality, affecting ~10% of pregnancies, but ranging 5 to 25% depending on the nutritional and health conditions of the population surveyed, with a higher prevalence among pregnant women of low socioeconomic status. In the clinic, FGR is normally defined by a fetal weight below the 10th percentile, however, new evidence shows that impaired intrauterine growth may affect several neonates born over the 10th percentile, which may be missed from the perinatal survey for preventing adverse outcomes. This points out the need for further studies to improve the understanding and identification of altered fetal growth trajectories and their consequences on vascular function. Studies in placenta show that FGR vascular dysfunction is also found at birth in chorionic and umbilical arteries. We have demonstrated the presence of functional and molecular markers (e.g. epigenetic changes) of endothelial dysfunction in human umbilical and chorionic vessels, findings that have been further confirmed by comparing systemic (aorta and femoral arteries) and umbilical arteries in animal models of FGR. These traits suggest that umbilical artery endothelial cells (HUAEC) can be used as a surrogate to explore the vascular programming within the fetus, however, their translation to clinical preventive applications for promoting healthy aging deserves further studies. It worth noting that fetal reduced oxygen supply (i.e. fetal hypoxia) and altered blood flow patterns (i.e. shear stress) are key clinical markers in the FGR, independently of the constraints leading to impaired growth, and both factors exert a tight control of vascular development and function across life. However, how these key stimuli interact and impose an epigenetic program on the endothelial function remains elusive. This proposal will focus on the crosstalk between hypoxia and shear stress that results in the endothelial programming related to impaired fetal growth, and the molecular mechanisms that mediate the vascular responses to these stimuli. Furthermore, we will address if these molecular markers may allow detecting early vascular aging in FGR subjects beyond the 10th centile cutoff. We hypothesize that “Impaired fetal growth conditions are associated with epigenetic programming of aging- and mechanosensing-related miRNAs and transcripts in the endothelium, which can be triggered by the confluence of altered flow patterns and hypoxia resulting in molecular and structural pro-hypertensive biomechanical vascular properties”. This hypothesis will be addressed by three General Objectives (GO) involving ex vivo, in vitro, and in vivo observational and mechanistic approaches: GO1 To demonstrate, in HUAEC, whether late FGR results in epigenetic changes related to the regulation of vascular aging and the expression of mechanosensing mechanisms involved in the endothelial-dependent relaxation, and their relationship with general prenatal parameters of vascular health. GO1 will be performed by recruiting HUAEC samples from late FGR and control pregnancies, to assess transcriptomic and DNA methylation analyses that will be crossed with prenatal clinical data. GO2 To study, in vivo, whether stimuli related to FGR (i.e. hypoxia and altered shear stress) differentially regulate mechanosensing pathways involved in the endothelial-dependent relaxation and their relationship with the in vivo and ex vivo vascular properties (e.g. functional and biomechanical). GO2 will be performed in chicken embryos exposed to hypoxia and treated with agents targeting mechanosensing pathways, in which wall shear stress will be determined by Ultrasound Localization Microscopy, with complementary functional, structural, and molecular analyses. GO 3. To study, in cultured HUAEC, whether stimuli related to impaired fetal growth converge in the regulation of mechanosensing-and aging-related transcripts and miRNA, contributing to the cellular programming of endothelial dysfunction. OG3 will be performed in HUAEC exposed, in vitro, to sustained hypoxia and diverse flow patterns (shear stress), in which target DNA methylation, miRNA, transcripts, and proteins will be assessed. Our expected outcome is to improve the knowledge about the endothelial epigenetic programming after FGR and enhance the characterization of in vivo shear stress patterns and mechanisms induced by chronic fetal hypoxia. This project is not only relevant to uncover the developmental approaches for diagnosing and treatments in complicated pregnancies.

Overview: We have recently observed that shear shock waves are generated and subsequently propagate in the brain
under impact conditions that are quite general. For example, a 35g impact, which is in the concussive range, propagates nonlinearly in the brain and develops into a thin, destructive 300g shock front. This highly localized increase in acceleration suggests that shear shock waves are a fundamental mechanism for traumatic injuries in the brain and in soft tissue. These observations were made with ultrasonic methods that we have developed based on clutter reducing high frame-rate (10,000 images/second) imaging sequences and high sensitivity (better than 1 micrometer) motion tracking algorithms. This imaging method offers a unique combination of imaging speed, accuracy, and penetration that interrogates a spatiotemporal regime not accessible to other imaging modalities. On the other hand, the physics of nonlinear elastic waves in soft solids has been practically unexplored. In particular, just a few theoretical papers have addressed the generation of nonlinear surfaces waves in soft solids. None experimental research has reached to the complete observation of nonlinear surface wave in soft solids. Therefore, the physics of the propagation of nonlinear surfaces waves and its consequences on soft solid, presents many experimental, theoretical, and numerical opportunities for investigation. With applications in the biomechanics of injuries as well as in geophysics due to that most of the damage produced by an earthquake is due to surface waves because they spread energy more efficiently.

Goals: The general objective of this proposal is to reveal the physics governing the propagation of nonlinear surface waves in soft solids. The origin of the nonlinearity in these waves is unclear. Few authors suggest that it comes only from a geometrical effect due to the definition of the nonlinear strain tensor. However, at increased amplitudes, we hypothesize that the material nonlinearity also should play a role. The effect of these two nonlinear components is unknown. It has been predicted that the nonlinearity might distort the wave profile producing discontinuities in the particle displacement velocity or acceleration. Until now, no experimental clues about the conditions and parameters that generate these discontinuities have been found. Another open question in this topic is related to the penetration depth. Surface wave typically penetrates few wavelengths within the surface of propagation. However, in soft solids, typical wavelength are in the order of centimeters, making the penetrating wave an important subject of study. The effect of the nonlinear distortion with depth is unknown and an aim of this proposal. Thus, here we propose to develop models, theory and experiments that elucidate this questions and give us a clear picture of the behavior of these waves in soft materials like gelatin.

Methodology: Unlike compressional shocks in fluids, elastic waves, such as surface waves, are practically unexplored
due to the experimental challenges associated with observing waves at depth in solids. Current observations of surface
waves are confined only at the free surface and restricted only to Rayleigh waves. Surface waves in other interfaces such as solid-fluid or solid-solid have not been experimentally explored in soft solids yet. Advanced ultrasound imaging techniques implemented on a highly customized imaging platform designed for high frame-rate imaging will be used to characterize fundamental surface wave physics in homogeneous soft solids. These observations and characterizations of nonlinear surface waves will be achieved with a number of steps that integrate advancements in ultrasound imaging, advancement in algorithms that measure the deformation and advancements in modeling. The advancement on the visualization of displacements will be validated using a fringe projection profilometry system, based on a high frame rate camera. We will perform experiments in the linear regime to characterize attenuation and dispersion, which interact with the nonlinearity and therefore, have a significant impact on the resulting kinematic of the medium, due to their frequency dependent nature. Custom two-dimensional imaging sequences, designed for shock wave tracking, will be implemented for a dedicated Linear array transducer that has 128 elements and can reach a spatial resolution of 200 microns at very high frame-rate in the order of 10000 frames per second. This ultrasound technology does not exist until now in Chile.

Expected results: The results of this proposal will elucidate the origin of the nonlinear response of soft materials for the
surface waves. We expect that at sufficiently high amplitude the material nonlinearity will be expressed. Additionally, due to the distortions of the wave profile generated by the nonlinearity, we expect to observe discontinuous particle displacement, velocity and/or acceleration. These discontinuities will be classified as a new type of shock wave. We hope to see that this new type of shock wave propagates over a longer distance than the compressional shock or shear shock, principally due to that surface waves spread reducing its amplitude proportionally to the square root of the propagation distance instead of typical reduction proportional to the propagation distance observed in bulk waves. We also expect the shock waves associated with surface waves are more likely to produce fracture or catastrophic event in soft solids. In the context of linear wave propagation, we expect to measure the power laws that govern the frequency dependent attenuation and dispersion for surface waves. If successful, this research would suggest the nonlinear surface waves as a new mechanism for injury. In addition, this research could become a platform to test shock wave ideas that are very difficult to prove in compressional waves. Thus, it would serve as an analogous physical system to study shock waves in general.

Introduction: Ultrasound (US) exams are extensively used in Chile and around the world. This non-invasive imaging technique has many advantages when compared to magnetic resonance, computed tomography, and others because it has a low cost, it does not need ionizing radiation, and it is portable equipment. However, this technique has many challenges; the most known is the balance between resolution and penetration depth. Recently, in 2011, a new technique of US has been described: the ultrasound localization microscopy (ULM). However, it was only in 2015 that this technique gained knowledge with the publication of Errico et al. (2015) who described the ultrafast ultrasound localization microscopy applied in vivo in rats’ brain. ULM eliminates the challenge of the balance between resolution and penetration; but a new challenge emerges: the balance between localization precision of microbubble, microbubble concentration, and acquisition time. The microbubbles (MB) are the contrast agent for the US technique. They have 1-5 µm in diameter and act as a blinking source. These MB are injected into the bloodstream and flow into the circulatory system. ULM is also known as super-resolution imaging; it can produce vascular images with a resolution around 10 µm, 10 times better than the conventional US image. This unprecedented resolution has numerous potential applications. In particular, ULM would have a high impact in oncology because the vascular structure of early tumors, that are in the range of 5 µm to 80 µm, provides information that can help in the early diagnosis and monitor therapy responses. The huge potentiality of ULM has produced a lot of excitement and expectation worldwide, and it became a hot topic in the medical ultrasound community. Unfortunately, this technique is not yet clinically approved because it is still in development stages and presents many challenges that must be solved before translating it into clinics. The mainly limitations to overcome before translating ULM into clinics are the following: contrast-to-tissue ratio (CTR), signal-to-noise ratio (SNR), acquisition time, microbubble concentration, motion, lack of a gold standard, data overdose, exploitation of ultrafast scanner uncommon in the clinic and so on. Therefore, the aim of this study is to optimize the technique to localize microbubbles, and to explore the physics of microbubble to provide a change in the paradigm of the processes to produce ULM by combining the superresolution processing with a controlled exterior force impulse. To achieve this aim, first a numerical study will be performed to simulate microbubbles into small vessels and find a better way to localize them. The robustness of the algorithm will be increased to consider the non-linear interactions between MB and US and to consider the parabolic velocity profile of the vessel/tube. Up to date, the studies on microbubbles localization in ULM are after the image acquisition. There are no tissue/flow simulations of the behavior of microbubbles into the vessels with this technique. To perform the simulation, we will use a computer with excellent storage capacity and great velocity of processing together with the MATLAB algorithm: The Full Wave Solver. Second, an experimental study will be performed to generate super resolution images in a conventional phantom. The state of art will be applied with a phantom made by microtubes and microbubbles and then, the improvement of the aim 1 will be considered into this experiment. The complexity of the phantom will be increased from a medium with only water, then gelatine and finally, we will add some respiratory simulated movement. To the experimental setup we will use the Verasonics Vantage 128 research ultrasound scanner with different types of ultrasound transducers, microbubbles, microtubes, gelatine and the respiratory movement will be simulated with a vibration testing system (Shaker VTS-100). Finally, the physics of microbubble will be explored to provide a change in the paradigm of the processes to produce ULM and to detect the MB in a more direct way, without the need to perform a filter, like the signal value decomposition (SVD). We want to apply the an external know push pulse that will produce differences in the shear waves between the microbubbles and the tissue around and with simulations we will be able to know the response of microbubbles and it may help us to separate them from the tissue. Expected results: As result of this study, we expect to develop a numerical simulation to the ULM method, by considering interactions of the US with the tissue and fluid dynamics of the blood into the vessel and significantly optimize the techniques of MB detection. Besides that, this project will help to improve the first fully programmable ultrasound scanner system in Chile. Potentially, this would open new research areas at the country level, such as ultrasound imaging, ultrasound super-resolution imaging and soft tissue characterization.