Power laws prevail in medical ultrasound.

Major topics in medical ultrasound rest on the physics of wave propagation through tissue. These include fundamental treatments of backscatter, speed of sound, attenuation, and speckle formation. Each topic has developed its own rich history, lexicography, and particular treatments. However, there is ample evidence to suggest that power law relations are operating at a fundamental level in all the basic phenomena related to medical ultrasound. This review paper develops, from literature over the past 60 years, the accumulating theoretical basis and experimental evidence that point to power law behaviors underlying the most important tissue-wave interactions in ultrasound and in shear waves which are now employed in elastography. The common framework of power laws can be useful as a coherent overview of topics, and as a means for improved tissue characterization.

Reverberant shear wave phase gradients for elastography.

Reverberant shear wave fields are produced when multiple sources and multiple reflections establish a complex three-dimensional wave field within an organ. The expected values are assumed to be isotropic across all directions and the autocorrelation functions for velocity are expressed in terms of spherical Bessel functions. These results provide the basis for adroit implementations of elastography from imaging systems that can map out the internal velocity or displacement of tissues during reverberant field excitations. By examining the phase distribution of the reverberant field, additional estimators can be derived. In particular, we demonstrate that the reverberantphase gradientis shown to be proportional to the local value of wavenumber. This phase estimator is less sensitive to imperfections in the reverberant field distribution and requires a smaller support window, relative to earlier estimators based on autocorrelation. Applications are shown in simulations, phantoms, andin vivoliver.

The quantification of liver fat from wave speed and attenuation.

A framework is developed for estimating the volume fraction of fat in steatotic livers from viscoelastic measures of shear wave speed and attenuation. These measures are emerging on clinical ultrasound systems' elastography options so this approach can become widely available for assessing and monitoring steatosis. The framework assumes a distribution of fat vesicles as spherical inhomogeneities within the liver and uses a composite rheological model (Christensen 1969J. Mech. Phys. Solids1723-41) to determine the shear modulus as a function of increasing volume of fat within the liver. We show that accurate measurements of shear wave speed and attenuation provide the necessary and sufficient information to solve for the unknown fat volume and the underlying liver stiffness. Extension of the framework to compression wave measurements is also possible. Data from viscoelastic phantoms, human liver studies, and steatotic animal livers are shown to provide reasonable estimates of the volume fraction of fat.

Fat and fibrosis as confounding cofactors in viscoelastic measurements of the liver.

Elastography provides significant information on staging of fibrosis in patients with liver disease and may be of some value in assessing steatosis. However, there remain questions as to the role of steatosis and fibrosis as cofactors influencing the viscoelastic measurements of liver tissues, particularly shear wave speed (SWS) and shear wave attenuation (SWA). In this study, by employing the theory of composite elastic media as well as two independent experimental measurements on oil-in-gelatin phantoms and also finite element simulations, it is consistently shown that fat and fibrosis jointly influence the SWS and SWA measurements. At a constant level of fat, fibrosis stages can influence the SWA by factors of 2-4. Moreover, the rate of increase in SWA with increasing fat is strongly influenced by the stages of fibrosis; softer background cases (low fibrosis stages) have higher rate of SWA increase with fat than those with stiffer moduli (higher fibrosis stages). Meanwhile, SWS results are influenced by the presence of fat, however the degree of variability is more subtle. The results indicate the importance of jointly considering fat and fibrosis as contributors to SWS and SWA measurements in complex liver tissues and in the design and interpretation of clinical trials.

Elastography imaging: the 30 year perspective.

From the development of x-ray imaging in the late 19th century, the field of medical imaging developed an impressive array of modalities. These can measure and image a variety of physical parameters from absorption coefficients to spin-spin relaxations. However, throughout most of the 20th century, the intrinsic biomechanical properties of tissues remained hidden from conventional radiology. This changed around 1990 when it was demonstrated that medical ultrasound systems with their fast pulse repetition rate and high sensitivity to motion could create images related to the stiffness of tissues and their shear wave properties. From there, vigorous development efforts towards imaging the elastic properties of tissues were launched across different modalities. These progressed from the research phase, through implementation on clinical scanners, through extensive clinical trials of selected diagnostic tasks, to government approvals, payer approvals, international standards statements, and into routine clinical practice around the globe. This review covers highlights of some major topics of the technical and clinical developments over the last 30 years with brief pointers to some of the remaining issues for the next decade of development.

Towards a consensus on rheological models for elastography in soft tissues.

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear viscometers, and a variety of calibrated stress-strain analyzers. From these many sources of disparate data, a common step in analyzing results is to fit the measurements of tissue response to some viscoelastic model. In the best scenario, this places the measurements within a theoretical framework and enables meaningful comparisons of the parameters against other types of tissues. However, there is a large set of established rheological models, even within the class of linear, causal, viscoelastic solid models, so which of these should be chosen? Is it simply a matter of best fit to a minimum mean squared error of the model to several data points? We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior. These arguments are presented with the goal of clarifying some distinctions between, and consequences of, some of the most commonly used models, and with the longer term goal of reaching a consensus among different sub-fields in acoustics, biomechanics, and elastography that have common interests in comparing tissue measurements.

Shapes and distributions of soft tissue scatterers.

What causes scattering of ultrasound from normal soft tissues such as the liver, thyroid, and prostate? Commonly, the answer is formulated around the properties of spherical scatterers, related to cellular shapes and sizes. However, an alternative view is that the closely packed cells forming the tissue parenchyma create the reference media, and the long cylindrical-shaped fluid vessels serve as the scattering sites. Under a weak scattering or Born approximation for the extracellular fluid in the vessels, and assuming an isotropic distribution of cylindrical channels across a wide range of diameters, consistent with a fractal branching pattern, some simple predictions can be made about the nature of backscatter as a function of frequency in soft tissues. Specifically, a number of plausible shapes would predict that backscatter increases as a power law of frequency, where the power law is determined by the function governing the number density of the vessels versus diameter. These results are compared with some historical models developed over the last 100 years in scattering theory and point to the need for higher spatial resolution and higher bandwidths to obtain more precise measures of the key parameters in normal tissues, and to better identify the dominant structures responsible for backscatter in everyday clinical imaging.

The biomechanics of simple steatosis and steatohepatitis.

Magnetic resonance and ultrasound elastography techniques are now important tools for staging high-grade fibrosis in patients with chronic liver disease. However, uncertainty remains about the effects of simple accumulation of fat (steatosis) and inflammation (steatohepatitis) on the parameters that can be measured using different elastographic techniques. To address this, we examine the rheological models that are capable of capturing the dominant viscoelastic behaviors associated with fat and inflammation in the liver, and quantify the resulting changes in shear wave speed and viscoelastic parameters. Theoretical results are shown to match measurements in phantoms and animal studies reported in the literature. These results are useful for better design of elastographic studies of fatty liver disease and steatohepatitis, potentially leading to improved diagnosis of these conditions.

Are rapid changes in brain elasticity possible?

Elastography of the brain is a topic of clinical and preclinical research, motivated by the potential for viscoelastic measures of the brain to provide sensitive indicators of pathological processes, and to assist in early diagnosis. To date, studies of the normal brain and of those with confirmed neurological disorders have reported a wide range of shear stiffness and shear wave speeds, even within similar categories. A range of factors including the shear wave frequency, and the age of the individual are thought to have a possible influence. However, it may be that short term dynamics within the brain may have an influence on the measured stiffness. This hypothesis is addressed quantitatively using the framework of the microchannel flow model, which derives the tissue stiffness, complex modulus, and shear wave speed as a function of the vascular and fluid network in combination with the elastic matrix that comprise the brain. Transformation rules are applied so that any changes in the fluid channels or the elastic matrix can be mapped to changes in observed elastic properties on a macroscopic scale. The results are preliminary but demonstrate that measureable, time varying changes in brain stiffness are possible simply by accounting for vasodynamic or electrochemical changes in the state of any region of the brain. The value of this preliminary exploration is to identify possible mechanisms and order-of-magnitude changes that may be testable in vivo by specialized protocols.

The microchannel flow model under shear stress and higher frequencies.

The microchannel flow model provides a framework for considering the effect of the vascular bed on the time domain and frequency domain response of soft tissues. The derivation originates with a single small fluid-filled vessel in an elastic medium under uniaxial compression. A fractal branching vasculature is also assumed to be present in the tissue under consideration. This note considers two closely related issues. First, the response of the element under compression or shear as a function of the orientation of the fluid-filled vessel is considered. Second, the transition from quasistatic (Poiseuille's Law) to dynamic (Womersley equations) fluid flow is examined to better predict the evolution of behavior at higher frequencies. These considerations expand the conceptual framework of the microchannel flow model, particularly the range and limits of validity.

Endocannabinoid signaling in social functioning: an RDoC perspective.

Core deficits in social functioning are associated with various neuropsychiatric and neurodevelopmental disorders, yet biomarker identification and the development of effective pharmacological interventions has been limited. Recent data suggest the intriguing possibility that endogenous cannabinoids, a class of lipid neuromodulators generally implicated in the regulation of neurotransmitter release, may contribute to species-typical social functioning. Systematic study of the endogenous cannabinoid signaling could, therefore, yield novel approaches to understand the neurobiological underpinnings of atypical social functioning. This article provides a critical review of the major components of the endogenous cannabinoid system (for example, primary receptors and effectors-Δ9-tetrahydrocannabinol, cannabidiol, anandamide and 2-arachidonoylglycerol) and the contributions of cannabinoid signaling to social functioning. Data are evaluated in the context of Research Domain Criteria constructs (for example, anxiety, chronic stress, reward learning, motivation, declarative and working memory, affiliation and attachment, and social communication) to enable interrogation of endogenous cannabinoid signaling in social functioning across diagnostic categories. The empirical evidence reviewed strongly supports the role for dysregulated cannabinoid signaling in the pathophysiology of social functioning deficits observed in brain disorders, such as autism spectrum disorder, schizophrenia, major depressive disorder, posttraumatic stress disorder and bipolar disorder. Moreover, these findings indicate that the endogenous cannabinoid system holds exceptional promise as a biological marker of, and potential treatment target for, neuropsychiatric and neurodevelopmental disorders characterized by impairments in social functioning.

Shear wave dispersion behaviors of soft, vascularized tissues from the microchannel flow model.

The frequency dependent behavior of tissue stiffness and the dispersion of shear waves in tissue can be measured in a number of ways, using integrated imaging systems. The microchannel flow model, which considers the effects of fluid flow in the branching vasculature and microchannels of soft tissues, makes specific predictions about the nature of dispersion. In this paper we introduce a more general form of the 4 parameter equation for stress relaxation based on the microchannel flow model, and then derive the general frequency domain equation for the complex modulus. Dispersion measurements in liver (ex vivo) and whole perfused placenta (post-delivery) correspond to the predictions from theory, guided by independent stress relaxation measurements and consideration of the vascular tree structure.

Scattering and reflection identification in H-scan images.

Medical ultrasound imaging scanners typically display the envelope of the reflected signal on a log scale. The properties of this image and speckle patterns from collections of scatterers have a number of well-known disadvantages. One is the inability to differentiate between different scatterers that may have fundamentally different frequency-dependent scattering cross sections. This study proposes a framework for characterizing scattering behavior and visualizing the results as color coding of the B-scan image. The methodology matches a model of pulse-echo formation from typical situations to the mathematics of Gaussian weighted Hermite functions. The results show an ability to reveal some of the information otherwise hidden in the conventional envelope display, and can be generalized to more conventional bandlimited pulse functions. This new class of images is termed H-scan where 'H' stands for 'Hermite' or 'hue' to distinguish it from conventional B-scan format.

Experimental evaluations of the microchannel flow model.

Recent advances have enabled a new wave of biomechanics measurements, and have renewed interest in selecting appropriate rheological models for soft tissues such as the liver, thyroid, and prostate. The microchannel flow model was recently introduced to describe the linear response of tissue to stimuli such as stress relaxation or shear wave propagation. This model postulates a power law relaxation spectrum that results from a branching distribution of vessels and channels in normal soft tissue such as liver. In this work, the derivation is extended to determine the explicit link between the distribution of vessels and the relaxation spectrum. In addition, liver tissue is modified by temperature or salinity, and the resulting changes in tissue responses (by factors of 1.5 or greater) are reasonably predicted from the microchannel flow model, simply by considering the changes in fluid flow through the modified samples. The 2 and 4 parameter versions of the model are considered, and it is shown that in some cases the maximum time constant (corresponding to the minimum vessel diameters), could be altered in a way that has major impact on the observed tissue response. This could explain why an inflamed region is palpated as a harder bump compared to surrounding normal tissue.

Cerebrospinal fluid and plasma oxytocin concentrations are positively correlated and negatively predict anxiety in children.

The neuropeptide oxytocin (OXT) exerts anxiolytic and prosocial effects in the central nervous system of rodents. A number of recent studies have attempted to translate these findings by investigating the relationships between peripheral (e.g., blood, urinary and salivary) OXT concentrations and behavioral functioning in humans. Although peripheral samples are easy to obtain in humans, whether peripheral OXT measures are functionally related to central OXT activity remains unclear. To investigate a possible relationship, we quantified OXT concentrations in concomitantly collected cerebrospinal fluid (CSF) and blood samples from child and adult patients undergoing clinically indicated lumbar punctures or other CSF-related procedures. Anxiety scores were obtained in a subset of child participants whose parents completed psychometric assessments. Findings from this study indicate that plasma OXT concentrations significantly and positively predict CSF OXT concentrations (r=0.56, P=0.0064, N=27). Moreover, both plasma (r=-0.92, P=0.0262, N=10) and CSF (r=-0.91, P=0.0335, N=10) OXT concentrations significantly and negatively predicted trait anxiety scores, consistent with the preclinical literature. Importantly, plasma OXT concentrations significantly and positively (r=0.96, P=0.0115, N=10) predicted CSF OXT concentrations in the subset of child participants who provided behavioral data. This study provides the first empirical support for the use of blood measures of OXT as a surrogate for central OXT activity, validated in the context of behavioral functioning. These preliminary findings also suggest that impaired OXT signaling may be a biomarker of anxiety in humans, and a potential target for therapeutic development in individuals with anxiety disorders.

A microchannel flow model for soft tissue elasticity.

A number of advances, including imaging of tissue displacements, have increased our ability to make measurements of tissue elastic properties of animal and human tissues. Accordingly, the question is increasingly asked, 'should our data be fit to a viscoelastic model, and if so which one?' In this paper we focus solely on soft tissues in a functional (non-pathological) state, and develop a model of elastic behavior that is based on the flow of viscous fluids through the extensive network of tissue microchannels in response to applied stress. This behavior can be captured in a 2-parameter model, and the model appears to predict the stress-relaxation behavior and the dispersive shear wave behavior of bovine liver specimens and other soft tissues and phantoms. The relationship of the microchannel flow model to more traditional models is also examined.

Imaging the elastic properties of tissue: the 20 year perspective.

After 20 years of innovation in techniques that specifically image the biomechanical properties of tissue, the evolution of elastographic imaging can be viewed from its infancy, through a proliferation of approaches to the problem to incorporation on research and then clinical imaging platforms. Ultimately this activity has culminated in clinical trials and improved care for patients. This remarkable progression represents a leading example of translational research that begins with fundamentals of science and engineering and progresses to needed improvements in diagnostic and monitoring capabilities applied to major categories of disease, surgery and interventional procedures. This review summarizes the fundamental principles, the timeline of developments in major categories of elastographic imaging, and concludes with recent results from clinical trials and forward-looking issues.

Three-dimensional registration and fusion of ultrasound and MRI using major vessels as fiducial markers.

This paper describes fusion of three-dimensional (3-D) ultrasound (US) and magnetic resonance imaging (MRI) data sets, without the assistance of external fiducial markers or external position sensors. Fusion of these two modalities combines real-time 3-D ultrasound scans of soft tissue with the larger anatomical framework from MRI. The complementary information available from multiple imaging modalities warrants the development of robust fusion capabilities. We describe the data acquisition, specialized algorithms, and results for 3-D fused data from phantom studies and in vivo studies of the normal human vasculature and musculoskeletal systems.

Central vasopressin administration regulates the onset of facultative paternal behavior in microtus pennsylvanicus (meadow voles).

Pharmacological experiments have implicated a role for central arginine vasopressin (AVP) in regulating paternal behavior in monogamous prairie voles. Although nonmonogamous meadow voles exhibit appreciable paternal care when housed under winter, short day lengths (SD), no research has examined whether the same neurobiological systems are involved in regulating paternal behavior in a nonmonogamous species when it behaves paternally. The goal of these experiments was to determine whether central administration of AVP, but not cerebrospinal fluid (CSF), affected the suppression of pup-directed aggression and/or the onset of paternal behavior in meadow voles. Data from experiment 1 implicated a role for AVP in facilitating changes in male behavior: central administration of 1 ng of AVP (but not 3 ng or CSF) inhibited pup-directed aggression in previously pup-aggressive males, and 3 ng of AVP (but not 1 ng or CSF) induced paternal behavior in previously nonpaternal males. In contrast, AVP (1 and 3 ng) did not enhance paternal behavior in already paternal males. Experiment 2 tested the specificity of AVP. Previous research indicated that 24 h of unmated cohabitation with a female reliably induced paternal behavior in SD males. Hence, experiment 2 examined whether administration of a V(1a) AVP antagonist (AVPA), but not CSF, prior to 24 h of unmated cohabitation would block the onset of paternal behavior. Males that received CSF displayed paternal behavior faster and engaged in more investigatory and paternal behaviors than males that received AVPA. Thus, pharmacological experiments support the hypothesis that AVP likely regulates paternal behavior in both facultatively and consistently paternal vole species.