Al‐Jumaily, Ahmed M.

The use of contrast agents is becoming a routine practice in diagnostic ultrasound imaging. Microbubble contrast agents are proving to be a safe and practical way of enhancing conventional ultrasound images. This paper discusses the concept of using microbubble contrast agents in the vibro-acoustography (VA) technique. A brief background of microbubbles and their clinical applications is given as well as a summary of the different attempts at modeling microbubble contrast agents in ultrasound fields. A general Keller–Herring equation is modified to mathematically model the interaction of encapsulated microbubbles in blood with VA ultrasound. The frequency response and scattered pressure of microbubbles with initial radius of 1 and 3 m are presented. This method is accurate for pressure amplitudes up to 500 kPa. Understanding this interaction is important for the correct interpretation of clinical investigations when using VA.

Vibro-acoustography is a technique that uses the radiation force of amplitude-modulated ultrasound to evaluate the dynamic response of an object at the modulation frequency. One potential application of this technique is to assess the reaction of the host tissue to the implant material by evaluating the mechanical properties of the tissue surrounding the implant. To do this, we use vibro-acoustography to measure the frequency response of the implant, and use this information to evaluate the mechanical parameters of the surrounding. Two theoretical models are developed to study the dynamic response of an implant in tissue. The first model is for an implant (1×25-mm steel beam) fully embedded in a viscoelastic medium (tissue). The second model is for a partially embedded implant with one part exposed to the open environment. The exposed end is rigidly connected to a base, and the other end is freely embedded in the viscoelastic medium. At the interface between the two media matching of boundary conditions is achieved to determine the force response. For both models eigenvalues and eigenfunctions are determined and transfer functions are evaluated. The first two natural frequencies compare well with available experimental and finite-element data.

Airway smooth muscle contraction is the main driving mechanism in asthma. However, in the dynamic environment of the ASM passive dynamics play an important role. The main aim of this research is to investigate the relative contribution of passive dynamics to ASM tissue dynamics and to characterize this behavior. The major finding of this study is the ability of the principle of logarithmic superposition to describe a wide range of dynamic behavior in relaxed (unstimulated) ASM and to a lesser extend in contracted ASM. The ability of this model to describe the force response to length oscillations in contracted muscle shows that cross-bridge cycling in ASM when fully contracted is not affected by oscillations. We hypothesize that this could be caused either by a very slow cross-bridge cycling rate, or by a large degree of non-contractile cross-linking which results in a greatly increased passive force.

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.

We present a systematic quantitative analysis of power-law force relaxation and investigate logarithmic superposition of force response in relaxed porcine airway smooth muscle (ASM) strips in vitro. The term logarithmic superposition describes linear superposition on a logarithmic scale, which is equivalent to multiplication on a linear scale. Additionally, we examine whether the dynamic response of contracted and relaxed muscles is dominated by cross-bridge cycling or passive dynamics. The study shows the following main findings. For relaxed ASM, the force response to length steps of varying amplitude (0.25–4% of reference length, both lengthening and shortening) are well-fitted with power-law functions over several decades of time (10−2 to 103 s), and the force response after consecutive length changes is more accurately fitted assuming logarithmic superposition rather than linear superposition. Furthermore, for sinusoidal length oscillations in contracted and relaxed muscles, increasing the oscillation amplitude induces greater hysteresivity and asymmetry of force-length relationships, whereas increasing the frequency dampens hysteresivity but increases asymmetry. We conclude that logarithmic superposition is an important feature of relaxed ASM, which may facilitate a more accurate prediction of force responses in the continuous dynamic environment of the respiratory system. In addition, the single power-function response to length changes shows that the dynamics of cross-bridge cycling can be ignored in relaxed muscle. The similarity in response between relaxed and contracted states implies that the investigated passive dynamics play an important role in both states and should be taken into account.

This article discusses the possibility of using microbubble contrast agents in the Vibro-Acoustography (VA) technique. An existing mathematical model is used to determine the interaction of encapsulated microbubbles with VA ultrasound fields. Such models may lead to a better understanding of the underlying mechanics and interactions in clinical settings.

Three non-destructive testing techniques are developed and investigated to determine the Young’s modulus of elasticity of the trachea and the results are compared with the standard uniaxial state of stress method. These techniques are based on: (1) simulating the trachea as a pressurized vessel and deducing a special relationship between the pressure and the radial strain; (2) using two hydrophones and determining the variation in acoustic transmittance caused by the presence of the trachea in a propagation path within a water-bath; (3) considering the trachea as a thin cylindrical shell and determining the resonance radial vibration response. Discussion is presented to identify the “pros” and “cons” of each technique and final practical recommendations are made.