Significance of single and multi-voxel 1H magnetic resonance spectroscopy in the quantification of myocellular lipid in young non-obese Asian Indian males

To prospectively assess intramyocellular lipids (IMCL) and extramyocellular lipids (EMCL) using single voxel spectroscopy (SVS) and multi voxel magnetic resonance spectroscopy (MVS) in soleus muscle and correlate results with metabolic variables in non-obese (BMI < 23 kg/m²) Asian Indian males. Thirty one patients with diabetes (cases) and twelve normoglycaemic subjects (controls) underwent point resolved spectroscopy sequence (PRESS) of soleus muscle using SVS and MVS in a 3 T MRI scanner. Visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT) were measured from MRI images and body composition was measured from dual-energy x-ray absorptiometry (DXA). The mean IMCL from SVS and MVS were 1.6% and 2.6% in cases and 2.3% and 3.4% in controls respectively. The mean EMCL from SVS and MVS were 1.8% and 3% in cases and 1.5% and 3% respectively in controls. A significant correlation between IMCL and total fat mass (rho = 0.42, p < 0.01) and total body fat (rho = 0.46; p < 0.01) were observed in cases while using the SVS technique and no correlations were found in the MVS technique. The SVS showed significant correlations between total myocellular lipids with VAT and SAT in cases alone. Total myocellular lipids acquired using both techniques showed a significant correlation with BMI, waist circumference, total fat mass, total body fat and truncal fat in cases alone. Quantification of IMCL of soleus muscle using the SVS technique is useful in studying the relationship with metabolic markers in non-obese Asian Indians with diabetes.     

运动训练大鼠的自体荧光研究

首次通过激光诱导荧光光谱技术(LIF)研究运动训练大鼠心脏、肾脏、肝脏、脂肪以及前腿肌和后腿的比目鱼肌和腓肠肌的自体荧光光谱特性。测量所用的激发光波长为250～650 nm而发射波长为300～700 nm。比较参照组和3组不同运动状态组的三维荧光光谱,主要在腓肠肌的光谱中发现了和运动相关且位于激发波长(340±10)nm和发射波长(460±10)nm区域的特有荧光峰。根据这一荧光峰可以判别其对应的荧光物质是NADH(还原态烟酰胺腺嘌呤二核苷酸)。比较3组不同运动模式组的荧光光谱,发现运动模式与其峰强具有明显的相关性。研究结果表明,运动大鼠腓肠肌的能量代谢强于前腿、比目鱼肌及其他脏器,且NADH自体荧光光谱特性是判断肌肉代谢程度的有效的指标之一。     

Technical evaluation of in vivo abdominal fat and IMCL quantification using MRI and MRSI at 3 T

OBJECTIVES: The objectives of this study were to develop protocols that measure abdominal fat and calf muscle lipids with magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS), respectively, at 3 T and to examine the correlation between these parameters and insulin sensitivity. MATERIALS AND METHODS: Ten nondiabetic subjects [five insulin-sensitive (IS) subjects and five insulin-resistant (IR) subjects] were scanned at 3 T. Visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT) were segmented semiautomatically from abdominal imaging. Intramyocellular lipids (IMCL) in calf muscles were quantified with single-voxel MRS in both soleus and tibialis anterior muscles and with magnetic resonance spectroscopic imaging (MRSI). RESULTS: The average coefficient of variation (CV) of VAT/(VAT+SAT) was 5.2%. The interoperator CV was 1.1% and 5.3% for SAT and VAT estimates, respectively. The CV of IMCL was 13.7% in soleus, 11.9% in tibialis anterior and 2.9% with MRSI. IMCL based on MRSI (3.8+/-1.2%) were significantly inversely correlated with glucose disposal rate, as measured by a hyperinsulinemic-euglycemic clamp. VAT volume correlated significantly with IMCL. IMCL based on MRSI for IR subjects was significantly greater than that for IS subjects (4.5+/-0.9% vs. 2.8+/-0.5%, P=.02). CONCLUSION: MRI and MRS techniques provide a robust noninvasive measurement of abdominal fat and muscle IMCL, which are correlated with insulin action in humans.     

A performance analysis of echographic ultrasonic techniques for non-invasive temperature estimation in hyperthermia range using phantoms with scatterers

Optimization of efficiency in hyperthermia requires a precise and non-invasive estimation of internal distribution of temperature. Although there are several research trends for ultrasonic temperature estimation, efficient equipments for its use in the clinical practice are not still available. The main objective of this work was to research about the limitations and potential improvements of previously reported signal processing options in order to identify research efforts to facilitate their future clinical use as a thermal estimator.In this document, we have a critical analysis of potential performance of previous ultrasonic research trends for temperature estimation inside materials, using different processing techniques proposed in frequency, time and phase domains. It was carried out in phantom with scatterers, assessing at their specific applicability, linearity and limitations in hyperthermia range. Three complementary evaluation indexes: technique robustness, Mat-lab processing time and temperature resolution, with specific application protocols, were defined and employed for a comparative quantification of the behavior of the techniques. The average increment per °C and mm was identified for each technique (3 KHz/°C in the frequency analysis, 0.02 rad/°C in the phase domain, while increments in the time domain of only 1.6 ns/°C were found). Their linearity with temperature rising was measured using linear and quadratic regressions and they were correlated with the obtained data.New improvements in time and frequency signal processing in order to reveal the potential thermal and spatial resolutions of these techniques are proposed and their subsequent improved estimation results are shown for simulated and measured A-scans registers. As an example of these processing novelties, an excellent potential resolution of 0.12 °C into hyperthermia range, with near-to-linear frequency dependence, could be achieved.Specifically defined “numerical” and physical multi-scatter phantoms are described, which mimic ultrasound velocity in tissues of about 1560 m/s @ 35 °C and have a quasi-uniform internal scattering structure designed to assure standard signal patterns adequate for processing comparisons in the same time and sound velocity conditions for all the techniques analyzed, and to obtain easily repeatable multi-pulse echo-patterns.A perfect lineal dependence (100% of correlation coefficient) between the unitary average increment measured by each technique and temperature rising was observed while working with simulated A-scan registers, where all the parameters are under an accurate control. Nevertheless a very small quadratic tendency appeared in the results obtained from experimental echo registers, which are more similar to a real tissues case. It would be an interesting future work to analyze the behavior of these techniques in real tissues in order to confirm or reject this light quadratic tendency.Finally, new methods were detailed and applied in order to precisely quantify the advantages of each estimation technique; their respective intrinsic limitations were also underlined.     

Feasibility of using ultrasound contrast agents to increase the size of thermal lesions induced by non-focused transducers: in vitro demonstration in tissue mimicking phantom

Miniature flat ultrasound transducers have shown to be effective for a large variety of thermal therapies, but the associated superficial heating implicates developing original strategies in order to extend therapeutic depth. The goal of the present paper is to use ultrasound contrast agents (UCA) to increase remote attenuation and heating. Theoretical simulations demonstrated that increasing attenuation from 0.27 to 0.8 Np/cm at 10 MHz beyond a distance of 18 mm from the transducer should result in longer thermal damages due to protein coagulation in a tissue mimicking phantom. Contrast agents (BR14, Bracco, Plan-les-Ouates, Switzerland) were embedded in thermo-sensitive gel and attenuations ranging from 0.27 to 1.33 Np/cm were measured at 10 MHz for concentrations of BR14 between 0 and 4.8%. Thermal damages were then induced in several gels, which had different layering configurations. Thermal damages, 12.8 mm in length, were obtained in homogeneous gels. When mixing contrast agents at a concentration of 3.2% beyond a first 18 mm-thick layer of homogeneous gel, the thermal damages reached 21.5 mm in length. This work demonstrated that contrast agents can be used for increasing attenuation remotely and extending therapeutic depth induced by a non-focused transducer. Additional work must be done in vivo in order to verify the remote-only distribution of bubbles and associated increase in attenuation.     

Ultrasonic assessment of tissue hydration status

Tissue water content is an important diagnostic parameter that can be used for estimation of water loss in muscles such as common dehydration during high endurance exercises. It could be also applied for evaluation of the increased fluids content in the tissue caused by the variety of pathological conditions or edemas. Ultrasonic method for tissue water content monitoring is based on the premise that the speed of a bulk or compression sound wave is determined mainly by the molecular content of the tissue. Most soft tissues, including muscles that consist of about 70-80% water, exhibit shift of the ultrasound velocity associated with the change in their water content. In the present paper, we tested the feasibility of assessing changes in tissue water content by measurements of ultrasound velocity in ex vivo animal muscle tissues. An increase in the ultrasound velocity correlated with the volumetric water loss in the tissue was observed when other tissue components (proteins, fat) remained constant. Possibility to assess muscle dehydration with 1% accuracy was confirmed in model dehydration experiments, where ultrasound velocity slope of about 3 m/s per 1% of water loss was revealed at measurement error less than 2 m/s. Hence, the ultrasonic approach can provide basis for a convenient, lightweight system in sports medicine for monitoring total body hydration during long-term endurance exercise in hot conditions, as well as for edemas monitoring and other medical applications.     

The Effect of Hemodialysis on Voice: An Acoustic Analysis

Because respiration is part of the well-coordinated process necessary for phonation, this study was conducted with the purpose of analyzing the effect of chronic hemodialysis on voice characteristics of patients with chronic renal failure. A total of 57 patients were recruited for the study, including 31 males and 26 females ranging in age from 16 to 85 years. Patients underwent evaluation of their voice directly before and after hemodialysis using the Kay Elemetric VISI Pitch (Model 330; Kay Elemetric Corporation, Lincoln Park, New Jersey). The vocal acoustic parameters studied include habitual pitch, pitch range, relative average perturbation, shimmer, noise-to-harmonic ratio, voice turbulence index, maximum phonation time, and voice energy. The data were analyzed using the paired t-test for the total sample and the nonparametric test for the female and male subgroups. The total sample analysis showed a statistically significant increase in the habitual pitch after the hemodialyis (p < 0.05), with a borderline increase in the pitch range and maximum phonation time (p < 0.10). In the female group, there was a statistically significant increase in the habitual pitch and a borderline increase in the relative average perturbation. In the male group, there was a significant increase in the habitual pitch with a borderline increase in maximum phonation time. Discussion of the after-mentioned results is presented.     

MR quantification of muscle fatty replacement in McArdle''s disease

McArdle's disease is an energy-dependant disorder of skeletal muscle caused by the inability to break down glycogen. The aim of this study was to quantify fatty replacement in patients with McArdle's disease. Calf and thigh axial spin echo T₁-weighted magnetic resonance (MR) images (repetition time 500 ms, echo time 25 ms) were obtained at 0.5 T in nine patients with McArdle's disease (age 51 ± 16 years, range 26–74) and nine sex- and age-matched healthy subjects (age 52 ± 16 years, range 29–78) to quantify intramuscular fat. Regions of interest were drawn manually, encompassing the largest cross section of muscle. A fatty replacement index (IF) was determined from histograms of signal in the regions of interest in calf and thigh muscles. In normal subjects, IF = 3.6 ± 2.8% in calf and 4.9 ± 2.3% in thigh. In patients, IF = 11 ± 9.3% in calf and 13.5 ± 10.4% in thigh, significantly different from IF values in normal subjects (p = .03). IF correlated well with age in patients (p = .03). In older patients, up to 25% of the muscle volume was replaced by fat. Patients with McArdle's disease, usually weakly disabled, exhibit significant muscle fatty replacement on MR images. These findings suggest a progressive muscle loss over time related to the disease process.     

Air-coupled ultrasound stimulated optical vibrometry for resonance analysis of rubber tubes

Air-coupled ultrasound stimulated optical vibrometry is proposed to generate and detect the resonances of a rubber tube in air. Amplitude-modulated (AM) focused ultrasound radiation force from a broadband air-coupled ultrasound transducer with center frequency of 500 kHz is used to generate a low frequency vibration in the tube. The resonances of several modes of the tube are measured with a laser vibrometer of 633 nm wavelength. A wave propagation approach is used to calculate the resonances of the tube from its known material properties. Theoretical and experimental resonance frequencies agree within 5%. This method may be useful in measuring the in vitro elastic properties of arteries from the resonance measurements in air. It may also be helpful to better understand the coupling effects of the surrounding tissue and interior blood on the vessel wall by measuring the resonance of the vessel in vitro and in vivo.     

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.     

Sensitivity to point-spread function parameters in medical ultrasound image deconvolution

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread function. However, it is difficult to obtain a sufficiently accurate estimate of the point-spread function in vivo because of the unknown properties of the soft tissue in clinical applications. Local variations in the speed of sound and attenuation change the pulse and beam shape. These in turn affect the point-spread function. The purpose and novelty of this paper is therefore to explore the sensitivity of a state-of-the-art deconvolution algorithm to uncertainty in the point-spread function. The point-spread function in our restoration algorithm is made shift invariant in the lateral dimension but shift dependent in the axial direction, and is modelled to match a 128-element 1D linear array often found in clinical use. We present simulated and in vitro sensitivity analyses of two-dimensional deconvolution while varying six parameters on which the point-spread function depends. Uncertainty in the ultrasound machine is analysed by varying the axial depths of lateral and elevational foci alongside height and width of transducer elements. Sensitivity to tissue influence is investigated by varying the speed of sound and frequency-dependent attenuation of the electro-mechanical impulse response. The results are analysed both quantitatively and in terms of the perceived image quality. First, the assessment of deconvolution using the logarithmic image amplitude is found to be a better indicator of the perceived improvement in the restoration. Secondly, the two most critical parameters for two-dimensional deconvolution are discovered to be the lateral focus and the speed of sound, because the success of deconvolution is perceived primarily in terms of deblurring. We also observed similar patterns for the simulation and in vitro experiment. Finally, we show that it is possible to restore in vivo ultrasound images using an assumed point-spread function and hence conclude that an exact point-spread function is not necessary for enhancing ultrasound image quality by deconvolution.     

Postural Sway during Local Vibratory Stimulation for Proprioception in Elderly Individuals with Pre-Sarcopenia

Objective: Many studies have demonstrated that the loss of muscle mass (LMM) poses a risk of postural instability in the elderly; however, few studies have shown how LMM decreases proprioception. In this study, we investigated the changes in postural sway among older individuals with LMM induced by application of a local vibratory stimulus. Method: We enrolled 64 older adults (mean age). Postural sway was measured while applying vibration stimuli of 30, 60, and 240 Hz to both the gastrocnemius and lumbar multifidus muscles. We also measured the relative proprioceptive weighting ratio (RPW) of postural sway. The patients were divided into LMM and non-LMM (NLMM) groups. The study subjects were compared in terms of their age, height, weight, body mass index (BMI), lower leg skeletal muscle mass index (LSMI), L4/5 lumbar multifidus cross-sectional area ratio, and RPW at 30, 60, and 240 Hz. Results: Subjects in the LMM group showed a significantly lower RPW at 60 Hz, LSMI, and BMI than did those in the NLMM group. Conclusions: Decrease in RPW with 60-Hz stimulation concerning the lower leg proprioception is a risk factor for LMM-associated postural instability in the elderly. Consequently, with respect to the gastrocnemius muscles proprioception in LMM, it is necessary to perform assessments using muscle spindle stimuli.     

High-speed observation of cavitation bubble clouds near a tissue boundary in high-intensity focused ultrasound fields

Cavitation bubble clouds generated near a tissue boundary by high-intensity focused ultrasound (HIFU) were studied using high-speed photography. In all, 171 image series were captured during the initial 100 ms of continuous HIFU exposure, which showed that cavitation bubble clouds at the tissue boundary organized into two structures - “cone-shape bubble cloud structure” recorded in 146 image series and “crown-shape bubble cloud structure” recorded in 18 image series. The remaining 7 image series showed the interchanging of these two structures. It was found that when cavitation bubbles first appeared at the tissue boundary, they developed to cone-shape bubble cloud. The cone-shape bubble cloud structure was characterized by a nearly fixed tip in front of the tissue boundary. When the cavitation bubbles initially appeared away from the tissue boundary they evolved into a crown-shape bubble cloud. Deformation of tissue boundary was shown in all the recorded image series.     

Acoustical method of whole-body hydration status monitoring

An acoustical handheld hydration monitor (HM) for assessing the water balance of the human body was developed. Dehydration is a critical public health problem. Many elderly over age of 65 are particularly vulnerable as are infants and young children. Given that dehydration is both preventable and reversible, the need for an easy-to-perform method for the detection of water imbalance is of the utmost clinical importance. The HM is based on an experimental fact that ultrasound velocity in muscle is a linear function of water content and can be referenced to the hydration status of the body. Studies on the validity of HM for the assessment of whole-body hydration status were conducted in the Appalachian State University, USA, on healthy young adults and on elderly subjects residing at an assisted living facility. The HM was able to track changes in total body water during periods of acute dehydration and rehydration in athletes and day-to-day and diurnal variability of hydration in elderly. Results of human studies indicate that HM has a potential to become an efficient tool for detecting abnormal changes in the body hydration status.     

Initial changes of non-traumatic osteonecrosis of femoral head in fat suppression images: bone marrow edema was not found before the appearance of band patterns

The present study examined initial changes in non-traumatic osteonecrosis of the femoral head (ONF) on T1- and T2-weighted MR images, and fat suppression images. The subjects were 57 renal transplant recipients (37 males and 20 females), whose median age at the time of transplantation was 31.5 years old (range, 10 to 58 years). Twelve patients developed band patterns (sign of established ONF) at an early postoperative period. Among them, 4 joints of 3 patients had a localized, faint signal abnormality in fat suppression images, where band pattern was confirmed later in T1- and T2-weighted images. In all the 57 patients, no bone marrow edema preceding to ONF was observed. Bone marrow edema would not be the cause of ONF in renal transplant patients. Early changes depicted in our fat suppression images would be useful information in the studies on pathogenesis of ONF.     

An interleaved sampling strategy for MR spectroscopy in vivo: applications on human calf musculature

Assessment of relaxation times, magnetization transfer rates, or apparent diffusion coefficients by volume selective (1)H MR spectroscopy requires data from several single spectra with variable sequence parameters. Unintentional movements during the examination lead to inaccuracies, especially if the spatial distribution of concentrations is inhomogeneous. Improved comparability of the single spectra in a series recorded in vivo were obtained using a modified spectroscopic technique with INTerleaved ACquisiTion of multiple SPECtra (INTACTSPEC). INTACTSPEC series of spectra from the tibialis anterior muscle (m. tib. ant.), soleus muscle (m. soleus), and tibial bone marrow of 20 healthy volunteers were analyzed. Transverse relaxation times T(2) of methylene signals in muscular lipid stores ranged from 77 ms (intramyocellular methylene component in m. tib. ant.) to 88 ms (intramyocellular methylene component in m. soleus) and were similar to those from yellow tibial bone marrow (T(2) = 84 ms). Echo time-dependent signal intensities of choline and creatine deviated markedly from a monoexponential behavior in m. tib. ant., but were nearly exponential in m. soleus. Results from water diffusion measurements parallel and perpendicular to the axis of the lower leg showed significant differences between m. tib. ant. and m. soleus, probably due to the spatial orientation of the muscle fibers. Apparent diffusion coefficients along the leg axis were found to be higher in m. tib. ant. (2.10 +/- 0.08 x 10(-3) mm(2)/s) compared to m. soleus (1.78 +/- 0.11 x 10(-3) mm(2)/s), but m. soleus showed less restricted diffusion in perpendicular orientation (1.59 +/- 0.19 x 10(-3) mm(2)/s versus 1.20 +/- 0.08 x 10(-3) mm(2)/s in m. tib. ant.). Magnetization transfer experiments with various RF preparation pulse amplitudes led to very similar results for m. tib. ant. and m. soleus.     

Medial tibial pain: a dynamic contrast-enhanced MRI study.

The purpose of this study was to compare the sensitivity of different magnetic resonance imaging (MRI) sequences to depict periosteal edema in patients with medial tibial pain. Additionally, we evaluated the ability of dynamic contrast-enhanced imaging (DCES) to depict possible temporal alterations in muscular perfusion within compartments of the leg. Fifteen patients with medial tibial pain were examined with MRI. T1-, T2-weighted, proton density axial images and dynamic and static phase post-contrast images were compared in ability to depict periosteal edema. STIR was used in seven cases to depict bone marrow edema. Images were analyzed to detect signs of compartment edema. Region-of-interest measurements in compartments were performed during DCES and compared with controls. In detecting periosteal edema, post-contrast T1-weighted images were better than spin echo T2-weighted and proton density images or STIR images, but STIR depicted the bone marrow edema best. DCES best demonstrated the gradually enhancing periostitis. Four subjects with severe periosteal edema had visually detectable pathologic enhancement during DCES in the deep posterior compartment of the leg. Percentage enhancement in the deep posterior compartment of the leg was greater in patients than in controls. The fast enhancement phase in the deep posterior compartment began slightly slower in patients than in controls, but it continued longer. We believe that periosteal edema in bone stress reaction can cause impairment of venous flow in the deep posterior compartment. MRI can depict both these conditions. In patients with medial tibial pain, MR imaging protocol should include axial STIR images (to depict bone pathology) with T1-weighted axial pre and post-contrast images, and dynamic contrast enhanced imaging to show periosteal edema and abnormal contrast enhancement within a compartment.     

Proton magnetic resonance spectroscopy and biochemical investigation of type 2 diabetes mellitus in Asian Indians: observation of high muscle lipids and C-reactive protein levels

We report the determination of intramyocellular lipids (IMCLs) of the soleus muscle of patients with type 2 diabetes mellitus (T2DM) using proton magnetic resonance spectroscopy. In addition, the various anthropometric and biochemical profiles of these patients were determined, including estimation of C-reactive protein (CRP), an inflammatory marker of coronary heart disease, and insulin resistance [Homeostasis Model Assessment (HOMA-IR)]. The estimated CRP level and the IMCL content in these patients were correlated with body mass index, percentage of body fat, other measures of abdominal obesity, serum lipoproteins, fasting and post-oral glucose load serum insulin levels and other surrogate markers of insulin resistance. The IMCL content (P=.04), CRP (P=.008) and insulin resistance (P=.0007) were significantly higher in T2DM patients compared to healthy controls. However, IMCL content did not correlate with values of fasting insulin, HOMA-IR or CRP in either group. These findings have strong implications of increased cardiovascular risk in Asian Indians with T2DM. The absence of relationship between CRP and IMCL needs to be explored further in a study using a large sample size.     

Disuse atrophy alterations in normal and low temperature environments during hindlimb unloading in Syrian hamsters

This study examined whether a hypothermic environment reduces experimentally-induced atrophy of skeletal muscle, as judged by histochemical findings. The hind limbs of hamsters in a hypothermic group were suspended and flexed into plantar positions at the ankle joint, and housed for one week at 8 to 12 degree celsius in a temperature-controlled room, while the normothermic group was housed at 23 to 25 degree celsius. Hypothermia did not significantly alter the average caloric intake, and the animals from the hypothermic group lost a significant amount of body weight when compared with the normothermic group. The hypothermic group retained more muscle wet-weight and myofibers cross-sectional area in the soleus and gastrocnemius muscles compared with the normothermic group. Our results indicate that a hypothermic environment inhibits short-term muscle atrophy. This inhibition may be caused by the increased caloric intake combined with a state similar to hibernation in low-temperature environments.     

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2-2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 × 10⁻⁸ kg/s to 2.63 × 10⁻⁸ kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03 μm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.