Nanointerrogation of ultrasonic contrast agent microbubbles using atomic force microscopy

Material Properties, Dissolution and Time Evolution of PEGylated Lipid-Shelled Microbubbles: Effects of the Polyethylene Glycol Hydrophilic Chain Configurations

Polyethylene glycol (PEG) is often added to the lipid coating of a contrast microbubble to prevent coalescence and improve circulation. At high surface density, PEG chains are known to undergo a transition from a mushroom configuration to an extended brush configuration. We investigated the effects of PEG chain configuration on attenuation and dissolution of microbubbles by varying the molar ratio of the PEGylated lipid in the shell with three (0%, 2% and 5%) in the mushroom configuration and two (10% and 20%) in the brush configuration. We measured attenuation through the bubble suspensions and used it to obtain the characteristic rheological properties of their shells according to two interfacial rheological models. The interfacial elasticity was found to be significantly lower in the brush regime (∼0.6 N/m) than in the mushroom regime (∼1.3 N/m), but similar in value within each regime. The dissolution behavior of microbubbles under acoustic excitation inside an air-saturated medium was studied by measuring the time-dependent attenuation. Total attenuation recorded a transient increase because of growth resulting from air influx and an eventual decrease caused by dissolution. Microbubble shell composition with varying PEG concentrations had significant effects on dissolution dynamics.

Multi-physics study of acoustofluidic delivery agents' clustering behavior

Acoustofluidicly manipulated microbubbles (MBs) and echogenic liposomes (ELIPs) have been suggested as drug delivery systems for the 'on demand' release of drug in target tissue. This requires a clear understanding of their behaviour during ultrasonication and after ultrasonication stops. The main focus of this study is to investigate the behaviour of MBs and ELIPs clusters after ultrasonication stops and the underlaying cause of cluster diffusion considering electrostatic repulsion, steric repulsion and Brownian motion. It also examines the capability of existing models used to predict MBs' attraction velocity due to secondary radiation force, on predicting ELIPs' attraction velocity. Tunable resistive pulse sensing (TRPS) and phase analysis light scattering (PALS) techniques were used to measure zeta potentials of the agents and the size distributions were measured using TRPS. The zeta potentials were found to be -2.43 mV and -0.62 mV for Definity™ MBs, and -3.62 mV and -2.35 mV for ELIPs using TRPS and PALS, respectively. Both agents were shown to have significant cluster formation at pressures as low as 6 kPa. Clusters of both agents were shown to diffuse as sonication stops at a rate that approximately equals the sum of the diffusion coefficients of the agents forming them. The de-clustering behaviours are due to Brownian motion as no sign of electrostatic repulsion was observed and particles movements were observed to be faster for smaller diameters. These findings are important to design and optimise effective drug delivery systems using acoustofluidically manipulated MBs and ELIPs.

Spatiotemporal control of micromechanics and microstructure in acoustically-responsive scaffolds using acoustic droplet vaporization

Acoustically-responsive scaffolds (ARSs), which are composite fibrin hydrogels, have been used to deliver regenerative molecules. ARSs respond to ultrasound in an on-demand, spatiotemporally-controlled manner via a mechanism termed acoustic droplet vaporization (ADV). Here, we study the ADV-induced, time-dependent micromechanical and microstructural changes to the fibrin matrix in ARSs using confocal fluorescence microscopy as well as atomic force microscopy. ARSs, containing phase-shift double emulsion (PSDE, mean diameter: 6.3 μm), were exposed to focused ultrasound to generate ADV - the phase transitioning of the PSDE into gas bubbles. As a result of ADV-induced mechanical strain, localized restructuring of fibrin occurred at the bubble-fibrin interface, leading to formation of locally denser regions. ADV-generated bubbles significantly reduced fibrin pore size and quantity within the ARS. Two types of ADV-generated bubble responses were observed in ARSs: super-shelled spherical bubbles, with a growth rate of 31 μm per day in diameter, as well as fluid-filled macropores, possibly as a result of acoustically-driven microjetting. Due to the strain stiffening behavior of fibrin, ADV induced a 4-fold increase in stiffness in regions of the ARS proximal to the ADV-generated bubble versus distal regions. These results highlight that the mechanical and structural microenvironment within an ARS can be spatiotemporally modulated using ultrasound, which could be used to control cellular processes and further the understanding of ADV-triggered drug delivery for regenerative applications.

A Review of Phospholipid Encapsulated Ultrasound Contrast Agent Microbubble Physics

Ultrasound contrast agent microbubbles have expanded the utility of biomedical ultrasound from anatomic imaging to the assessment of microvascular blood flow characteristics and ultrasound-assisted therapeutic applications. Central to their effectiveness in these applications is their resonant and non-linear oscillation behaviour. This article reviews the salient physics of an oscillating microbubble in an ultrasound field, with particular emphasis on phospholipid-coated agents. Both the theoretical underpinnings of bubble vibration and the experimental evidence of non-linear encapsulated bubble dynamics and scattering are discussed and placed within the context of current and emerging applications.

Long-term physical evolution of an elastomeric ultrasound contrast microbubble

HYPOTHESIS

One of the main assets of crosslinked polymer-shelled microbubbles (MBs) as ultrasound-active theranostic agents is the robustness of the shells, combined with the chemical versatility in modifying the surface with ligands and/or drugs. Despite the long shelf-life, subtle modifications occur in the MB shells involving shifts in acoustic, mechanical and structural properties.

EXPERIMENTS

We carried out a long-term morphological and acoustic evolution analysis on elastomeric polyvinyl-alcohol (PVA)-shelled MBs, a novel platform accomplishing good acoustic and surface performances in one agent. Confocal laser scanning microscopy, acoustic spectroscopy and AFM nanomechanics were integrated to understand the mechanism of PVA MBs ageing. The changes in the MB acoustic properties were framed in terms of shell thickness and viscoelasticity using a linearised oscillation theory, and compared to MB morphology and to nanomechanical analysis.

FINDINGS

We enlightened a novel, intriguing ageing time evolution of the PVA MBs with double behaviour with respect to a crossover time of ∼50 days. Before, significant changes occur in MB stiffness and shell thickness, mainly due to a massive release of entangled PVA chains. Then, the MB resonance frequency increases together with shell thickening and softening. Our benchmark study is of general interest for emerging viscoelastomeric bubbles towards personalised medicine.

Acoustofluidic Measurements on Polymer-Coated Microbubbles: Primary and Secondary Bjerknes Forces

The acoustically-driven dynamics of isolated particle-like objects in microfluidic environments is a well-characterised phenomenon, which has been the subject of many studies. Conversely, very few acoustofluidic researchers looked at coated microbubbles, despite their widespread use in diagnostic imaging and the need for a precise characterisation of their acoustically-driven behaviour, underpinning therapeutic applications. The main reason is that microbubbles behave differently, due to their larger compressibility, exhibiting much stronger interactions with the unperturbed acoustic field (primary Bjerknes forces) or with other bubbles (secondary Bjerknes forces). In this paper, we study the translational dynamics of commercially-available polymer-coated microbubbles in a standing-wave acoustofluidic device. At increasing acoustic driving pressures, we measure acoustic forces on isolated bubbles, quantify bubble-bubble interaction forces during doublet formation and study the occurrence of sub-wavelength structures during aggregation. We present a dynamic characterisation of microbubble compressibility with acoustic pressure, highlighting a threshold pressure below which bubbles can be treated as uncoated. Thanks to benchmarking measurements under a scanning electron microscope, we interpret this threshold as the onset of buckling, providing a quantitative measurement of this parameter at the single-bubble level. For acoustofluidic applications, our results highlight the limitations of treating microbubbles as a special case of solid particles. Our findings will impact applications where knowing the buckling pressure of coated microbubbles has a key role, like diagnostics and drug delivery.

Encapsulated microbubbles and echogenic liposomes for contrast ultrasound imaging and targeted drug delivery

Micron- to nanometer-sized ultrasound agents, like encapsulated microbubbles and echogenic liposomes, are being developed for diagnostic imaging and ultrasound mediated drug/gene delivery. This review provides an overview of the current state of the art of the mathematical models of the acoustic behavior of ultrasound contrast microbubbles. We also present a review of the in vitro experimental characterization of the acoustic properties of microbubble based contrast agents undertaken in our laboratory. The hierarchical two-pronged approach of modeling contrast agents we developed is demonstrated for a lipid coated (Sonazoid™) and a polymer shelled (poly D-L-lactic acid) contrast microbubbles. The acoustic and drug release properties of the newly developed echogenic liposomes are discussed for their use as simultaneous imaging and drug/gene delivery agents. Although echogenicity is conclusively demonstrated in experiments, its physical mechanisms remain uncertain. Addressing questions raised here will accelerate further development and eventual clinical approval of these novel technologies.

On the interplay of shell structure with low- and high-frequency mechanics of multifunctional magnetic microbubbles

Polymer-shelled magnetic microbubbles have great potential as hybrid contrast agents for ultrasound and magnetic resonance imaging. In this work, we studied US/MRI contrast agents based on air-filled poly(vinyl alcohol)-shelled microbubbles combined with superparamagnetic iron oxide nanoparticles (SPIONs). The SPIONs are integrated either physically or chemically into the polymeric shell of the microbubbles (MBs). As a result, two different designs of a hybrid contrast agent are obtained. With the physical approach, SPIONs are embedded inside the polymeric shell and with the chemical approach SPIONs are covalently linked to the shell surface. The structural design of hybrid probes is important, because it strongly determines the contrast agent's response in the considered imaging methods. In particular, we were interested how structural differences affect the shell's mechanical properties, which play a key role for the MBs' US imaging performance. Therefore, we thoroughly characterized the MBs' geometric features and investigated low-frequency mechanics by using atomic force microscopy (AFM) and high-frequency mechanics by using acoustic tests. Thus, we were able to quantify the impact of the used SPIONs integration method on the shell's elastic modulus, shear modulus and shear viscosity. In summary, the suggested approach contributes to an improved understanding of structure-property relations in US-active hybrid contrast agents and thus provides the basis for their sustainable development and optimization.

Single bubble acoustic characterization and stability measurement of adherent microbubbles

This article examines how the acoustic and stability characteristics of single lipid-shelled microbubbles (MBs) change as a result of adherence to a target surface. For individual adherent and non-adherent MBs, the backscattered echo from a narrowband 2-MHz, 90-kPa peak negative pressure interrogation pulse was obtained. These measurements were made in conjunction with an increasing amplitude broadband disruption pulse. It was found that, for the given driving frequency, adherence had little effect on the fundamental response of an MB. Examination of the second harmonic response indicated an increase of the resonance frequency for an adherent MB: resonance radius increasing of 0.3 ± 0.1 μm for an adherent MB. MB stability was seen to be closely related to MB resonance and gave further evidence of a change in the resonance frequency due to adherence.

Nanomechanics of lipid encapsulated microbubbles with functional coatings

Microbubbles (MBs) are increasingly being proposed as delivery vehicles for targeted therapeutics, as well as being contrast agents for ultrasound imaging. MBs formed with a lipid shell are promising candidates due to their biocompatibility and the opportunity for surface functionalization, both for specific targeting of tissues and as a means to tune their mechanical response for localized ultrasound induced destruction in vivo. Herein, we acquired force-deformation data on coated lipid MBs using tip-less microcantilevers in an atomic force microscope. Model lipid MBs were designed to test the effects of adding a functional coating on the outside of the lipid leaflet, including a protein coat (streptavidin) or the addition of quantum dots (Q-dots) as optical reporters. MBs (~3 μm diameter) were repeatedly compressed for deformations up to ~50% to obtain a full bubble response. Addition of a coating increased the initial deformation stiffness related to shell bending ~2-fold for streptavidin and ∼3-fold for Q-dots. The presence of a polyethylene glycol (PEG) linker in between the lipid and functional coating, led to enhanced stiffening at high deformations. The plasticity index has been determined and only those MBs that included the PEG linker showed a force dependent short time-scale (<~1s) plasticity. This study demonstrates modulation of the mechanical response of biocompatible MBs through the addition of functional coatings necessary for rationale design of therapeutic lipid MBs for targeted drug delivery.

An experimental study on the stiffness of size-isolated microbubbles using atomic force microscopy

To fully assess contrast-enhanced acoustic bioeffects in diagnostic and therapeutic procedures, the mechanical properties of microbubbles need to be considered. In the present study, direct measurements of the microbubble stiffness were performed using atomic force microscopy by applying nanoscale compressions (up to 25 nN/s) on size-isolated, lipidcoated microbubbles (diameter ranges of 4 to 6 μm and 6 to 8 μm). The stiffness was found to lie between 4 and 22 mN/m and to decrease exponentially with the microbubble size within the diameter range investigated. No cantilever spring constant effect was found on the measured stiffness. The Young's modulus of the size-isolated microbubbles used in our study ranged between 0.4 and 2 MPa. Microstructures on the surface of the microbubbles were found to influence the overall microbubble elasticity. Our results indicated that more detailed theoretical models are needed to account for the size-dependent microbubble mechanical properties to accurately predict their acoustic behavior. The findings provided useful insights into guidance of cavitation-induced drug and gene delivery and could be used as part of the framework in studies on the shear stresses induced on the blood vessel walls by oscillating microbubbles.

Acoustical properties of individual liposome-loaded microbubbles

A comparison between phospholipid-coated microbubbles with and without liposomes attached to the microbubble surface was performed using the ultra-high-speed imaging camera (Brandaris 128). We investigated 73 liposome-loaded microbubbles (loaded microbubbles) and 41 microbubbles without liposome loading (unloaded microbubbles) with a diameter ranging from 3-10 μm at frequencies ranging from 0.6-3.8 MHz and acoustic pressures ranging from 5-100 kPa. The experimental data showed nearly the same shell elasticity for the loaded and unloaded bubbles, but the shell viscosity was higher for loaded bubbles compared with unloaded bubbles. For loaded bubbles, a higher pressure threshold for the bubble vibrations was noticed. In addition, an "expansion-only" behavior was observed for up to 69% of the investigated loaded bubbles, which mostly occurred at low acoustic pressures (≤30 kPa). Finally, fluorescence imaging showed heterogeneity of liposome distributions of the loaded bubbles.

Nanomechanical properties of phospholipid microbubbles

This study uses atomic force microscopy (AFM) force-deformation (F-Δ) curves to investigate for the first time the Young's modulus of a phospholipid microbubble (MB) ultrasound contrast agent. The stiffness of the MBs was calculated from the gradient of the F-Δ curves, and the Young's modulus of the MB shell was calculated by employing two different mechanical models based on the Reissner and elastic membrane theories. We found that the relatively soft phospholipid-based MBs behave inherently differently to stiffer, polymer-based MBs [Glynos, E.; Koutsos, V.; McDicken, W. N.; Moran, C. M.; Pye, S. D.; Ross, J. A.; Sboros, V. Langmuir2009, 25 (13), 7514-7522] and that elastic membrane theory is the most appropriate of the models tested for evaluating the Young's modulus of the phospholipid shell, agreeing with values available for living cell membranes, supported lipid bilayers, and synthetic phospholipid vesicles. Furthermore, we show that AFM F-Δ curves in combination with a suitable mechanical model can assess the shell properties of phospholipid MBs. The "effective" Young's modulus of the whole bubble was also calculated by analysis using Hertz theory. This analysis yielded values which are in agreement with results from studies which used Hertz theory to analyze similar systems such as cells.

Production of uniformly sized serum albumin and dextrose microbubbles

Uniformly-sized preparations with average microbubble (MB) diameters from 1 to 7 μm were produced reliably by sonicating decafluorobutane-saturated solutions of serum albumin and dextrose. Detailed protocols for producing and size-separating the MBs are presented, along with the effects that changing each production parameter (serum albumin concentration, sonication power, sonication time, etc.) had on MB size distribution and acoustic stability. These protocols can be used to produce MBs for experimental applications or serve as templates for developing new protocols that yield MBs with physical and acoustic properties better suited to specific applications. Size stability and ultrasonic performance quality control tests were developed to assure that successive MB preparations perform identically and to distinguish the physical and acoustic properties of identically sized MBs produced with different serum albumin-dextrose formulations and sonication parameters. MBs can be stored at 5 °C for protracted periods (2 weeks to one year depending on formulation).

Microbubble sizing and shell characterization using flow cytometry

Experiments were performed to size, count, and obtain shell parameters for individual ultrasound contrast microbubbles using a modified flow cytometer. Light scattering was modeled using Mie theory, and applied to calibration beads to calibrate the system. The size distribution and population were measured directly from the flow cytometer. The shell parameters (shear modulus and shear viscosity) were quantified at different acoustic pressures (from 95 to 333 kPa) by fitting microbubble response data to a bubble dynamics model. The size distribution of the contrast agent microbubbles is consistent with manufacturer specifications. The shell shear viscosity increases with increasing equilibrium microbubble size, and decreases with increasing shear rate. The observed trends are independent of driving pressure amplitude. The shell elasticity does not vary with microbubble size. The results suggest that a modified flow cytometer can be an effective tool to characterize the physical properties of microbubbles, including size distribution, population, and shell parameters.

The acoustic scatter from single biSphere microbubbles

Single microbubble acoustic acquisitions provide information on the behaviour of microbubble populations by enabling the generation of large amounts of data. Acoustic signals from single polylactide-shelled and albumin coated biSphere™ microbubbles have been acquired. The responses observed from a range of incident frequencies and acoustic pressures varied in duration. Partial echoes shorter than the incident pulse duration have been observed for low frequency pulses of sufficient amplitude, suggesting release of gas from bubbles. The results presented suggest that the mechanism of scatter from hard shelled agents may be shell disruption and gas release, or partly from gas leaking from defected shell sites, which has previously not been observed optically. These results can provide the basis for improved imaging through optimization of incident pulse parameters, with potential benefits to both diagnostic and therapeutic techniques.

The assessment of microvascular flow and tissue perfusion using ultrasound imaging

Imaging microvascular flow is of diagnostic value for a wide range of diseases including cancer, inflammation, and cardiovascular disease. The introduction of microbubbles as ultrasound contrast agents offers significant signal enhancement to the otherwise weakly scattered signal from blood in the circulation. Microbubbles provide maximum impedance mismatch, but are not linear scatterers. Their complex response to ultrasound has generated research on both their behaviour and their scattered-signal processing. Nearly 20 years ago signal processing started with simple spectral filtering of harmonics showing contrast-enhanced images. More recent pulse encoding techniques have achieved good cancellation of tissue echoes. The good quality contrast-only images enabled ultrasound contrast-imaging applications to be established in microvascular measurements in the liver and the myocardium. The field promises to advance the quantification of microvascular flow kinetics.

Microbubbles as ultrasound triggered drug carriers

Originally developed as contrast agents for ultrasound imaging and diagnostics, in the past years, microbubbles have made their way back from the patients' bedside to the researcher's laboratory. Microbubbles are currently believed to have great potential as carriers for drugs, small molecules, nucleic acids, and proteins. This review provides insight into this intriguing new frontier from the perspective of the pharmaceutical scientist. First, basic aspects on the application of ultrasound-targeted microbubble destruction for drug delivery will be presented. Next, we will review the recently applied approaches for manufacturing and drug-loading microbubbles. Important quality issues and characterization techniques for advanced microbubble formulation will be discussed. Finally, we will provide an assessment of the prospects for microbubbles in drug and gene therapy, illustrating the problems and requirements for their future development.

Nanomechanics of biocompatible hollow thin-shell polymer microspheres

The nanomechanical properties of biocompatible thin-shell hollow polymer microspheres with approximately constant ratio of shell thickness to microsphere diameter were measured by nanocompression tests in aqueous conditions. These microspheres encapsulate an inert gas and are used as ultrasound contrast agents by releasing free microbubbles in the presence of an ultrasound field as a result of free gas leakage from the shell. The tests were performed using an atomic force microscope (AFM) employing the force-distance curve technique. An optical microscope, on which the AFM was mounted, was used to guide the positioning of tipless cantilevers on top of individual microspheres. We performed a systematic study using several cantilevers with spring constants varying from 0.08 to 2.3 N/m on a population of microspheres with diameters from about 2 to 6 microm. The use of several cantilevers with various spring constants allowed a systematic study of the mechanical properties of the microsphere thin shell at different regimes of force and deformation. Using thin-shell mechanics theory for small deformations, the Young's modulus of the thin wall material was estimated and was shown to exhibit a strong size effect: it increased as the shell became thinner. The Young's modulus of thicker microsphere shells converged to the expected value for the macroscopic bulk material. For high applied forces, the force-deformation profiles showed a reversible and/or irreversible nonlinear behavior including "steps" and "jumps" which were attributed to mechanical instabilities such as buckling events.

Observation of the ultrastructure of anterior cruciate ligament graft by atomic force microscopy

This study presented the fibril ultrastructure of retrieved grafts from the reconstruction of anterior cruciate ligament (ACL) using atomic force microscopy (AFM). The tapping mode images of the AFM were taken from different areas of the longitudinally cut grafts. Regular arrangement of collagen fibrils was found in certain areas of the graft. In many areas, however, the fibrils were not well arranged in a single direction, with some smaller fibrils oriented vertically to larger parallel fibrils. The crossing and tangling of fibrils in ACL grafts was well represented in the three-dimensional AFM image. This abnormality of graft ultrastructure might indicate the possible alteration of the mechanical environment after ACL reconstruction. This study demonstrated the suitability and importance of ultrastructure observation of ACL grafts by AFM.

Response of contrast agents to ultrasound

Microbubbles are used as ultrasonic contrast agents that enhance the ultrasound signals of the vascular bed. The recent development of site-targeted microbubbles opened up the possibility for molecular imaging as well as localised drug and gene delivery. Initially the microbubbles' physical properties and their response to the ultrasound beam were not fully understood. However, the introduction of fast acquisition microscopy has allowed the observation of the microbubble behaviour in the presence of ultrasound. In addition, acoustical techniques can determine the scatter of single microbubbles. Sonoporation experiments promise high-specificity drug and gene delivery, but the responsible physical mechanisms, particularly for in vivo applications, are not fully understood. An improvement of microbubble technology may address variability related problems in both imaging and drug/gene delivery.

Nanomechanical probing of microbubbles using the atomic force microscope

Atomic force microscopy (AFM) is a versatile mechanical nanosensor that can be used to quantify the mechanical properties of microbubbles (MBs) and the adhesion mechanisms of targeted MBs. Mechanical properties were investigated using AFM tipless cantilevers to microcompress the MBs. The range of compressive stiffness for biSphere was found to be between 1 and 10Nm(-1) using a cantilever with a spring constant of 0.6 Nm(-1). This stiffness was shown to decrease with the MB size in a non-linear fashion. It is also possible to calculate a theoretical Young's modulus of the shell. The adhesion properties of targeted lipid based MBs that use avidin-biotin chemistry for the attachment of targeting ligands were also studied. The MBs were attached to poly-L-lysine treated tipless cantilevers with spring constants ranging from 0.03 to 0.1 Nm(-1). This system interrogated individual cells with pulling cantilever distance of 15 microm, and scan rate at 0.2 Hz. The depth of contact was not larger than 0.4 microm. The targeted MBs provided a significantly larger adhesion to the cells compared to control ones. Average adhesion force was dependent on depth of contact. Analysis of the data demonstrated a single distribution of adhesion events with median at 89 pN, which is in agreement with the literature for such interactions. The nanointerrogation of MBs using AFM provides new insight into their mechanical properties, and should be of assistance to MB design and manufacture.

Ultrasonic bubbles in medicine: influence of the shell

Ultrasound contrast agents consist of microscopically small bubbles encapsulated by an elastic shell. These microbubbles oscillate upon ultrasound insonification, and demonstrate highly nonlinear behavior, ameliorating their detectability. (Potential) medical applications involving the ultrasonic disruption of contrast agent microbubble shells include release-burst imaging, localized drug delivery, and noninvasive blood pressure measurement. To develop and enhance these techniques, predicting the cracking behavior of ultrasound-insonified encapsulated microbubbles has been of importance. In this paper, we explore microbubble behavior in an ultrasound field, with special attention to the influence of the bubble shell. A bubble in a sound field can be considered a forced damped harmonic oscillator. For encapsulated microbubbles, the presence of a shell has to be taken into account. In models, an extra damping parameter and a shell stiffness parameter have been included, assuming that Hooke's Law holds for the bubble shell. At high acoustic amplitudes, disruptive phenomena have been observed, such as microbubble fragmentation and ultrasonic cracking. We analyzed the occurrence of ultrasound contrast agent fragmentation, by simulating the oscillating behavior of encapsulated microbubbles with various sizes in a harmonic acoustic field. Fragmentation occurs exclusively during the collapse phase and occurs if the kinetic energy of the collapsing microbubble is greater than the instantaneous bubble surface energy, provided that surface instabilities have grown big enough to allow for break-up. From our simulations it follows that the Blake critical radius is not a good approximation for a fragmentation threshold. We demonstrated how the phase angle differences between a damped radially oscillating bubble and an incident sound field depend on shell parameters.