**1. Introduction**

238 Acoustic Waves – From Microdevices to Helioseismology

Stockmayer, W. H. (1943). Theory of molecular size distribution and gel formation in branched –chain polymers, Journal of chemical physics, Vol. 11, pp. 45-55 Vogel S. M. & Skinner D. W., (1965). Natural frequencies of transversely vibrating uniform

Walstra, P. & Vliet, V. (1986). The physical chemistry of curd making, Netherlands. milk

annular plates, Journal of applied mechanics, Vol. 32, pp. 926-931

dairy journal, Vol. 40, pp. 241-259

Biological interfaces and accompanying interfacial processes constitute one of the most dynamic and expanding fields in science and technology such as biomaterials, tissue engineering, and biosensors. For example, in biomaterials, the bio-interfacial processes between biomaterials and surrounding tissue plays a crucial role in the biocompatibility of the layer (Werner, 2008). In tissue engineering, cellular adhesion plays an important role in the regulation of cell behavior, such as the control of growth and differentiation during development and the modulation of cell migration in wound healing, metastasis, and angiogenesis (Hong et al., 2006). Performance of a biosensor is highly dependent on interfacial processes involving the sensor sensing interface and a target analyte. Therefore, quantitative information on the novel and robust immobilization of detector molecules is one the most important aspects of the biosensor field (Kroger et al., 1998).

Thickness shear mode (TSM) sensors have been used in a variety of studies including interfacial biological processes, cells, tissue and properties of various proteins and their reaction (Cote et al., 2003). Phenomena such as cell adhesion (Soonjin et al., 2006.), superhydrophobicity (Sun et al., 2006, Roach et al., 2007), particle-surface interactions (Zhang et al.,2005), organic and inorganic particle manipulation (Desa et al., 2010) and rheological and interfacial properties of blood coagulation (Ergezen et al. 2007) were studied using TSM sensors. Due to the high interfacial sensitivity of TSM sensors, it has been shown that cell motility can be monitored by analyzing the noise of the TSM sensor response (Sapper et al., 2006). It has also been demonstrated that the number of motile sperm in a semen sample can be assessed in real-time using a flow-chamber integrated with a thickness shear mode sensor (Newton et al., 2007).

## **1.1 Quantification of Thickness Shear Mode (TSM) sensor response**

The TSM sensor response is affected by the complex nature of the interface. Its response is influenced by the geometrical and material properties of the interacting surfaces such as surface roughness (Cho et al., 2007), hydrophobicity (Ayad and Torad, 2009), interfacial

<sup>\*</sup> Johann Desa, Matias Hochman, Robert Weisbein Hart, Qiliang Zhang, Sun Kwoun, Piyush Shah and Ryszard Lec

*School of Biomedical Engineering, Health and Sciences, Drexel University, Philadelphia USA*

Modeling of Biological Interfacial Processes Using Thickness–Shear Mode Sensors 241

shear mode (MTSM) measurement technique and genetic algorithm-based data analysis

1. Identification of all four parameter by using the MTSM sensor's single harmonic response results in an under-determined problem. The MTSM sensor response enables the identification of two parameters by providing imaginary and real components of the mechanical impedance. In other words, there are fewer equations than the material/geometrical parameters of the interface, therefore, the stochastic method is the only approach that can address this problem mathematically. In this project it was shown that combination of the MTSM measurement technique and the genetic algorithm-based data analysis technique (called as MTSM/GA technique) was used to solve this under-determined problem. *It was reported for the first time, a novel approach that enables determining all four parameters, which define the response of the MTSM* 

2. Most of the biological interfaces constitute multi-layer structures. Multi-layer modeling of biological interfacial processes was proposed by several researchers and by us (Wegener et al., 1999, Ergezen et al., 2007). In contrast, there has been very limited (Lucklum et al., 2001) theoretical study and no experimental studies based on the MTSM sensor for quantitative characterization of multi-layer biological processes. *It was reported, for the first time, the most comprehensive theoretical and experimental study for* 

A new approach merging the multi-harmonic thickness shear mode (MTSM) sensor and a data extraction technique based on stochastic global optimization procedure has been proposed. For this purpose, the MTSM/GA technique is being developed and calibrated with a polymer layer (having known properties). This was then used to estimate the properties of a protein layer with unknown properties adsorbed to the MTSM sensor surface. It was demonstrated that this new method has the potential to be a novel tool for

Piezoelectric MTSM sensors transmit acoustic shear waves into a medium under test, and the waves interact with the medium. Shear waves monitor local properties of a medium in the vicinity of the sensor and of the medium/sensor interface (on the order of nm - μm); thus, they provide a very attractive technique to study interfacial processes. Measured parameters of acoustic waves are correlated with medium properties such as interfacial mass/density, viscosity, or elasticity changes taking place during chemical or biological

The shear acoustic wave penetrates the medium over a very short distance. The square of the depth of penetration of an acoustic shear wave in MTSM sensor is related to medium viscosity, elasticity, density and the frequency of the wave (please see Appendix IA.) (Kwoun et al. 2006). Figure 1a shows the acoustic wave penetrating the adjacent medium and Figure 1b shows that the depth of penetration decreases at higher harmonic frequencies

Therefore, by changing the frequency, one can control the distance at which the wave probes the medium. Multi-harmonic operation of MTSM sensor will enable to control the interrogating depth into the biological processes. Therefore it will provide a more in depth

*quantitative characterization of multi-layer biological interfacial processes.*

quantitatively characterization of interfacial biological layers.

**2.1 Multi-Harmonic Thickness Shear Mode (MTSM) sensor** 

technique has been used. This novel method was utilized to solve two unmet needs:

*technique.* 

**2. Theory** 

processes.

in a semi-infinite medium.

slippage (Zhuang et al., 2008), coverage area (Johanssmann et al., 2008), sensitivity profile (Edvardsson et al., 2005) and penetration depth of the shear acoustic wave (Kunze et al., 2006).

Various theoretical models have been developed for quantitative characterization of the TSM sensor response to interfacial interactions. Nunalee et al (2006) developed model to predict of the TSM sensor response to a generalized viscoelastic material spreading at the sensor surface in a liquid medium. Cho et al (2007) created a model system to study the viscoelastic properties of two distinct layers, a layer of soft vesicles and a rigid bilayer. Urbakh and Daikhin (2007) developed a model to characterize the effect of surface morphology of non-uniform surface films on TSM sensor response in contact with liquid. Hovgaard et al (2007) have modeled TSM sensor data using an extension to Kevin-Voigt viscoelastic model for studying glucagon fibrillation at the solid-liquid interface. Kanazawa and Cho (2009) discussed the measurement methodologies and analytical models for characterizing macromolecular assembly dynamics.

The physical description based on a wave propagation concept in a one-dimensional approximation has been proven as the best model of thickness shear mode (TSM) sensors. The fundamentals have been published in several books (Rosenbaum, 1998). Martin et al. have (1994) applied this background to sensors by using Mason's equivalent circuit to describe the thickness shear mode sensor itself and transmission lines as well as lumped elements for viscoelastic coatings, semi-infinite liquids etc.. Follow-up papers have introduced a more straightforward definition of the elements of the BVD-model (Behling et al, 1998) as well as several additional approximations, e.g. based on perturbation theory, to derive less complex equations, have suggested a simplified notation to separate the mass from so-called nongravimetric effects, or have applied the transmission line model to several subsystems (Voinova et al, 2002) for demonstration of specific situations just to call some examples. More recent papers deal with deviations from the one-dimensional approximations, e.g. by introducing generalized parameters by deriving specific solutions e.g. for surface roughness or with discontinuity at boundaries.

TSM sensors combined with the theoretical models mentioned above were used to determine the properties of liquids (Lin et al., 1993), high protein concentration solutions (Saluja et al., 2005), and thin polymer films (Katz et al., 1996).

For viscoelastic layers, their mechanical impedance depends upon the density, thickness, and the complex shear modulus of the loading. Identification of the all the system parameters from the impedance measurements has been very challenging and uncertain without a priori knowledge of the thicknesses and/or some of the material properties (Lucklum et al. 1997).

Furthermore, Kwoun (2006) showed the beneficial features of the multi-resonance operation of the TSM (called as "multi-resonance thickness shear mode) sensor to study the formation of biological samples, specifically collagen and albumin, on the sensor surface. In this work, it was demonstrated that the different harmonic frequency clearly showed the different characteristics of mechanical properties, especially shear modulus, of the biological sample. Although this work was one of the pioneer studies to demonstrate the strengths of the MTSM measurement technique, it is limited as it is a semi-quantitative method. Exact values of mechanical properties of anisotropic collagen and albumin samples were not able to be defined due to complexity of the non-linear simultaneous equations of the model. An improved MTSM technique combined with an advanced data analysis technique was proposed by Ergezen et al (2010). A new approach merging the multi-harmonic thickness shear mode (MTSM) measurement technique and genetic algorithm-based data analysis technique has been used. This novel method was utilized to solve two unmet needs:


A new approach merging the multi-harmonic thickness shear mode (MTSM) sensor and a data extraction technique based on stochastic global optimization procedure has been proposed. For this purpose, the MTSM/GA technique is being developed and calibrated with a polymer layer (having known properties). This was then used to estimate the properties of a protein layer with unknown properties adsorbed to the MTSM sensor surface. It was demonstrated that this new method has the potential to be a novel tool for quantitatively characterization of interfacial biological layers.
