Relationship between Viscoelastic and Dielectric Properties of Biological Soft Tissues
Electromechanical Correlations in Biological Soft Tissues
The measurement of electrical and mechanical properties of soft tissues and organs are highly useful to analyze the physiological system and to classify normal and diseased tissues (Woo et ah, 1981; Fatemi et ah, 2003; Howe et ah, 1995). Estimation of these properties of soft tissues is important as they are closely related to the tissue structure, biological conditions and pathology (Konofagou et ah, 2004). Moreover, the properties of soft tissues are often investigated for the staging of several disease states (Duck, 2013; O’Rourke et ah, 2007), as well as to understand and diagnose tissue pathologies (Fatemi et ah, 2003; Asbach et ah, 2008). Although it is known that the elastic modulus of soft tissues can vary as much as four orders of magnitude in healthy and diseased tissues (Duck, 2013; Sarvazyan, 1993), it is a very complicated biomechanical problem to measure the mechanical properties of living tissues (Novacek et ah, 2002). A medical system that can predict or assess the mechanical properties of tissues could provide an important lead for the diagnosis of several soft tissue pathologies (Greenleaf et ah, 2003).
The viscoelastic nature of soft tissues is described by the complex shear modulus, which has a real part known as the elastic or storage modulus and an imaginary part known as the viscous or loss modulus (Devi et ah, 2007; Dasgupta & Weitz, 2005). The storage modulus and loss modulus are frequency dependent. The viscoelastic properties of biological tissue can be measured experimentally using various methods such as magnetic resonance elastography, ultrasound imaging methods, indentation devices and tactile sensors (Dhar & Zu, 2007). However, the cost of these measurement systems is high and in-vivo measurements are difficult to obtain. Moreover, some of the methods to measure the viscoelastic properties are highly invasive.
The dielectric properties of biological tissues have been a subject of active research as these properties fundamentally determine the propagation and interaction of electromagnetic fields within the tissue (Lazebnik et ah, 2006). There is always significant variation in the dielectric properties of tissues in normal and abnormal cases (Lazebnik et ah, 2007). For instance, the dielectric properties of malignant liver tissue is 19%-30% higher than normal liver tissue (O’Rourke et ah, 2007).
The frequency-dependent dielectric property of the tissue is a complex quantity known as complex permittivity, which has a real part knowrn as relative permittivity (dielectric constant) and an imaginary part known as conductivity (dielectric loss). Analyzing these quantities over a wide range of frequencies is useful to better understand tissue behavior (Gabriel et al., 1996; Foster & Schwan, 1989). The dielectric properties of biological tissues can be easily and efficiently estimated using electrical impedance spectrometers over a wide range of frequencies (Kun et al., 1999).
The interrelation and correlation between mechanical and electrical properties are intricate in case of soft tissues, and hence, the variations in mechanical properties may be estimated from electrical measurements (Kamalanand et al., 2010). Few evidence establish the interrelation between the electrical and mechanical properties of soft tissues from a biological viewpoint. The electrical and mechanical parameters are found to be interdependent in the case of cardiac tissues, cartilage, muscles and tendons (Whiteley et al., 2007; Youn et al., 2003). Keshtkar et al. (2008) assessed the urinary bladder volume changes on the bladder tissue impedance. Nash and Panfilov (2004) reported that a coupled electromechanical approach must be used in future modeling studies for the proper analysis of the physiological system. The dielectric permeability and conductivity of soft tissues were reported as a function of compressive strain by Chammas et al. (1994). Sierpowska et al. (2003) suggested that measurement of electrical properties of bone has the potential to provide the means for quantitative analysis of bone changes. The electrical and mechanical properties of tissue mimicking polyacrylamide phantoms were found to be closely correlated (Krishnamurthy et al., 2009; Kamalanand et al., 2010).
This chapter focuses on the correlations between the electrical and mechanical properties of soft tissues and intelligent models for the prediction of mechanical properties from electrical measurements. Furthermore, this chapter discusses two optimization algorithms for the estimation of the Cole-Cole model parameters from measurements of relative permittivity and conductivity as a function of frequency.