Tissue anisotropy

Permittivity is usually higher in liquids than in solids (e.g., water/iee) heeause the charges are more loosely hound in a liquid. A liquid such as water is polar hut isotropic when all moleeules are free to find their statistieal positions. 

In bioimpedanee theory, there are free eharge carriers and the current density is J = oE (Eq. 2.1). The dimensions of interest are usually much larger than in the dielectric polarization cases, and the applied field is macroscopically disturbed by the anisotropy. 

Anisotropy implies that the possible seleetive measurement of defined tissue volumes is disturbed. This leads to serious objeetions and problems in impedance tomography, numerical modeling such as the finite element method, and immittance plethysmography. 

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The curves are broadened in the near-field range for high g-values which are found very often in biological tissues (see lower curve that has been calculated for a typical tissue anisotropy ofg = 0.95). In all cases, the fluorescence diffuses much wider than the primary radiation but as far as we know no exact values are available for high anisotropy parameters. 

Roberts, D. and Scher, A.M. 1982. Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ. Res. 50 342. 

Tissue anisotropy may be strong, as shown in Table 10.1 for a muscle with 10 times higher longitude than perpendicular conductivity (Epstein and Foster 1983). They found that the anisotropy almost disappeared at 1 MHz it is an LF phenomenon. The conductivity of muscle tissue is dependent on other factors such as mechanical contraction (Shiffman et al. 2003). 

Equation 2.2 J = aE is not valid in anisotropic materials if a is a sealar. Tissue as a rule is anisotropic. Plonsey and Barr (2000) discussed some important eomplications posed by tissue anisotropy and also emphasized the necessity of introdueing the concept of the bidomain for cardiac tissue A hidomain model is useful when the eeUs are connected by two different types of junctions tight junctions and gap junctions with the cell interiors directly connected. The intracellular space is one domain and the interstitial space the other domain. Bidomain models have also been used for neural tissue (Sadleir, 2010). 

Christie GW, Medland IC (1981) The effects of tissue anisotropy on the mechanics of bioprothetic heart valves. Biomechanics Symposium 11-14... 

Diffusion is defined as the random translational motion of molecules or ions that is driven by internal thermal energy - the so-called Brownian motion. The mean movement of a water molecule due to diffusion amounts to several tenth of micrometres during 100 ms. Magnetic resonance is capable of monitoring the diffusion processes of molecules and therefore reveals information about microscopic tissue compartments and structural anisotropy. Especially in stroke patients diffusion sensitive imaging has been reported to be a powerful tool for an improved characterization of ischemic tissue. 

Anisotropy and nonuniformity are at least in part due to inhomogeneities in the distribution of gap junctions and the biophysical properties of the tissue are in fact influenced by the intercellular coupling. At least four features have to be considered. (1) Cardiac cells express different gap junction proteins (so-called connexins in the heart, connexin 40, connexin 43 and connexin 45 are most abundantly found for details see chapters 2 and 3). Channels formed by these connexins are different with regard to their biophysical properties. In various parts of the heart the content of each of these isoforms is different. 

If there is a systematic (i.e., highly ordered) tissue substructure such as in white matter, diffusion is usually more restricted in one than in another direction, i.e., the molecular mobility of water is not the same in all directions. In white matter, diffusion is less restricted parallel to than perpendicular to fiber tracts. If diffusion is different along various directions, then it is termed anisotropic diffusion. In stroke imaging the avoidance of the confounding effects of anisotropy is a common goal. However,... 

In DTI, diffusion is no longer described by a single diffusion coefficient, but by an array of nine coefficients that fully characterize how diffusion in space varies according to direction (Basser 1995). With this approach, diffusion anisotropy can be exploited to provide details on tissue microstructure and fiber tracts (le Bihan 2003). To obtain sufficient information on the direction of diffusion, the full diffusion tensor needs to be sampled [for a review on theoretical foundations of DTI see Basser and Jones (2002)]. 

Brain lesion analysis is also an active area of research. DTI metrics have been found to help differentiate between tumor types and promises to provide a sensitive method for abnormal tissue characterization. Fractional anisotropy has already been found to correlate with the cell density of brain tumors (Beppu et al., 2003 Beppu et al., 2005). The ability of FA to correlate with cell density likely accounts for the sensitivity of FA to tissue typing in brain lesions. Fractional anisotropy has been found to differentiate between low grade and anaplastic astrocytomas, to help differentiate between brain metastasis and high grade gliomas, and there is evidence that FA may help to detect tumor infiltration not visible by conventional MRI (Holmes et al., 2004 Tsuchiya et al., 2005 Goebell et al., 2006). Other DTI metrics have been utilized in brain lesion analysis and the early findings point to the breadth of future possibilities. 

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