Extending Continuous Cuts Anisotropic Metrics and Expansion Moves

Anisotropy

Anisotropy might be important for extrasynaptic transmission by channeling the flux of substances in a preferential direction, and its loss may severely disrupt extrasynaptic communication in the CNS, which has been suggested to play an important role in memory formation.

From: Encyclopedia of Neuroscience , 2009

Fundamentals of Neuromuscular Ultrasound

David C. Preston MD , in Electromyography and Neuromuscular Disorders , 2021

Anisotropy

The most common and most important artifact is anisotropy. When a sound wave encounters an acoustic barrier at 90°, the sound wave will bounce back as an echo. If the sound wave is not perpendicular to the barrier, the echoes will be directed back at an angle, and only some of the echoes will reach the probe. If the angle is great enough, no echoes may ever return to the probe ( Fig. 17.3B). In these situations, when the ultrasound beam is tilted such that only some echoes or none of the echoes bounce back to reach the probe, normally bright echoes become darker. This property of tissue, whereby the echoes that bounce back to the probe are dependent on the angle at which they hit the tissue, is known as anisotropy. Anisotropy is easily demonstrated by gentle tilting of the probe from side to side (Fig. 17.26). As the probe is tilted, the imaged structure becomes darker, depending on the amount of anisotropy in the tissue beingstudied. The amount of anisotropy varies among tissues. In tissues with high anisotropy, normally bright echoes will become increasing dark (hypoechoic) as the probe is tilted away from 90°. Conversely, tissues with low anisotropy will not change much in terms of brightness as the probe is tilted. Anisotropy is most helpful in identifying tendons, which display high anisotropy. Indeed, one of the best ways to help confirm that a structure is tendon versus nerve is to assess the amount of anisotropy (tendon: high anisotropy; nerve: low anisotropy). Anisotropy is best demonstrated in one of two ways. On a transverse scan, anisotropy is best demonstrated by gently "rocking" the probe from side to side (tilting the probe around the long axis) (Fig. 17.27). When looking at a structure on a longitudinal scan, the probe is gently moved in the "heel-to-toe" maneuver (tilting the probe along the short axis) (Fig. 17.28). It is essential that the neuromuscular ultrasonographer be very familiar with these two common manipulations of the ultrasound probe to either bring out or minimize anisotropy. When one tilts or rocks the probe to the angle where the echoes are the brightest, the anisotropy is minimized and the probe is now perpendicular to the tissue creating the echoes. For example, when measuring the cross-sectional area (CSA) to assess peripheral nerves, the probe must be at 90°. To ensure one is at 90°, the amount of anisotropy should be minimized (i.e., the probe should be gently tilted back and forth until the echoes are at their brightest). If the probe is not at 90°, the CSA may be erroneously measured as too high (seeFig. 18.6 for full discussion).

Diffusion Tensor Imaging in the Study of Aging and Age-Associated Neural Disease

David H. Salat , in Diffusion MRI (Second Edition), 2014

12.2.2 Anisotropy

Anisotropy measures describe the directional dominance of water diffusion within a region. Within a voxel, the anisotropy provides an index of the degree of uniformity of water diffusion for a specific orientation. Strongly directionally organized tissue, such as the corpus callosum which is primarily composed of tightly packed medial–lateral projecting fibers, has a high degree of anisotropy because there is a tendency for diffusion to be highly restricted along the fiber membranes to follow this medial–lateral direction. However, when the callosal fibers intersect other pathways, such as the corticospinal tracts, this unidirectional organization is disrupted and the anisotropy is reduced. Thus, there is a normal anatomy of the cerebral white matter of both high and low regions of anisotropy, and it is therefore not the case that greater anisotropy is always indicative of greater tissue integrity. Anisotropy is most typically examined using the calculation for fractional anisotropy (FA; described in Basser and Pierpaoli, 1996; applied in several manuscripts, e.g. Pfefferbaum et al., 2000; Abe et al., 2002), yet similar metrics such as relative anisotropy (RA) have also been applied in the diffusion-imaging literature examining lifespan changes (e.g. Huppi et al., 1998, 2001; Nusbaum et al., 2001; Miller et al., 2002; van Pul et al., 2005; Y. Zhang et al., 2005; Camara et al., 2007; Schneiderman et al., 2007; Stahl et al., 2007).

The comparative signal-to-noise benefits of FA over RA have been discussed (Hasan et al., 2004; Poonawalla and Zhou, 2004), however, the advantage of one metric over the other may depend on the specific region of the brain examined (Kingsley and Monahan, 2005).

Anisotropy has found popular utility as a measure that could potentially elucidate changes in regional fiber composition (Basser et al., 1994). For the purpose of this review, we refer to measures of anisotropy generally, as opposed to FA or RA individually. The limitation of anisotropy measures such as FA is that they are a summary of the diffusion information across all directions, and thus provide little information about directional basis of the specific diffusion changes that cause the change in anisotropy. Because anisotropy is a relative metric, it is low when all directions have low and undetectable differences in diffusivity, but it is also low when all directions have high diffusivity, even in cases where the quantitative differences in diffusivity are within the resolution of detection.

Regions of low anisotropy are typically considered potentially confounded and excluded from analysis as regions of non-interest. However, such regions may have properties that are measurable with other diffusion metrics (Douaud et al., 2011), and care must be taken when analyzing brains that have regional variations in diffusivity due to disease processes that data from regions of anatomical interest are not excluded based on their low anisotropy. Similarly, given the variation in anisotropy across individuals and with disease, the use of additional information to assure that homologous measurements are performed across samples is warranted. More recent studies have examined the value of the "mode" of anisotropy (Ennis and Kindlmann, 2006), a measurement of shape that assesses the degree to which the anisotropy is linear anisotropic, orthotropic, or planar anisotropic, as a potentially more sensitive variant of anisotropy for the measurement of degeneration (Douaud et al., 2011).

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780123964601000123

Biomechanics of Fractures

Bruce D. Browner MD, MHCM, FACS, FAOA , in Skeletal Trauma: Basic Science, Management, and Reconstruction , 2020

Other Material Properties (Viscoelasticity, Anisotropy, Creep and Relaxation, Fatigue,S-N Curve)

Several other important material properties cannot be determined from simple stress-strain curves. Most biologic tissues display some form of viscoelasticity, which simply indicates that they respond differently to forces depending on how fast the load is applied. In other words, viscoelastic materials have different stress-strain curves when they are applied at a fast rate (e.g., cutting maneuvers in sports) rather than a slow rate (e.g., yoga stretching). The amount of viscoelasticity in a material is represented by how much its stress-strain curves change for different rates of loading. Viscoelastic properties are often reported in terms of a dynamic modulus or a creep time–constant. Experimentally, viscoelastic properties are determined either by cyclically loading the material at different rates or by conducting relaxation tests, where a sample is held at a constant load and the long-term change in deformation, or creep, is recorded.

The unloading curve will be different from the loading curve because more energy is absorbed during loading than is dissipated during unloading. This variation between loading and unloading is calledhysteresis and ultimately means that energy is lost during the loading of viscoelastic materials (Fig. 6.9).

Soft tissues, such as cartilage and ligaments, demonstrate high viscoelasticity, as shown inFig. 6.9. Bone also has a viscoelastic response, but it is not as pronounced. Stretching before exercising helps protect muscle, tendons, and ligaments and demonstrates their viscoelastic properties. When measured in vitro, muscle-tendon units achieved sustained elongations (e.g., flexibility) after repetitive stretching, whereas greater peak tension and greater energy absorptions—and thus an increased risk of tendinous injury—occurred at faster stretch rates, as shown inFig. 6.9. ¹

Rotator cuff healing demonstrates how soft tissues are vulnerable to a combination of mechanical and biologic factors. In multiple studies, the amount of retraction of the tear at the time of surgery is an independent predictor of healing. ² Massive tears, especially in the anterior rotator cuff, likely have a detrimental effect on healing tissues by increasing regional strains. ³ In one animal model of supraspinatus tears, the tension required to repair the tendon increased early after detachment and progressively increased with the chronicity of the tear. ⁴ Repair tension also correlated with an increase in stiffness and cross-sectional area but a decrease in the failure properties (e.g., failure load and stress) and viscoelastic peak stress. ⁴ In another study, diabetes was accompanied by less fibrocartilage and less organized collagen, which translated into a significantly reduced load to failure and stiffness. ⁵ Nicotine causes a delay in tendon–bone healing, with poor expression of type I collagen and inferior biomechanical properties. ⁶ Given that the tendon–bone interface plays a key role in surgical failure of tendon repair, recent developments in tissue engineering have aimed to mimic the structure and function of soft-to-hard-tissue junctions. Scaffolds must be stratified with interconnected and preintegrated layers to capture the multitissue matrix organization seen in natural interfaces. ⁷ Most recently, spatially patterned structural and chemical cues have been incorporated into these scaffolds and triggered mechanobiologic pathways for cell differentiation and growth, helping create a gradient of mechanical properties and mineral distribution on the scaffold. ⁸

DTI in Development and Aging

David H. Salat , ... P. Ellen Grant , in Diffusion MRI, 2009

B Anisotropy

Anisotropy measures describe the directional dominance of water diffusion within a region. Within a voxel, the anisotropy provides an index of the degree of uniformity of water diffusion for a specific orientation. Strongly directionally organized tissue, such as the corpus callosum which is primarily comprised of tightly packed medial–lateral projecting fibers, has a high degree of anisotropy because there is a tendency for diffusion to be highly restricted along the fiber membranes to follow this medial–lateral direction. However, when the callosal fibers intersect other pathways such as the corticospinal tracts, this unidirectional organization is disrupted and the anisotropy is reduced. Anisotropy is most typically examined using the calculation for fractional anisotropy (FA) described in Basser and Pierpaoli (1996) and applied in several manuscripts (e.g. Pfefferbaum et al., 2000) and Abe et al., 2002), yet similar metrics such as relative anisotropy (RA) have also been applied in the diffusion imaging literature examining lifespan changes (e.g. Huppi et al., 1998, 2001; Nusbaum et al., 2001; Miller et al., 2002; Van Pul et al., 2005; Zhang et al., 2005; Camara et al., 2007; Schneiderman et al., 2007; Stahl et al., 2007). The relative signal-to-noise benefits of FA over RA have been discussed in recent literature (Hasan et al., 2004; Poonawalla and Zhou, 2004); however, the advantage of one metric over the other may depend on the specific region of the brain examined (Kingsley and Monahan, 2005). Anisotropy has been in popular use as a measure that could potentially elucidate changes in regional fiber composition (Basser et al., 1994). For the purpose of this review, we refer to measures of anisotropy generally, as opposed to FA or RA individually. The limitation of anisotropy measures such as FA is that they are a summary of the diffusion information across all directions, and thus provide little information about directional basis of the specific diffusion changes that cause the change in anisotropy. As anisotropy is a ratio, it is low when all directions have low and undetectable differences in diffusivity but it is also low when all directions have high diffusivity even in cases where the quantitative differences in diffusivity are within the resolution of detection. Regions of low anisotropy are typically considered potentially confounded and excluded from analysis as regions of non-interest. However, such regions may have properties that are measurable with other diffusion metrics, and care must be taken when analyzing brains that have regional variations in diffusivity due to immaturity or disease processes that data from regions of high diffusivity are not excluded based on their low anisotropy. Finally, anisotropy measures do not capitalize on information in adjacent voxels to determine if there is significant underlying tissue organization which could be important towards understanding the growth and decline of neural connectivity.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780123747099000109

Biophysical, Chemical, and Functional Probes of RNA Structure, Interactions and Folding: Part B

Xuesong Shi , Daniel Herschlag , in Methods in Enzymology, 2009

7 Salt Dependence and Normalization of FPA with a Short Control Duplex

FPA results obtained at different salt conditions may not be directly comparable because the fluorescence properties of 6-MI, including the lifetime (τ), are salt dependent. The salt dependence of the FPA of a helix in a complex construct should thereby be normalized relative to the FPA of a short control duplex of the same sequence of the targeted helix to account for salt effects on the local environment of the 6-MI fluorophore. The normalization ratio, r _norm, can be calculated as the ratio between the apparent rotational correlation time, θ, of the constructs and the control duplex only, r _norm  =   θ_construct/θ_control . θ is related to the rate of anisotropy decay, with larger θ associated with higher anisotropy. If the basic Perrin equation for a sphere ( Eq. (14.3)) is used to simplify calculation, then

$r_{\text{norm}}=\frac{(r_1^{\text{app}}/r_{\text{control}})-1}{(r_1^{\text{app}}/r_{\text{construct}})-1}.$

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/S0076687909690145

Principles, Methods, and Applications of Diffusion Tensor Imaging

Susumu Mori , in Brain Mapping: The Methods (Second Edition), 2002

A. Anisotropy Measurement

Analysis of anisotropy is straightforward because it is scalar and can be analyzed in the same way as other MR images. For example, regions of interest can be manually drawn and indicators of the anisotropy, such as fractional anisotropy, can be quantified. Measurements of anisotropy have been performed for various brain diseases, and abnormalities (mostly reduction) have been reported.

Interpretation of the anisotropy change may not be as straightforward as the measurements. This is because we still do not know the exact mechanisms that control the diffusion anisotropy and it is likely that there are multiple factors that lead to the reduction. As a consequence, changes in anisotropy may not pinpoint specific cellular events. On the other hand, as explained in Section III.A.2, it is likely that anisotropy and other conventional contrasts reflect different cellular statuses. Therefore, it is worth examining the anisotropy to judge whether it increases the sensitivity and/or specificity of diagnosing brain diseases. However, it should be stressed that DTI is an inherently time-consuming, low-resolution, and artifact-prone technique and, therefore, it is important to confirm whether anisotropy measurements provide unique and important information that cannot be obtained by conventional MR images and, thus, the DTI studies are justifiable in clinical settings.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780126930191500174

Pitfalls of Gray-Scale Artifacts

Laszlo Irsay , ... Peter V. Balint , in Essential Applications of Musculoskeletal Ultrasound in Rheumatology, 2010

Anisotropy

Anisotropy of fibers was first described by Theodore Dussik in 1958. ¹⁹ Anisotropy is the property of being directionally dependent, as opposed to isotropy, which means homogeneity in all directions. It can be defined as a difference in the physical property of a certain material when measured along different axes. Anisotropy in ultrasound examination is an angle-generated artifact. It is produced in tissue that contains multiple, parallel linear sound interfaces (e.g., tendons, ligaments) that lead to the preferential reflection of the beam in one direction. Connective tissue elements in muscles, ligaments, and tendons (e.g., epimysium, endomysium, perimysium collagen fibers) are echogenic when the ultrasound beam is perpendicular to the long axis of the corresponding fibers as the reflection of the beam is maximal at that angle. This echogenic area may wander as the beam is moved longitudinally along the axis of the tendon; this is known as the wandering echo phenomenon. ²⁰

The larger the deviation from this angle, the fewer reflected sound waves are detected by the transducer. If the structures are not visualized with the transducer array perpendicular to the long axis of the linear interface, there is a reflection of the beam away from the transducer, causing a dramatic reduction in echogenicity of the tissue. This may mimic pathologic alterations of these structures, and it is a pitfall in the assessment of tendons and muscles. ^21,22 The same phenomenon, however, may be of value by allowing the identification of tendons based on their changing echogenicity, especially in the presence of tenosynovitis. Several normal anatomic structures show anisotropy on sonographic examination, including the Achilles tendon near its insertion on the calcaneus, the quadriceps tendon near its insertion on the patella, and the supraspinatus and infraspinatus tendons in the area where tendon fibers change from a horizontal to a more vertical alignment as they approach the insertion. In these cases, anisotropy can be partially avoided by tilting the transducer. Muscle contraction can also reduce anisotropy; for instance, contraction of quadriceps muscle can decrease anisotropy of the patellar tendon (Fig. 3-14). In other cases, such as the posterior cruciate ligament of the knee, the tendon shows anisotropy due to its oblique path, which prohibits its appropriate assessment. The previously defined and measured extension of the anterior hip recess consisted of the anisotropic iliofemoral ligament along with the capsule (and optional synovial fluid within the recess), because these structures could not be accurately differentiated on older machines. ²³

Every structure that is not perpendicular to the ultrasound beam may appear anisotropic. Multibeam compound imaging is a technical innovation that reduces the development of anisotropy. In practice, sonographers must be aware that the phenomenon of anisotropy can mimic tendinosis or tears, and it is advisable to assess tendons in their long and short axes to avoid misinterpretation. A lesion can only be confirmed when a poorly reflective area remains—when the angle of insonation is perpendicular to the long axis of the tendon. Several methods have been developed to overcome the technical difficulties of maintaining perpendicularity with tendons in certain positions (e.g., extensor and flexor tendons of fingers), including the use of standoffs, large amounts of gel, water baths, or beam angulation. ²⁴

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9781437701272100036

Fluorescence Theory

Karen G. Fleming , in Encyclopedia of Spectroscopy and Spectrometry (Third Edition), 2017

Fluorescence Anisotropy

Anisotropy measurements provide information on the size and shape of proteins or the rigidity of various molecular environments. These are based on the principle of photo-selective excitation of fluorophores by polarized light. In an isotropic solution, the fluorophores are oriented randomly. Excitation with polarized light will result in a selective excitation of those fluorophore molecules whose absorption transition dipole is parallel to the electric vector of the excitation as shown in Figure 7 . This selective excitation results in a partially oriented population of polarized fluorescence emission. Emission also occurs with the light polarized along a fixed axis in the fluorophore. The relative angle between these moments determines the maximum measured anisotropy in the absence of other molecular rearrangements. The fluorescence anisotropy, R, and polarization, P are defined by:

Figure 7. Principle of the fluorescence anisotropy experiment.

[10] $R=\frac{I_{\Vert }-I_{\text{Per}}}{I_{\Vert }+2I_{\text{Per}}}$

and

[11] $P=\frac{I_{\Vert }-I_{\text{Per}}}{I_{\Vert }+I_{\text{Per}}}$

where I _∥ and I _Per are the fluorescence intensities of the vertically and horizontally polarized emission when the sample is excited with vertically polarized light. The anisotropy is a dimensionless quantity that is independent of the total intensity of the sample.

Several phenomena can decrease the measured anisotropy to values lower than the maximum theoretical values. The most common cause is rotational diffusion of a macromolecule to which the fluorophore is attached. Such rotation diffusion occurs during the lifetime of the excited state and displaces the emission dipole of the fluorophore. Conveniently, rotation correlation times for macromolecules are on the order of nanoseconds. For example, the rotational correlation time for human serum albumin is approximately 50   ns. Anisotropy is especially useful for measuring binding; when a macromolecule binds a ligand, the complex will be bigger and will have a longer rotational correlation time. This can be observed as a change in the anisotropy of the complex with respect to the unliganded macromolecule.

In addition to binding, there can be segmental motion of the fluorophore about its bonds, which happens on the picoseconds timescale. In this case, the fluorescent molecules can rotate many times during the 1–10-ns excited-state lifetime, and the orientation of the polarized emission can be randomized. When this occurs, there is a diminished ability to observe any changes in the rotational correlation time of the molecule to which the fluorophore is attached, but this can be countered if the fluorophore becomes immobilized when the macromolecule binds a ligand.

When bound to a macromolecule and assuming no other processes result in loss of anisotropy, the expected anisotropy is given by the Perrin equation:

[12] $r=\frac{r_0}{1+(\tau /\theta )}$

where r ₀ is the anisotropy that would be measured in the absence of rotational diffusion and θ is the rotational correlation time for the diffusion process. For a sphere

[13] $\theta =\frac{\eta V}{\mathit{RT}}$

where η is the viscosity and V is the molecular volume equal to $M(\overline{v}+h)$ , where M is the molecular weight, $\overline{v}$ is the partial specific volume, and h is the hydration of the molecule. In this case, the binding of the probe has slowed the probes' rate of rotational motion.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128032244003575

Ultrasound-Guided Regional Anesthesia

Manoj K. Karmakar , Wing H. Kwok , in A Practice of Anesthesia for Infants and Children (Sixth Edition), 2019

Anisotropy

Anisotropy, or angular dependence, is a term used to describe the change in echogenicity of a structure with a change in the angle of insonation of the incident US beam (Fig. 43.9). ⁴⁷ It is frequently observed during scanning of nerves, muscles, and tendons. This occurs because the amplitude of the echoes returning to the transducer varies with the angle of insonation. Nerves are best visualized when the incident beam is at right angles (Fig. 43.9A); small changes in the angle away from the perpendicular can significantly reduce their echogenicity (Fig. 43.9B). Therefore during USGRA procedures, the transducer should be tilted, from side to side, to minimize anisotropy and optimize visualization of the nerve. ⁴⁸

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780323429740000434

Ultrasound

Gandikota. Girish MBBS, FRCS(ed), FRCR , Jon A. Jacobson MD , in Imaging of Arthritis and Metabolic Bone Disease, 2009

ULTRASOUND PITFALLS

Anisotropy should not be mistaken for tendinosis; anisotropy occurs when the sound beam is oblique to the tendon fibers, producing an artifactual hypoechoic appearance. Another pitfall is that the lack of increased flow on color or power Doppler imaging does not always indicate inactive synovitis. It is hypothesized that increased synovial volume in a tight joint space with stretched capsule may demonstrate a pressure effect, inhibiting the detection of vascularity. Synovial proliferation seen in inflammatory arthritis should be differentiated from less common synovial proliferative disorders, such as pigmented villonodular synovitis and synovial chondromatosis. Intraarticular amyloidosis could have a similar appearance. Cortical contour variation representing the normal physeal plate should not be mistaken for erosion in the small joints of the hand (Table 7-2).

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780323041775000070

rankborgy1964.blogspot.com

Source: https://www.sciencedirect.com/topics/neuroscience/anisotropy

Share this post