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Diffusion MRI

Diffusion-weighted magnetic resonance imaging (DWI or DW-MRI) is the use of specific MRI sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not random, but reflects interactions with many obstacles, such as macromolecules, fibers, and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state. A special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain.

Introduction
In diffusion weighted imaging (DWI), the intensity of each image element (voxel) reflects the best estimate of the rate of water diffusion at that location. Because the mobility of water is driven by thermal agitation and highly dependent on its cellular environment, the hypothesis behind DWI is that findings may indicate (early) pathologic change. For instance, DWI is more sensitive to early changes after a stroke than more traditional MRI measurements such as T1 or T2 relaxation rates. A variant of diffusion weighted imaging, diffusion spectrum imaging (DSI), was used in deriving the Connectome data sets; DSI is a variant of diffusion-weighted imaging that is sensitive to intra-voxel heterogeneities in diffusion directions caused by crossing fiber tracts and thus allows more accurate mapping of axonal trajectories than other diffusion imaging approaches.

Diffusion-weighted images are very useful to diagnose vascular strokes in the brain. It is also used more and more in the staging of non-small-cell lung cancer, where it is a serious candidate to replace positron emission tomography as the 'gold standard' for this type of disease. Diffusion tensor imaging is being developed for studying the diseases of the white matter of the brain as well as for studies of other body tissues (see below). DWI is most applicable when the tissue of interest is dominated by isotropic water movement e.g. grey matter in the cerebral cortex and major brain nuclei, or in the body—where the diffusion rate appears to be the same when measured along any axis. However, DWI also remains sensitive to T1 and T2 relaxation. To entangle diffusion and relaxation effects on image contrast, one may obtain quantitative images of the diffusion coefficient, or more exactly the apparent diffusion coefficient (ADC). The ADC concept was introduced to take into account the fact that the diffusion process is complex in biological tissues and reflects several different mechanisms.

Diffusion tensor imaging (DTI) is important when a tissue—such as the neural axons of white matter in the brain or muscle fibers in the heart—has an internal fibrous structure analogous to the anisotropy of some crystals. Water will then diffuse more rapidly in the direction aligned with the internal structure (axial diffusion), and more slowly as it moves perpendicular to the preferred direction (radial diffusion). This also means that the measured rate of diffusion will differ depending on the direction from which an observer is looking.

Diffusion Basis Spectrum Imaging (DBSI) further separates DTI signals into discrete anisotropic diffusion tensors and a spectrum of isotropic diffusion tensors to better differentiate sub-voxel cellular structures. For example, anisotropic diffusion tensors correlate to axonal fibers, while low isotropic diffusion tensors correlate to cells and high isotropic diffusion tensors correlate to larger structures (such as the lumen or brain ventricles). DBSI has been shown to differentiate some types of brain tumors and multiple sclerosis with higher specificity and sensitivity than conventional DTI. DBSI has also been useful in determining microstructure properties of the brain.

Traditionally, in diffusion-weighted imaging (DWI), three gradient-directions are applied, sufficient to estimate the trace of the diffusion tensor or 'average diffusivity', a putative measure of edema. Clinically, trace-weighted images have proven to be very useful to diagnose vascular strokes in the brain, by early detection (within a couple of minutes) of the hypoxic edema.

More extended DTI scans derive neural tract directional information from the data using 3D or multidimensional vector algorithms based on six or more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming homogeneity and linearity of the diffusion within each image voxel. From the diffusion tensor, diffusion anisotropy measures such as the fractional anisotropy (FA), can be computed. Moreover, the principal direction of the diffusion tensor can be used to infer the white-matter connectivity of the brain (i.e. tractography; trying to see which part of the brain is connected to which other part).

Recently, more advanced models of the diffusion process have been proposed that aim to overcome the weaknesses of the diffusion tensor model. Amongst others, these include q-space imaging and generalized diffusion tensor imaging.

Mechanism
Diffusion imaging is an MRI method that produces in vivo magnetic resonance images of biological tissues sensitized with the local characteristics of molecular diffusion, generally water (but other moieties can also be investigated using MR spectroscopic approaches). MRI can be made sensitive to the motion of molecules. Regular MRI acquisition utilizes the behavior of protons in water to generate contrast between clinically relevant features of a particular subject. The versatile nature of MRI is due to this capability of producing contrast related to the structure of tissues at the microscopic level. In a typical $$T_1$$-weighted image, water molecules in a sample are excited with the imposition of a strong magnetic field. This causes many of the protons in water molecules to precess simultaneously, producing signals in MRI. In $$T_2$$-weighted images, contrast is produced by measuring the loss of coherence or synchrony between the water protons. When water is in an environment where it can freely tumble, relaxation tends to take longer. In certain clinical situations, this can generate contrast between an area of pathology and the surrounding healthy tissue.

To sensitize MRI images to diffusion, the magnetic field strength (B1) is varied linearly by a pulsed field gradient. Since precession is proportional to the magnet strength, the protons begin to precess at different rates, resulting in dispersion of the phase and signal loss. Another gradient pulse is applied in the same magnitude but with opposite direction to refocus or rephase the spins. The refocusing will not be perfect for protons that have moved during the time interval between the pulses, and the signal measured by the MRI machine is reduced. This "field gradient pulse" method was initially devised for NMR by Stejskal and Tanner who derived the reduction in signal due to the application of the pulse gradient related to the amount of diffusion that is occurring through the following equation:

 * $$\frac{S(TE)}{S_0} = \exp \left[ -\gamma^2 G^2\delta^2 \left( \Delta-\frac{\delta}{3}\right)D \right]$$

where $$ S_0 $$ is the signal intensity without the diffusion weighting, $$S$$ is the signal with the gradient, $$ \gamma$$ is the gyromagnetic ratio, $$G$$ is the strength of the gradient pulse, $$ \delta$$ is the duration of the pulse, $$ \Delta$$ is the time between the two pulses, and finally, $$ D$$ is the diffusion-coefficient.

In order to localize this signal attenuation to get images of diffusion one has to combine the pulsed magnetic field gradient pulses used for MRI (aimed at localization of the signal, but those gradient pulses are too weak to produce a diffusion related attenuation) with additional "motion-probing" gradient pulses, according to the Stejskal and Tanner method. This combination is not trivial, as cross-terms arise between all gradient pulses. The equation set by Stejskal and Tanner then becomes inaccurate and the signal attenuation must be calculated, either analytically or numerically, integrating all gradient pulses present in the MRI sequence and their interactions. The result quickly becomes very complex given the many pulses present in the MRI sequence, and as a simplification, Le Bihan suggested gathering all the gradient terms in a "b factor" (which depends only on the acquisition parameters) so that the signal attenuation simply becomes:

 * $$\frac{S(TE)}{S_0} = \exp (-b\cdot ADC)$$

Also, the diffusion coefficient, $$ D$$, is replaced by an apparent diffusion coefficient, $$ ADC$$, to indicate that the diffusion process is not free in tissues, but hindered and modulated by many mechanisms (restriction in closed spaces, tortuosity around obstacles, etc.) and that other sources of IntraVoxel Incoherent Motion (IVIM) such as blood flow in small vessels or cerebrospinal fluid in ventricles also contribute to the signal attenuation. At the end, images are "weighted" by the diffusion process: In those diffusion-weighted images (DWI) the signal is more attenuated the faster the diffusion and the larger the b factor is. However, those diffusion-weighted images are still also sensitive to T1 and T2 relaxivity contrast, which can sometimes be confusing. It is possible to calculate "pure" diffusion maps (or more exactly ADC maps where the ADC is the sole source of contrast) by collecting images with at least 2 different values, $$b_1$$ and $$b_2$$, of the b factor according to:

 * $$\mathrm{ADC}(x,y,z)= \ln [S_2(x,y,z)/S_1(x,y,z)]/(b_1-b_2)$$

Although this ADC concept has been extremely successful, especially for clinical applications, it has been challenged recently, as new, more comprehensive models of diffusion in biological tissues have been introduced. Those models have been made necessary, as diffusion in tissues is not free. In this condition, the ADC seems to depend on the choice of b values (the ADC seems to decrease when using larger b values), as the plot of ln(S/So) is not linear with the b factor, as expected from the above equations. This deviation from a free diffusion behavior is what makes diffusion MRI so successful, as the ADC is very sensitive to changes in tissue microstructure. On the other hand, modeling diffusion in tissues is becoming very complex. Among most popular models are the biexponential model, which assumes the presence of 2 water pools in slow or intermediate exchange and the cumulant-expansion (also called Kurtosis) model, which does not necessarily require the presence of 2 pools.

Diffusion model
Given the concentration $$ \rho $$ and flux $$ J $$, Fick's first law gives a relationship between the flux and the concentration gradient:

 * $$ J(x,t)=-D\nabla\rho(x,t) $$

where D is the diffusion coefficient. Then, given conservation of mass, the continuity equation relates the time derivative of the concentration with the divergence of the flux:

 * $$ \frac{\partial\rho(x,t)}{\partial t}=-\nabla\cdot J(x,t) $$

Putting the two together, we get the diffusion equation:

 * $$ \frac{\partial\rho(x,t)}{\partial t}=D\nabla^2\rho(x,t). $$

Magnetization dynamics
With no diffusion present, the change in nuclear magnetization over time is given by the classical Bloch equation

 * $$ \frac{d\vec{M}}{dt}=\gamma\vec{M}\times\vec{B}-\frac{M_x\vec{i}+M_y\vec{j}}{T_2}-\frac{(M_z-M_0)\vec{k}}{T_1} $$

which has terms for precession, T2 relaxation, and T1 relaxation.

In 1956, H.C. Torrey mathematically showed how the Bloch equations for magnetization would change with the addition of diffusion. Torrey modified Bloch's original description of transverse magnetization to include diffusion terms and the application of a spatially varying gradient. Since the magnetization $$ M $$ is a vector, there are 3 diffusion equations, one for each dimension. The Bloch-Torrey equation is:

 * $$ \frac{d\vec{ M}}{dt}=\gamma\vec{M}\times\vec{B}-\frac{M_x\vec{i}+M_y\vec{j}}{T_2}-\frac{(M_z-M_0)\vec{k}}{T_1}+\nabla\cdot \vec{D}\nabla\vec{M} $$

where $$ \vec{D} $$ is now the diffusion tensor.

For the simplest case where the diffusion is isotropic the diffusion tensor is a multiple of the identity:

 * $$\vec{D} = D \cdot \vec{I} = D \cdot \begin{bmatrix}

1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix},$$

then the Bloch-Torrey equation will have the solution

 * $$ {M}={M}_{\text{bloch}}e^{-\frac13\gamma^2G^2t^3D}\sim e^{-bD_0} $$

The exponential term will be referred to as the attenuation $$ A $$. Anisotropic diffusion will have a similar solution for the diffusion tensor, except that what will be measured is the apparent diffusion coefficient (ADC). In general, the attenuation is:

 * $$ A=e^{ -\sum_{i,j}b_{ij}D_{ij} } $$

where the $$ b_{ij} $$ terms incorporate the gradient fields $$ G_x $$, $$ G_y $$, and $$ G_z $$.

Grayscale
The standard grayscale of DWI images is to represent increased diffusion restriction as brighter.

ADC image
An apparent diffusion coefficient (ADC) image, or an ADC map, is an MRI image that more specifically shows diffusion than conventional DWI, by eliminating the T2 weighting that is otherwise inherent to conventional DWI. ADC imaging does so by acquiring multiple conventional DWI images with different amounts of DWI weighting, and the change in signal is proportional to the rate of diffusion. Contrary to DWI images, the standard grayscale of ADC images is to represent a smaller magnitude of diffusion as darker.

Cerebral infarction leads to diffusion restriction, and the difference between images with various DWI weighting will therefore be minor, leading to an ADC image with low signal in the infarcted area. A decreased ADC may be detected minutes after a cerebral infarction. The high signal of infarcted tissue on conventional DWI is a result of its partial T2 weighting.

Diffusion tensor imaging
Diffusion tensor imaging (DTI) is a magnetic resonance imaging technique that enables the measurement of the restricted diffusion of water in tissue in order to produce neural tract images instead of using this data solely for the purpose of assigning contrast or colors to pixels in a cross-sectional image. It also provides useful structural information about muscle—including heart muscle—as well as other tissues such as the prostate.

In DTI, each voxel has one or more pairs of parameters: a rate of diffusion and a preferred direction of diffusion—described in terms of three-dimensional space—for which that parameter is valid. The properties of each voxel of a single DTI image are usually calculated by vector or tensor math from six or more different diffusion weighted acquisitions, each obtained with a different orientation of the diffusion sensitizing gradients. In some methods, hundreds of measurements—each making up a complete image—are made to generate a single resulting calculated image data set. The higher information content of a DTI voxel makes it extremely sensitive to subtle pathology in the brain. In addition the directional information can be exploited at a higher level of structure to select and follow neural tracts through the brain—a process called tractography.

A more precise statement of the image acquisition process is that the image-intensities at each position are attenuated, depending on the strength (b-value) and direction of the so-called magnetic diffusion gradient, as well as on the local microstructure in which the water molecules diffuse. The more attenuated the image is at a given position, the greater diffusion there is in the direction of the diffusion gradient. In order to measure the tissue's complete diffusion profile, one needs to repeat the MR scans, applying different directions (and possibly strengths) of the diffusion gradient for each scan.

Mathematical foundation—tensors
Diffusion MRI relies on the mathematics and physical interpretations of the geometric quantities known as tensors. Only a special case of the general mathematical notion is relevant to imaging, which is based on the concept of a symmetric matrix. Diffusion itself is tensorial, but in many cases the objective is not really about trying to study brain diffusion per se, but rather just trying to take advantage of diffusion anisotropy in white matter for the purpose of finding the orientation of the axons and the magnitude or degree of anisotropy. Tensors have a real, physical existence in a material or tissue so that they do not move when the coordinate system used to describe them is rotated. There are numerous different possible representations of a tensor (of rank 2), but among these, this discussion focuses on the ellipsoid because of its physical relevance to diffusion and because of its historical significance in the development of diffusion anisotropy imaging in MRI.

The following matrix displays the components of the diffusion tensor:

 * $$ \bar{D} = \begin{vmatrix}

D_{\color{red}xx} & D_{xy} & D_{xz} \\ D_{xy} & D_{\color{red}yy} & D_{yz} \\ D_{xz} & D_{yz} & D_{\color{red}zz} \end{vmatrix}$$

The same matrix of numbers can have a simultaneous second use to describe the shape and orientation of an ellipse and the same matrix of numbers can be used simultaneously in a third way for matrix mathematics to sort out eigenvectors and eigenvalues as explained below.

Physical tensors
The idea of a tensor in physical science evolved from attempts to describe the quantity of physical properties. The first properties they were applied to were those that can be described by a single number, such as temperature. Properties that can be described this way are called scalars; these can be considered tensors of rank 0, or 0th-order tensors. Tensors can also be used to describe quantities that have directionality, such as mechanical force. These quantities require specification of both magnitude and direction, and are often represented with a vector. A three-dimensional vector can be described with three components: its projection on the x, y, and z axes. Vectors of this sort can be considered tensors of rank 1, or 1st-order tensors.

A tensor is often a physical or biophysical property that determines the relationship between two vectors. When a force is applied to an object, movement can result. If the movement is in a single direction, the transformation can be described using a vector—a tensor of rank 1. However, in a tissue, diffusion leads to movement of water molecules along trajectories that proceed along multiple directions over time, leading to a complex projection onto the Cartesian axes. This pattern is reproducible if the same conditions and forces are applied to the same tissue in the same way. If there is an internal anisotropic organization of the tissue that constrains diffusion, then this fact will be reflected in the pattern of diffusion. The relationship between the properties of driving force that generate diffusion of the water molecules and the resulting pattern of their movement in the tissue can be described by a tensor. The collection of molecular displacements of this physical property can be described with nine components—each one associated with a pair of axes xx, yy, zz, xy, yx, xz, zx, yz, zy. These can be written as a matrix similar to the one at the start of this section.

Diffusion from a point source in the anisotropic medium of white matter behaves in a similar fashion. The first pulse of the Stejskal Tanner diffusion gradient effectively labels some water molecules and the second pulse effectively shows their displacement due to diffusion. Each gradient direction applied measures the movement along the direction of that gradient. Six or more gradients are summed to get all the measurements needed to fill in the matrix, assuming it is symmetric above and below the diagonal (red subscripts).

In 1848, Henri Hureau de Sénarmont applied a heated point to a polished crystal surface that had been coated with wax. In some materials that had "isotropic" structure, a ring of melt would spread across the surface in a circle. In anisotropic crystals the spread took the form of an ellipse. In three dimensions this spread is an ellipsoid. As Adolf Fick showed in the 1850s, diffusion exhibits many of the same patterns as those seen in the transfer of heat.

Mathematics of ellipsoids
At this point, it is helpful to consider the mathematics of ellipsoids. An ellipsoid can be described by the formula: $$ax^2 + by^2 + cz^2 = 1$$. This equation describes a quadric surface. The relative values of a, b, and c determine if the quadric describes an ellipsoid or a hyperboloid.

As it turns out, three more components can be added as follows: $$ax^2 + by^2 + cz^2 + dyz + ezx + fxy = 1$$. Many combinations of a, b, c, d, e, and f  still describe ellipsoids, but the additional components (d, e, f) describe the rotation of the ellipsoid relative to the orthogonal axes of the Cartesian coordinate system. These six variables can be represented by a matrix similar to the tensor matrix defined at the start of this section (since diffusion is symmetric, then we only need six instead of nine components—the components below the diagonal elements of the matrix are the same as the components above the diagonal). This is what is meant when it is stated that the components of a matrix of a second order tensor can be represented by an ellipsoid—if the diffusion values of the six terms of the quadric ellipsoid are placed into the matrix, this generates an ellipsoid angled off the orthogonal grid. Its shape will be more elongated if the relative anisotropy is high.

When the ellipsoid/tensor is represented by a matrix, we can apply a useful technique from standard matrix mathematics and linear algebra—that is to "diagonalize" the matrix. This has two important meanings in imaging. The idea is that there are two equivalent ellipsoids—of identical shape but with different size and orientation. The first one is the measured diffusion ellipsoid sitting at an angle determined by the axons, and the second one is perfectly aligned with the three Cartesian axes. The term "diagonalize" refers to the three components of the matrix along a diagonal from upper left to lower right (the components with red subscripts in the matrix at the start of this section). The variables $$ax^2$$, $$by^2$$, and $$cz^2$$ are along the diagonal (red subscripts), but the variables d, e and f are "off diagonal". It then becomes possible to do a vector processing step in which we rewrite our matrix and replace it with a new matrix multiplied by three different vectors of unit length (length=1.0). The matrix is diagonalized because the off-diagonal components are all now zero. The rotation angles required to get to this equivalent position now appear in the three vectors and can be read out as the x, y, and z components of each of them. Those three vectors are called "eigenvectors" or characteristic vectors. They contain the orientation information of the original ellipsoid. The three axes of the ellipsoid are now directly along the main orthogonal axes of the coordinate system so we can easily infer their lengths. These lengths are the eigenvalues or characteristic values.

Diagonalization of a matrix is done by finding a second matrix that it can be multiplied with followed by multiplication by the inverse of the second matrix—wherein the result is a new matrix in which three diagonal (xx, yy, zz) components have numbers in them but the off-diagonal components (xy, yz, zx) are 0. The second matrix provides eigenvector information.

Measures of anisotropy and diffusivity
In present-day clinical neurology, various brain pathologies may be best detected by looking at particular measures of anisotropy and diffusivity. The underlying physical process of diffusion causes a group of water molecules to move out from a central point, and gradually reach the surface of an ellipsoid if the medium is anisotropic (it would be the surface of a sphere for an isotropic medium). The ellipsoid formalism functions also as a mathematical method of organizing tensor data. Measurement of an ellipsoid tensor further permits a retrospective analysis, to gather information about the process of diffusion in each voxel of the tissue.

In an isotropic medium such as cerebrospinal fluid, water molecules are moving due to diffusion and they move at equal rates in all directions. By knowing the detailed effects of diffusion gradients we can generate a formula that allows us to convert the signal attenuation of an MRI voxel into a numerical measure of diffusion—the diffusion coefficient D. When various barriers and restricting factors such as cell membranes and microtubules interfere with the free diffusion, we are measuring an "apparent diffusion coefficient", or ADC, because the measurement misses all the local effects and treats the attenuation as if all the movement rates were solely due to Brownian motion. The ADC in anisotropic tissue varies depending on the direction in which it is measured. Diffusion is fast along the length of (parallel to) an axon, and slower perpendicularly across it.

Once we have measured the voxel from six or more directions and corrected for attenuations due to T2 and T1 effects, we can use information from our calculated ellipsoid tensor to describe what is happening in the voxel. If you consider an ellipsoid sitting at an angle in a Cartesian grid then you can consider the projection of that ellipse onto the three axes. The three projections can give you the ADC along each of the three axes ADCx, ADCy, ADCz. This leads to the idea of describing the average diffusivity in the voxel which will simply be

(ADC_x + ADC_y + ADC_z)/3 = ADC_i $$

We use the i subscript to signify that this is what the isotropic diffusion coefficient would be with the effects of anisotropy averaged out.

The ellipsoid itself has a principal long axis and then two more small axes that describe its width and depth. All three of these are perpendicular to each other and cross at the center point of the ellipsoid. We call the axes in this setting eigenvectors and the measures of their lengths eigenvalues. The lengths are symbolized by the Greek letter λ. The long one pointing along the axon direction will be λ1 and the two small axes will have lengths λ2 and λ3. In the setting of the DTI tensor ellipsoid, we can consider each of these as a measure of the diffusivity along each of the three primary axes of the ellipsoid. This is a little different from the ADC since that was a projection on the axis, while λ is an actual measurement of the ellipsoid we have calculated.

The diffusivity along the principal axis, λ1 is also called the longitudinal diffusivity or the axial diffusivity or even the parallel diffusivity λ∥. Historically, this is closest to what Richards originally measured with the vector length in 1991. The diffusivities in the two minor axes are often averaged to produce a measure of radial diffusivity

\lambda_{\perp} = (\lambda_2 + \lambda_3)/2. $$

This quantity is an assessment of the degree of restriction due to membranes and other effects and proves to be a sensitive measure of degenerative pathology in some neurological conditions. It can also be called the perpendicular diffusivity ($$ \lambda_{\perp}$$).

Another commonly used measure that summarizes the total diffusivity is the Trace—which is the sum of the three eigenvalues,

\mathrm{tr}(\Lambda) = \lambda_1 + \lambda_2 + \lambda_3 $$ where $$\Lambda$$ is a diagonal matrix with eigenvalues $$\lambda_1$$, $$\lambda_2$$ and $$\lambda_3$$ on its diagonal.

If we divide this sum by three we have the mean diffusivity,

\mathrm{MD} = (\lambda_1 + \lambda_2 + \lambda_3) /3 $$

which equals ADCi since

\begin{align} \mathrm{tr}(\Lambda)/3 &= \mathrm{tr}(V^{-1}V\Lambda)/3 \\ &= \mathrm{tr}(V\Lambda V^{-1})/3 \\ &= \mathrm{tr}(D)/3 \\ &= ADC_i \end{align} $$ where $$V$$ is the matrix of eigenvectors and $$D$$ is the diffusion tensor. Aside from describing the amount of diffusion, it is often important to describe the relative degree of anisotropy in a voxel. At one extreme would be the sphere of isotropic diffusion and at the other extreme would be a cigar or pencil shaped very thin prolate spheroid. The simplest measure is obtained by dividing the longest axis of the ellipsoid by the shortest = (λ1/λ3). However, this proves to be very susceptible to measurement noise, so increasingly complex measures were developed to capture the measure while minimizing the noise. An important element of these calculations is the sum of squares of the diffusivity differences = (λ1 − λ2)2 + (λ1 − λ3)2 + (λ2 − λ3)2. We use the square root of the sum of squares to obtain a sort of weighted average—dominated by the largest component. One objective is to keep the number near 0 if the voxel is spherical but near 1 if it is elongate. This leads to the fractional anisotropy or FA which is the square root of the sum of squares (SRSS) of the diffusivity differences, divided by the SRSS of the diffusivities. When the second and third axes are small relative to the principal axis, the number in the numerator is almost equal the number in the denominator. We also multiply by $$1/\sqrt{2}$$ so that FA has a maximum value of 1. The whole formula for FA looks like this:

 * $$ \mathrm{FA}=\frac{\sqrt{3( (\lambda_1-\operatorname E[\lambda])^2+(\lambda_2-\operatorname E[\lambda])^2+(\lambda_3-\operatorname E[\lambda])^2 )}}{\sqrt{2( \lambda_1^2+\lambda_2^2+\lambda_3^2 )}} $$

where $\operatorname E[\lambda] = (\lambda_1 + \lambda_2 + \lambda_3) / 3\,.$

The fractional anisotropy can also be separated into linear, planar, and spherical measures depending on the "shape" of the diffusion ellipsoid. For example, a "cigar" shaped prolate ellipsoid indicates a strongly linear anisotropy, a "flying saucer" or oblate spheroid represents diffusion in a plane, and a sphere is indicative of isotropic diffusion, equal in all directions. If the eigenvalues of the diffusion vector are sorted such that $$\lambda_1 \geq \lambda_2 \geq \lambda_3 \geq 0$$, then the measures can be calculated as follows:

For the linear case, where $$ \lambda_1 \gg \lambda_2 \simeq \lambda_3 $$,

C_l=\frac{\lambda_1 - \lambda_2}{\lambda_1 + \lambda_2 + \lambda_3} $$

For the planar case, where $$ \lambda_1 \simeq \lambda_2 \gg \lambda_3 $$,

C_p=\frac{2(\lambda_2 - \lambda_3)}{\lambda_1 + \lambda_2 + \lambda_3} $$

For the spherical case, where $$ \lambda_1 \simeq \lambda_2 \simeq \lambda_3 $$,

C_s=\frac{3\lambda_3}{\lambda_1 + \lambda_2 + \lambda_3} $$

Each measure lies between 0 and 1 and they sum to unity. An additional anisotropy measure can used to describe the deviation from the spherical case:

C_a=C_l+C_p=1-C_s=\frac{\lambda_1 + \lambda_2 - 2\lambda_3}{\lambda_1 + \lambda_2 + \lambda_3} $$

There are other metrics of anisotropy used, including the relative anisotropy (RA):

 * $$ \mathrm{RA}=\frac{\sqrt{(\lambda_1-\operatorname E[\lambda])^2+(\lambda_2-\operatorname E[\lambda])^2+(\lambda_3-\operatorname E[\lambda])^2}}{\sqrt{3}\operatorname E[\lambda]} $$

and the volume ratio (VR):

 * $$ \mathrm{VR}=\frac{\lambda_1\lambda_2\lambda_3}{\operatorname E[\lambda]^3} $$

Applications
The most common application of conventional DWI (without DTI) is in acute brain ischemia. DWI directly visualizes the ischemic necrosis in cerebral infarction in the form of a cytotoxic edema, appearing as a high DWI signal within minutes of arterial occlusion. With perfusion MRI detecting both the infarcted core and the salvageable penumbra, the latter can be quantified by DWI and perfusion MRI.

Another application area of DWI is in oncology. Tumors are in many instances highly cellular, giving restricted diffusion of water, and therefore appear with a relatively high signal intensity in DWI. DWI is commonly used to detect and stage tumors, and also to monitor tumor response to treatment over time. DWI can also be collected to visualize the whole body using a technique called 'diffusion-weighted whole-body imaging with background body signal suppression' (DWIBS). Some more specialized diffusion MRI techniques such as diffusion kurtosis imaging (DKI) have also been shown to predict the response of cancer patients to chemotherapy treatment.

The principal application is in the imaging of white matter where the location, orientation, and anisotropy of the tracts can be measured. The architecture of the axons in parallel bundles, and their myelin sheaths, facilitate the diffusion of the water molecules preferentially along their main direction. Such preferentially oriented diffusion is called anisotropic diffusion.

The imaging of this property is an extension of diffusion MRI. If a series of diffusion gradients (i.e. magnetic field variations in the MRI magnet) are applied that can determine at least 3 directional vectors (use of 6 different gradients is the minimum and additional gradients improve the accuracy for "off-diagonal" information), it is possible to calculate, for each voxel, a tensor (i.e. a symmetric positive definite 3×3 matrix) that describes the 3-dimensional shape of diffusion. The fiber direction is indicated by the tensor's main eigenvector. This vector can be color-coded, yielding a cartography of the tracts' position and direction (red for left-right, blue for superior-inferior, and green for anterior-posterior). The brightness is weighted by the fractional anisotropy which is a scalar measure of the degree of anisotropy in a given voxel. Mean diffusivity (MD) or trace is a scalar measure of the total diffusion within a voxel. These measures are commonly used clinically to localize white matter lesions that do not show up on other forms of clinical MRI.

Applications in the brain:
 * Tract-specific localization of white matter lesions such as trauma and in defining the severity of diffuse traumatic brain injury. The localization of tumors in relation to the white matter tracts (infiltration, deflection), has been one of the most important initial applications. In surgical planning for some types of brain tumors, surgery is aided by knowing the proximity and relative position of the corticospinal tract and a tumor.
 * Diffusion tensor imaging data can be used to perform tractography within white matter. Fiber tracking algorithms can be used to track a fiber along its whole length (e.g. the corticospinal tract, through which the motor information transit from the motor cortex to the spinal cord and the peripheral nerves). Tractography is a useful tool for measuring deficits in white matter, such as in aging.  Its estimation of fiber orientation and strength is increasingly accurate, and it has widespread potential implications in the fields of cognitive neuroscience and neurobiology.
 * The use of DTI for the assessment of white matter in development, pathology and degeneration has been the focus of over 2,500 research publications since 2005. It promises to be very helpful in distinguishing Alzheimer's disease from other types of dementia. Applications in brain research include the investigation of neural networks in vivo, as well as in connectomics.

Applications for peripheral nerves:
 * Brachial plexus: DTI can differentiate normal nerves (as shown in the tractogram of the spinal cord and brachial plexus and 3D 4k reconstruction here) from traumatically injured nerve roots.
 * Cubital Tunnel Syndrome: metrics derived from DTI (FA and RD) can differentiate asymptomatic adults from those with compression of the ulnar nerve at the elbow
 * Carpal Tunnel Syndrome: Metrics derived from DTI (lower FA and MD) differentiate healthy adults from those with carpal tunnel syndrome

Research
Early in the development of DTI based tractography, a number of researchers pointed out a flaw in the diffusion tensor model. The tensor analysis assumes that there is a single ellipsoid in each imaging voxel—as if all of the axons traveling through a voxel traveled in exactly the same direction. This is often true, but it can be estimated that in more than 30% of the voxels in a standard resolution brain image, there are at least two different neural tracts traveling in different directions that pass through each other. In the classic diffusion ellipsoid tensor model, the information from the crossing tract appears as noise or unexplained decreased anisotropy in a given voxel.

David Tuch was among the first to describe a solution to this problem. The idea is best understood by conceptually placing a kind of geodesic dome around each image voxel. This icosahedron provides a mathematical basis for passing a large number of evenly spaced gradient trajectories through the voxel—each coinciding with one of the apices of the icosahedron. We can then look into the voxel from a large number of different directions (typically 40 or more). We use "n-tuple" tessellations to add more evenly spaced apices to the original icosahedron (20 faces)—an idea that also had its precedents in paleomagnetism research several decades earlier. We want to know which direction lines turn up the maximum anisotropic diffusion measures. If there is a single tract, there will be only two maxima, pointing in opposite directions. If two tracts cross in the voxel, there will be two pairs of maxima, and so on. We can still use tensor mathematics to use the maxima to select groups of gradients to package into several different tensor ellipsoids in the same voxel, or use more complex higher-rank tensor analyses, or we can do a true "model free" analysis that picks the maxima, and then continue to do the tractography.

The Q-Ball method of tractography is an implementation in which David Tuch provides a mathematical alternative to the tensor model. Instead of forcing the diffusion anisotropy data into a group of tensors, the mathematics used deploys both probability distributions and some classic geometric tomography and vector mathematics developed nearly 100 years ago—the Funk Radon Transform.

Note, there is ongoing debate about the best way to preprocess DW-MRI. Several in-vivo studies have shown that the choice of software and functions applied (directed at correcting artefacts arising from e.g. motion and eddy-currents) have a meaningful impact on the DTI parameter estimates from tissue. Consequently, this is the topic of a multinational study directed by the diffusion-study group of the ISMRM.

Summary
For DTI, it is generally possible to use linear algebra, matrix mathematics and vector mathematics to process the analysis of the tensor data.

In some cases, the full set of tensor properties is of interest, but for tractography it is usually necessary to know only the magnitude and orientation of the primary axis or vector. This primary axis—the one with the greatest length—is the largest eigenvalue and its orientation is encoded in its matched eigenvector. Only one axis is needed as it is assumed the largest eigenvalue is aligned with the main axon direction to accomplish tractography.

title: Diffusion MRI


text:
Multiple endocrine neoplasia type 2

Multiple endocrine neoplasia type 2 (also known as "Pheochromocytoma (codons 630 and 634) and amyloid producing medullary thyroid carcinoma", "PTC syndrome," and "Sipple syndrome" ) is a group of medical disorders associated with tumors of the endocrine system. The tumors may be benign or malignant (cancer). They generally occur in endocrine organs (e.g. thyroid, parathyroid, and adrenals), but may also occur in endocrine tissues of organs not classically thought of as endocrine. MEN2 is a sub-type of MEN (multiple endocrine neoplasia) and itself has sub-types, as discussed below. Variants in MEN2A have been associated with Hirschsprung disease. Screening for this condition can begin as young as eight years old for Pheochromocytoma.

Signs and symptoms
MEN2 can present with a sign or symptom related to a tumor or, in the case of multiple endocrine neoplasia type 2b, with characteristic musculoskeletal and/or lip and/or gastrointestinal findings. Medullary thyroid carcinoma (MTC) represents the most frequent initial diagnosis. Occasionally pheochromocytoma or primary hyperparathyroidism may be the initial diagnosis.

Pheochromocytoma occurs in 33-50% of MEN2 cases. In MEN2A, primary hyperparathyroidism occurs in 10–50% of cases and is usually diagnosed after the third decade of life. Rarely, it may present in childhood or be the sole clinical manifestation of this syndrome.MEN2A associates medullary thyroid carcinoma with pheochromocytoma in about 20–50% of cases and with primary hyperparathyroidism in 5–20% of cases. MEN2B associates medullary thyroid carcinoma with pheochromocytoma in 50% of cases, with marfanoid habitus and with mucosal and digestive neurofibromatosis.

In familial isolated medullary thyroid carcinoma the other components of the disease are absent. In a review of 85 patients 70 had MEN2A and 15 had MEN2B. The initial manifestation of MEN2 was medullary thyroid carcinoma in 60% of patients, medullary thyroid carcinoma synchronous with pheochromocytoma in 34% and pheochromocytoma alone in 6%. 72% had bilateral pheochromocytomas.

Causes
The table in the multiple endocrine neoplasia article lists the genes involved in the various MEN syndromes. Most cases of MEN2 derive from a variation in the RET proto-oncogene, and are specific for cells of neural crest origin. A database of MEN-implicated RET mutations is maintained by the University of Utah Department of Physiology.

The protein produced by the RET gene plays an important role in the TGF-beta (transforming growth factor beta) signaling system. Because the TGF-beta system operates in nervous tissues throughout the body, variations in the RET gene can have effects in nervous tissues throughout the body. MEN2 generally results from a gain-of-function variant of a RET gene. Other diseases, such as Hirschsprung disease, result from loss-of-function variants. OMIM # lists the syndromes associated with the RET gene.

Genetics
When inherited, multiple endocrine neoplasia type 2 is transmitted in an autosomal dominant pattern, which means affected people have one affected parent, and possibly affected siblings and children. Some cases, however, result from spontaneous new mutations in the RET gene. These cases occur in people with no family history of the disorder. In MEN2B, for example, about half of all cases arise as spontaneous new mutations.

Diagnosis
Diagnosis is suspected when a patient with family history of two of the three classical tumors (medullary thyroid cancer, pheochromocytoma, parathyroid adenoma) or MEN2 presents with one of the classical tumors. It is confirmed by genetic testing for mutation in RET gene.

Differences in presentation
As noted, all types of MEN2 include pheochromocytoma and medullary thyroid carcinoma.

MEN2A is additionally characterized by the presence of parathyroid hyperplasia.

MEN2B is additionally characterized by the presence of mucocutaneous neuroma, gastrointestinal symptoms (e.g. constipation and flatulence), and muscular hypotonia.

MEN2B can present with a Marfanoid habitus.

Classification
Before gene testing was available, the type and location of tumors determined which type of MEN2 a person had. Gene testing now allows a diagnosis before tumors or symptoms develop. A table in the multiple endocrine neoplasia article compares the various MEN syndromes. MEN2 and MEN1 are distinct conditions, despite their similar names. MEN2 includes MEN2A, MEN2B and familial medullary thyroid cancer (FMTC).

The common feature among the three sub-types of MEN2 is a high propensity to develop medullary thyroid carcinoma.

A variant of MEAs 2A was described in 1989. This variant also has patches of cutaneous amyloidosis in the mid/upper back and is inherited in an autosomal dominant fashion.

Management
Management of MEN2 patients includes thyroidectomy including cervical central and bilateral lymph nodes dissection for MTC, unilateral adrenalectomy for unilateral pheochromocytoma or bilateral adrenalectomy when both glands are involved and selective resection of pathologic parathyroid glands for primary hyperparathyroidism. Familial genetic screening is recommended to identify at risk subjects who will develop the disease, permitting early management by performing prophylactic thyroidectomy, giving them the best chance of cure.

Prognosis
Prognosis of MEN2 is mainly related to the stage-dependant prognosis of MTC indicating the necessity of a complete thyroid surgery for index cases with MTC and the early thyroidectomy for screened at risk subjects.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Multiple endocrine neoplasia type 2


text:
Dean Hammond

Dean John Hammond (born 7 March 1983) is an English former professional footballer and is currently a coach at National League South club Worthing. He previously played in the Football League for Brighton & Hove Albion, Leyton Orient, Colchester United, Leicester City and Southampton.

Brighton & Hove Albion
Born in Hastings, England, Hammond began his career at Brighton & Hove Albion when he was eleven years and then started in 1998 on YTS forms and started to progress at the club's development squad. Hammond made his Brighton & Hove Albion debut on 6 December 2000, in the first round of the Southern Section of Football League Trophy, in a 2–0 win over Cardiff City. This turned out to be his only appearance in the 2000–01 season.

Following this, Hammond returned to the club's reserve for the next two seasons before signing his first professional contract on 11 May 2002. Following this, Hammond was promoted to the first team at the start of the 2002–03 season. Hammond made his league debut for the club on 14 September 2002, coming on as a late substitute, in a 4–2 loss against Gillingham. Ten days later, on 24 September 2002, he scored his first Brighton & Hove Albion goal, in a 3–1 loss against Ipswich Town in the second round of League Cup. After the match, Manager Martin Hinshelwood praised Hammond's performance, including his first goal for the side. Under the new management of Steve Coppell, Hammond struggled to regain his first team place and never played again for the rest of the 2002–03 season.

In the 2003–04 season, Hammond was loaned out to lower league teams, starting with Aldershot Town during September. After making seven appearances at Aldershot Town, he returned to his parent club despite intending to extend his loan spell at the club. Following this, Hammond was loaned out to Leyton Orient shortly after. After extending his loan spell for another month with Leyton Orient, and went on to make nine appearances for the side. At the end of the 2003–04 season, Hammond was offered a new contract.

He was given a six-month ultimatum at the start of the 2004–05 season by then manager Mark McGhee. However, Hammond suffered an injury in the pre–season friendly that saw him sidelined at the start of the 2004–05 season. After returning to the first team from injury, Hammond was given a handful of first team appearances and making a huge impression, resulting him signing a contract until the end of the next season. Despite being on the substitute bench between October and March, he became a first team regular as a midfielder for the rest of the season and then scored his first league goal for the club on 16 March 2005, in a 4–2 loss against Wigan Athletic. Hammond scored again on 16 April 2005, in a 1–1 draw against Burnley, followed up by scoring twice, in a 2–2 draw against West Ham United on 23 April 2005. At the end of the 2004–05 season, Hammond finished the season making 30 appearances and scoring 4 times in all competitions.

At the beginning of the 2005–06 season, Hammond was handed the vacant number 11 shirt at the club, and became a first-team regular, either playing on the left hand side of midfield or in his preferred natural position of central midfield. He then started the 2005–06 season well when he scored the opening game of the season, in a 1–1 draw against Derby County and then scored again a week later, in a 2–2 draw against Crewe. For his good form at the club led him to sign a contract extension, keeping him until 2008. By the end of 2005, he went on to score two more goals against Ipswich Town and Millwall. However, Hammond received two red cards this season, with both of them came as a second bookable offence. Despite suffering setbacks from injury and suspension,  Hammond went on to make 41 appearances scoring four times in all competitions.

In the 2006–07 season, Hammond was handed the captain's armband at the club after injuries to both Richard Carpenter and Charlie Oatway. He started the 2006–07 season well when he scored his first goal of the season, in a 2–2 draw against Brentford on 12 August 2006. His second goal then came on 12 September 2006, in a 2–2 draw against AFC Bournemouth. By the end of 2006, Hammond went on to score four more goals against Bradford City, Cheltenham Town (twice) and Oldham Athletic. After being sidelined with injury and suspension, Hammond became the new official club captain after Carpenter was released by Brighton at the end of January 2007. Weeks after being appointed as a new captain, Hammond scored two goals in two matches between 13 February 2007 and 17 February 2007 against Leyton Orient and Nottingham Forest. However, he suffered a hamstring injury that ruled him out for the rest of the season. Hammond also scored three times in cup competitions, with two came from Football League Trophy against Boston United and MK Dons, while the other one came from FA Cup against Stafford Rangers. Hammond finished the 2006–07 season making 39 appearances and scoring 11 times, making him the top–scorer both in the league and in all competitions. For his performance, Hammond was named the club's player of the year this season.

Ahead of the 2007–08 season, Hammond returned from injury in the pre–season. At the start of the 2007–08 season, he started the season well, scoring on his 100th league appearance start on 18 August 2007, in a 2–1 win over Northampton Town. Two weeks later, on 1 September 2007, Hammond scored again, in a 3–2 win over Southend United, followed up by scoring in a 3–0 win over Millwall in the next game. Two weeks later, on 22 September 2007, Hammond scored his fourth goal of the season, in a 2–1 loss against Yeovil Town. It wasn't until on 20 November 2007 when he scored again in the FA Cup round, in a 2–1 win over Cheltenham Town. On 15 December 2007, Hammond scored his fifth league goal of the season, in a 3–0 win over Swindon Town. However, as the 2007–08 season progressed, with Hammond having one-year remaining on his contract at the Withdean, manager Dean Wilkins was keen to offer Hammond a new deal, with the club and representatives for the player beginning talks in October 2007. During January 2008, it was revealed that Hammond would only sign a new deal for the club if they showed the ambition of returning to the Championship. In the final months to his departure, Hammond was sent–off on his last appearance for a straight red card, just ten minutes into the game, in a 1–1 draw against Oldham Athletic. When the £300,000 capture of striker Glenn Murray from Rochdale failed to change Hammond's mind, the club placed him on the transfer list with little more than a week of the transfer window remaining.

Colchester United
On 30 January 2008, Brighton accepted an offer of £250,000 plus add-ons for the player. Hammond completed the deal the following day, moving to Colchester United.

However, Hammond suffered a setback since moving to Colchester United, as he suffered a calf injury, delaying his Colchester United. It wasn't until on 23 February 2008 when he finally made his Colchester United debut, coming on as second-half substitute, in a 2–1 loss against Bristol City. Since making his Colchester United debut, Hammond established himself in the first team there at the club, but subsequently unable to help the club survive relegation and went on to make 13 appearances.

Ahead of the 2008–09 season, Hammond dismissed suggestions that he would leave Colchester United following their relegation and stated that he was given an opportunity to play. Nevertheless, Hammond continued to be a first team regular at Colchester United and then scored his first Colchester United goal on 25 October 2008, in a 5–0 win over Carlisle United. Following Chris Coyne's absent from the first team, Hammond was appointed captain in December for the rest of the season. Weeks after being given the captain role, Hammond scored again to give Colchester United their first ever win against Leeds United at Elland Road. It wasn't until on 17 January 2009 when he scored his third Colchester United goal, in a 3–1 win over Cheltenham Town. After missing out for one game, due to injury, Hammond scored on his return from injury, in a 2–2 draw against Huddersfield Town on 3 March 2009. Following the match, Hammond's return was praised by Manager Paul Lambert, describing him as "terrific". For the rest of the season, Hammond continued to be a first team regular, resulting him being named the club's Player of the Year and Gazette Player of the Year award. At the end of the season, Hammond finished his full season at Colchester United making 43 appearances and scoring 5 times in all competitions.

In the 2009–10 season, Hammond found himself in the transfer speculation when Colchester United accepted a bid from Southampton, having previously turned down two bids from them. Amid to the transfer move to Southampton, Hammond made three appearances in all competitions, including a 7–1 win over Norwich City in the opening game of the season. Hammond made 63 appearances during his time with The U's, scoring 5 times in all competitions before his move to St. Mary's.

Southampton
On 19 August 2009, Hammond signed a three-year contract with Southampton for an undisclosed fee. As a result of moving to Southampton, his former club, Brighton, received a 20% of any profit as part of the clause following his move to Colchester United a year before.

Hammond made his Southampton debut on 22 August 2009, where he made his first start and played the whole game, in a 1–1 draw against Brentford. Since making his Southampton debut, Hammond became a first team regular. It wasn't until on 17 October 2009 when Hammond scored his first goal against Oldham Athletic, and made the scoresheet again a week later, against Milton Keynes Dons. In November 2009, it was announced that Hammond was appointed as the new Southampton captain, succeeding goalkeeper Kelvin Davis. A week later, he scored again in the second round of the FA Cup, in a 2–1 win over Northampton Town and then scored a week later, in the league, in a 3–1 win over Walsall. However, during a 1–1 draw against Millwall on 16 January 2010, Hammond suffered an Achilles injury in the first half, resulted him being substituted and after the match, it was announced that he would be out for several weeks. After returning to the first team around mid–February, Hammond scored again, as well as, setting up one of the goals, in a 5–0 win over Huddersfield Town on 2 March 2010. He played for Southampton in the 2010 Football League Trophy final win against Carlisle United. On 1 April 2010, Hammond scored in a 2–2 draw against his former club, Brighton & Hove Albion, where he celebrated in front of the Brighton supporters by "running along the touchline cupping his hand to his ear, angering them". Although Southampton finished seventh place and having failed to reach the play–offs, having started the season with 15 points deduction, due to the club's financial problems, Hammond finished his first season at the club making 49 appearances and scoring 6 times in all competitions.

In the 2010–11 season, Hammond continued to be the club's captain and after a slow start in the first two league' matches of the season, Hammond set up one of the goals, in a 4–0 win over Bristol Rovers on 28 August 2010. It wasn't until on 13 November 2010 when Hammond scored his first goal of the season, in a 3–2 loss against Carlisle United. Two months later, on 5 February 2011, Hammond scored again, in a 4–4 thrilling draw against Peterborough United. Then on 5 March 2011, he scored the second goal with a drive from the edge of the area against former club Colchester United to complete a 2–0 away win, and one week later on 12 March 2011, he, once again, scored an important second goal against AFC Bournemouth in a 3–1 away win. Despite suffering setbacks on three occasions from injuries during the season, Hammond eventually helped the club reach promotion to the Championship after two seasons at League One following a 3–1 win over Walsall on 7 May 2011. At the end of the 2010–11 season, Hammond finished the season making 47 appearances and scoring 4 times in all competitions.

Hammond started the season when he scored the first Southampton goal of the 2011–12 season, a 25-yard effort in a 3–1 victory over Leeds United, in their first game back in the Championship for two years. The season also saw Hammond found himself in a competition over the central midfielder position, which he described it as "take it to a new height". On 22 September 2011, Hammond then signed a contract extension with the club, keeping him until 2014. However, in a 1–1 draw against Reading on 22 October 2011, Hammond was sent–off in the second half and served one match, which came in the League Cup game. However, as the 2011–12 season progressed, he continued to be a first team regular despite being on the substitute bench on several time, which "he has adapted well to the style Saints have adopted." On 29 April 2012, Hammond gained promotion with Southampton to the Premier League. At the end of the 2011–12 season, Hammond went on make 48 appearances scoring once in all competitions.

However, in the 2012–13 season, Hammond struggled to regain his first team place in the Premier League and even lost his captaincy to Adam Lallana. Despite this, Hammond made his only appearance of the 2012–13 season, captained in the second round of the League Cup, in a 4–1 win over Stevenage.

Brighton & Hove Albion (loan)
On 31 August 2012, Hammond re-joined his former club Brighton & Hove Albion on loan for the remainder of the 2012–13 season. Upon re–joining the club, Hammond stated his aim is to win over his fans, having previously upset them when he scored against his former club, whilst at Southampton.

Hammond re–debuted for the club on 14 September 2012, where he made his first start and played the whole game, in a 3–0 win over Sheffield Wednesday. From that moment since re–debuting for the side, Hammond began to established himself in the first team at midfield position under Gus Poyet management, alongside Liam Bridcutt. It wasn't until on 28 November 2012 when he scored his first goal for the club since 2007, in a 2–0 win over Bristol City. His second goal then came on 1 January 2013, in a 2–0 win over Ipswich Town. Despite being on the substitute bench on numerous occasion, Hammond went on to make 39 appearances scoring two times in all competitions in the 2012–13 season. Following this, the club allowed him to return to his parent club after it came to an end.

Leicester City
On 30 August 2013, Hammond joined Leicester City for an undisclosed fee, signing a two-year deal. Upon joining the club, Hammond said Leicester City move would benefited him to play in the Premier League one day.

Hammond made his Leicester City debut, coming on as a late second-half substitute, in a 2–0 win over Wigan Athletic on 14 September 2013. It wasn't until on 23 November 2013 when he made his first start for the club, in a 2–0 win over Ipswich Town. Hammond scored his first goal for Leicester with a late, headed equaliser against Wigan Athletic on 1 April 2014, helping the Foxes extend their lead at the top of the Sky Bet Championship to seven points. However, since his move to Leicester City, Hammond appeared on the substitute bench, due to strong competitions from central–midfielders duo Danny Drinkwater and Matty James. Hammond played 29 times as Leicester won the Championship en route to promotion to the Premier League.

In the 2014–15 season, Hammond made his Premier League debut as a substitute for the injured Danny Drinkwater in the opening day 2–2 draw with Everton. Since making his Premier League, Hammond cemented his place with impressive performances against Chelsea, Arsenal and Stoke City. However, Hammond began to suffer a setback when he injured his calf and was out for a month. After making two more appearances in January, Hammond, again, suffered a calf injury that kept him out for another month. Although he returned in May, Hammond went on to make 12 appearances in the 2014–15 season. Subsequently, Hammond was offered a new contract by the club.

On 2 July 2015, Hammond signed a one-year contract extension until the summer of 2016. However, Hammond's first team opportunities became further limited under Claudio Ranieri following the arrival of new midfielders Gökhan Inler and N'Golo Kanté. As a result, Hammond was told by the club management to be loaned out in order to get a regular first team football. At the end of the 2015–16 season, which saw Leicester City win the English top-flight for the first time, Hammond was released by the club.

Sheffield United (loan)
On 20 October 2015, Hammond joined Sheffield United on loan until the end of January, rejoining his former manager from Southampton, Nigel Adkins.

Hammond made his debut the same day in a 3–0 victory over Fleetwood Town. It wasn't until on 24 November 2015 when he scored his first Sheffield United goal, in a 4–2 loss against Shrewsbury Town. From that moment on, Hammond became a first team regular for the rest of the season and extended his loan spell until the end of the season. Hammond then scored his second goal for the club on 30 March 2016, in a 3–1 loss against Southend United. Hammond went on to make 34 appearances scoring twice for the side. During his time there, Hammond was considered by Manager Adkins as an 'unsung hero', due to his commitment at Sheffield United.

On 20 May 2016, Hammond activated his option of a permanent contract with the club which had been inserted as part of his loan move. However, new manager Chris Wilder was seemingly less keen on the services of Hammond and instantly placed him on the transfer list. On 2 July 2016, Hammond left the club by mutual consent.

After leaving Sheffield United, Hammond went on trial at Coventry City in January 2017. However, the club decided against offering a new contract to Hammond following a trial.

Return to Leicester and retirement
Hammond returned to former club Leicester City in the spring of 2017, featuring as an over age player in under-21 matches, whilst assisting with coaching.

Hammond featured for Leicester City in a pre season friendly match against Leamington in July 2017.

In August 2017, it was revealed that Hammond had moved back to Sussex, and has retired as a player but is keen to remain involved in football in some capacity.

As of March 2018, he was still involved with Leicester City, as 'Loans Manager' within the academy setup.

Worthing
On 22 March 2020, it was announced that Hammond would return to football to play for Isthmian League Premier Division club Worthing in the 7th tier of English football. However, the COVID-19 pandemic halted football across the nation before he could make an appearance.

Personal life
Growing up, Hammond revealed that his ambition was to become a professional footballer, stating that he wanted to play as best he could, and at the highest level.

During his early Brighton & Hove Albion career, Hammond lived in a four-bedroom house in Hastings. Hammond began dating his then-19-year-old girlfriend, Rachel, who studied property surveying at Oxford Brookes University. They were married and together, the couple have three children, a daughter (born in 2009), a son (born in 2012) and another son (born 2016). However, their first son was just three weeks old when he was diagnosed with meningitis.

Honours
Southampton
 * Football League Championship second-place promotion: 2011–12
 * Football League One second-place promotion: 2010–11
 * Football League Trophy: 2009–10

Leicester City
 * Football League Championship: 2013–14

Individual
 * Brighton & Hove Albion Player of the Year: 2006–07
 * Colchester United Player of the Year: 2008–09

title: Dean Hammond


text:
Talk:City of Kogarah

the use of the title "Municipality" has been abolished as of 1999
Eregli bob 13:00, 9 May 2007 (UTC)

Separate page for the Local Government Area
As per discussion at Talk:List of Sydney suburbs, I have created a separate page for the Municipality of Kogarah, the Local Government Area. -- Ianblair23 09:01, 30 August 2005 (UTC)

Cleaning suburbs in LGAs to remove redlinks
Hi, Can people who know or care about this LGA please have a look at this message and see if they can please help solve any of the 4 redlinks in the "suburbs in this LGA" section of this page? (Usually solution is either to add a stub about the suburb / locality in question, or to remove it from the LGA's list). -- All the best, Nickj (t) 04:12, 23 January 2006 (UTC)

Kogarah is now a City
The article will need to be updated and renamed. Not sure who is happy to have a crack at this. Mustard Pot (talk) 06:52, 31 July 2009 (UTC)

Infobox Update
This page has had its infobox updated to Infobox Australian Place. This update has been automatically preformed by TheJoshBot. Please be aware that poorly filled templates can have infomation lost in the transition that is unknown to the bot. Check the page history for more infomation. The following infomation has been lost in the transition, and will need to be converted to the document prose:

Requested technical move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Moved. EdJohnston (talk) 18:47, 30 July 2014 (UTC)

 * Municipality of Kogarah → City of Kogarah ([ move]) – In 2008, the residents of the Municipality of Kogarah voted to change the name to the City of Kogarah Rangasyd (talk) 06:39, 4 November 2012 (UTC) See here for details. Rangasyd (talk) 06:39, 4 November 2012 (UTC)
 * I copied the request to Requested moves/Technical requests. Wbm1058 (talk) 14:23, 30 July 2014 (UTC)

 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

title: Talk:City of Kogarah


text: User talk:193.63.61.130

title: User talk:193.63.61.130


text:
Wikipedia:Articles for deletion/Valladares (2nd nomination)

 This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was keep. There was no clear consensus after well over two weeks of discussion, even if I were inclined to cast aside 212.101.64.4's contribution to the discussion (which I'm not). --Tony Sidaway Talk 10:47, 10 September 2005 (UTC)

Valladares
Not notable and family-name-vanity. --fvw *  20:05, August 23, 2005 (UTC)
 * As seen above, Valladares was nominated for deletion on August 23, but since then, no further votes have been received. I am resubmitting this to the August 30 VFD list, and abstain from voting. I think this as a good time as any to remind people to use and not  when nominating articles for deletion, especially these days when there have been some conflicts over the wording of the vfd template. Sjakkalle  (Check!)  09:02, 30 August 2005 (UTC)
 * Ooh, no votes at all, don't think I've ever seen that happen before. As for vs. , I've yet to be given any argument for it and it's more typing, so I'm just not convinced. If you really want to dredge the matter up again, have a look at my comments in the argument on talk back when the subst: was first added to the instructions. I'll grant you, it would have prevented some of the collateral damage caused by the namechange war, but that damage and a lot more would have been prevented if people had thought of way to migrate from one name to the other without lots of breakage before fucking with the template. Anyway, that's not a discussion for here, but if you feel like it please do come to my talk page, I'm sure I can find much more bile to spew.
 * Oh, and still delete, but I suppose you guessed that. --fvw *  11:24, August 30, 2005 (UTC)

 * Keep - What's wrong with including articles on the orgins of names and other things of interest? 212.101.64.4 09:03, 30 August 2005 (UTC)
 * Delete. As per fvw. Demogorgon's Soup-taster 13:25, 30 August 2005 (UTC)
 * Delete, WP:ISNOT a genealogy database. Zoe 21:46, August 30, 2005 (UTC)
 * Keep. Nothing wrong with the article. Pengo 13:29, 8 September 2005 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.


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User:Charles Matthews/MathematicsC

Crystalline cohomology - completely reducible - contact transformation - Calderon operator - Calderon-Vaillancourt theorem - Canonical curve - Cap product - Carleman kernel - Carleman's criterion - Carleman's inequality - Carleman transform - Cartan conjugacy theorem - Cartan criterion - Cartan-Kuranishi theorem - Cartan subgroup - Casson invariant - Castelnuovo curve - Castelnuovo-Enriques theorem - Castelnuovo lemma - Cauchy characteristic vector - Cauchy data - Cauchy formula for convex bodies - Cauchy kernel - Cayley-Brill formula - Chern-Lashof theorem - Chevalley basis - Chevalley theorem - Chordal variety - Christoffel-Darboux formula - Closed unbounded operator - Coercive form - Cohn-Vossen theorem - Complete maximum principle - Compressible mapping - Condensation of singularities - Contingent (mathematics) - Continuity principle - Coincident point - Conley-Zehnder theorem - Conley-Zehnder-Franks theorem -Cotlar-Knapp-Stein lemma - Cotlar's lemma - Coxeter element - Cremona transformation - Crofton formula - Cuspidal point of a surface - Cut locus - Crystalline cohomology - Cartan integer - Cartan involution  - Cartan subgroup - Casimir polynomial - Central character - Central eigendistribution - Chevalley's criterion - Chevalley's restriction theorem - Class one representation - Closure of an operator - Compactification of a Riemannian symmetric space - Complete set of representations - Completely invariant set - Complex distance - Complex semisimple group - Complexification of a reductive group - Connection index - Contragrediant representation - co-root - countable at infinity - Coxeter-Killing transformation - Cuspidal parabolic subgroup - Cap-product - Cellular map - Chain homotopy - Characteristic map - Characteristic number - Closure-finite - Clutching function - Coaction of H-cogroup  - Coexact sequence of spaces - Cofibre sequence - Cohomology theory associated with a spectrum - Cotensor product - CW-substitute - c-function  - Coadjoint action - Coherence theorem -Calculus of two errors - Cech homology - Caratheodory conjecture - Clemens conjecture - Cherlin-Zilber conjecture - Canonical element conjecture - Chinburg conjecture - Connes-Kasparov conjecture - Coates-Sinnott conjecture - Connes-Kreimer conjecture

Cartan subgroup - Cartier dual - Chow scheme - CM-field - Complete reducibility - Cremona group -

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title: User:Charles Matthews/MathematicsC


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Yoine Goldstein

Yoine J. Goldstein (May 11, 1934 – March 18, 2020) was a Canadian lawyer, academic, and former Senator.

Born in Montreal, Quebec, his education includes a Bachelor of Arts from McGill University in 1955, a Bachelor of Civil Law (with honours) from McGill University in 1958 (where he was selected as the Articles Editor for the McGill Law Journal), and a Doctor of Laws from the Université de Lyon in 1960. He was called to the Quebec Bar in 1961. He specializes in insolvency, bankruptcy and commercial litigation. Prior to becoming a senator, he was a senior and managing partner of the Montreal law firm, Goldstein, Flanz & Fishman.

From 1973 until 1997, he was a lecturer at the Faculty of Law of the Université de Montréal. He is a Fellow of the American College of Trial Lawyers and the American College of Bankruptcy. In 1992, he received the Lord Reading Law Society Human Rights Award, and the Lord Reading Law Society Service Award in 1998.

Active in Montreal's Jewish community, he was president of Federation CJA (a funding, planning, and coordinating body of services for some of the 93,000 Jews in Montreal) from 1995 to 1997. He is also a member of the Community Advisory Board of the Concordia University Chair of Canadian Jewish Studies.

Senate career
On August 29, 2005, he was appointed to the Senate on the advice of Paul Martin and sat as a member of the Liberal caucus.

He was vice-chairman of the Banking, Trade and Commerce committee and the Standing Committee on Banking, Trade and Commerce.

During the 40th Canadian Parliament he introduced the following bills: S-219: An Act to amend the Bankruptcy and Insolvency Act (student loans), S-220: An Act respecting commercial electronic messages, S-231: An Act to amend the Investment Canada Act (human rights violations), and S-232: An Act to amend the Patent Act (drugs for international humanitarian purposes) and to make a consequential amendment to another Act.

He retired, per Senate rules, on May 11, 2009, his 75th birthday. He died on March 18, 2020.

title: Yoine Goldstein


text: User talk:68.6.197.164

title: User talk:68.6.197.164


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Transcaspian Oblast

The Transcaspian Oblast, or simply Transcaspia, was an oblast of the Russian Empire and early Soviet Russia to the east of the Caspian Sea during the second half of the 19th century until 1924.

It was bounded to the south by Iran's Khorasan Province and Afghanistan, to the north by the former Russian province of Uralsk, and to the northeast by the former Russian protectorates of Khiva and Bukhara. Part of Russian Turkestan, it corresponded roughly to the territory of present-day Turkmenistan and southwestern Kazakhstan.

The name of the oblast (literally, 'Beyond [the] Caspian') is explained by the fact that until the construction of the Trans-Aral Railway in the early 20th century the easiest way to reach this oblast from central Russia (or from Russian Transcaucasia) was across the Caspian Sea, by boat from Astrakhan or Baku.

History
Transcaspia was conquered by Russia in 1879–1885, in a series of campaigns led by Generals Nikolai Lomakin, Mikhail Skobelev, and Mikhail Annenkov. The construction of the Transcaspian Railway was started from the shores of the Caspian in 1879 in order to secure Russian control over the region and provide a rapid military route to the Afghan border. In 1885 a crisis was precipitated by the Russian annexation of the Panjdeh oasis, to the south of Merv, which nearly led to war with Britain, as it was thought that the Russians were planning to march on to Herat in Afghanistan. Until 1898 Transcaspia was part of the Governor-Generalship of the Caucasus Viceroyalty administered from Tiflis, but in that year it was made an oblast of Russian Turkestan governed from Tashkent. The best known military governor to have ruled the region from Ashkhabad was probably General Kuropatkin, whose authoritarian methods and personal style of governance made the province very difficult for his successors to control. Consequently, the administration of Transcaspia became a byword for corruption and brutality within Russian Turkestan, as Russian administrators turned their districts into petty fiefdoms and extorted money from the local population. These abuses were fully exposed by the Pahlen Report of 1908–1910.

During the revolutionary period of 1917 to 1919, parts of Transcaspia were briefly occupied by British Indian forces from Meshed. The oblast was one of the last centres of Basmachi resistance to Bolshevik rule, with the last of the rebellious Turkmen fleeing across the border to Afghanistan and Iran in 1922 and 1923.

Demographics
As of 1897, 382,487 people populated the oblast. Turkmens constituted the majority of the population, and significant minorities were Kazakhs and Russians. The total Turkic-speaking population was 328,059 (85.8%).

Overall
According to the 1897 Russian census, the ethnic groups by population were:

By okrug
Ethnic groups by percentage of the Transcaspian population according to the 1897 census:

Ethnic groups by population in Transcaspia according to the 1897 census:

title: Transcaspian Oblast


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Oxandrolone

Oxandrolone is an androgen and synthetic anabolic steroid (AAS) medication to help promote weight gain in various situations, to help offset protein catabolism caused by long-term corticosteroid therapy, to support recovery from severe burns, to treat bone pain associated with osteoporosis, to aid in the development of girls with Turner syndrome, and for other indications. It is taken by mouth. It was sold under the brand names Oxandrin and Anavar, among others.

The drug is a synthetic androgen and anabolic steroid, hence is an agonist of the androgen receptor (AR), the biological target of androgens such as testosterone and dihydrotestosterone. Side effects of oxandrolone include severe cases of peliosis hepatis, sometimes associated with liver failure and intra-abdominal hemorrhage; liver tumors, sometimes fatal; and blood lipid changes associated with increased risk of atherosclerosis. Additional warnings include the risks associated with cholestatic hepatitis, hypercalcemia in patients with breast cancer, and increased risk for the development of prostatic hypertrophy and prostatic carcinoma in older patients. It has strong anabolic effects and weak androgenic effects, which gave it a mild side effect profile in that regard and made it especially suitable for use in women. Milder side effects in women were increased sexual desire, symptoms of hyperandrogenism such as acne, and symptoms of masculinization such as increased hair growth and voice changes.

Oxandrolone was first described in 1962 and introduced for medical use in 1964. The drug was a controlled substance in many countries, so non-medical use for purposes such as improving physique and performance it has been generally illicit. In the United States, the FDA withdrew in 2023 the approval for the drug for reasons of safety or effectiveness, following a 2019 letter from Gemini, a drug manufacturer, stating that the product was no longer being marketed.

Medical uses
Oxandrolone has been researched and prescribed as a treatment for a wide variety of conditions. It was FDA-approved for treating bone pain associated with osteoporosis, aiding weight gain following surgery or physical trauma, during chronic infection, or in the context of unexplained weight loss, and counteracting the catabolic effect of long-term corticosteroid therapy. Oxandrolone is used to quicken recovery from severe burns.

In the management of severe burn injuries, numerous clinical trials have demonstrated the therapeutic advantages of oxandrolone, and it was widely adopted as a standard treatment protocol in burn centers globally. Meta-analyses of clinical trials substantiate the efficacy of oxandrolone in severe burn cases: the benefits are manifold and significant, and include a reduction in catabolic weight loss, augmentation of lean body mass, enhancement of donor-site wound healing, and a decrease in the duration of both intensive care unit (ICU) and overall hospital stay. These benefits do not appear to be accompanied by an increased risk of infection, hyperglycemia, or hepatic dysfunction, which underscores the safety profile of oxandrolone in severe burn patient population. Data analysis confirms oxandrolone's significant advantage in promoting skin healing as an adjunct therapy for adult burn patients. Oxandrolone improves weight regain, bone mineral density, lean body mass, and accelerates wound healing for donor graft sites. Oxandrolone is recommended as an adjunctive therapy, alongside insulin, metformin, and closely monitored propranolol, in severe burn patients, for metabolic and nutritional support. Oxandrolone improves both short-term and long-term outcomes in people recovering from severe burns and was well-established as a safe treatment for this indication. One of the underlying mechanisms in burn management is that oxandrolone helps reduce hypermetabolic response, which is characterized by increased energy expenditure, elevated stress hormones levels such as cortisol, insulin resistance, muscle wasting, and impaired wound healing; this response is reduced by improving whole-body nitrogen balance as well as preserving lean body mass during recovery.

As of 2019, oxandrolone was prescribed off-label for the development of girls with Turner syndrome, and counteract wasting of diverse origin.

As of 2012, oxandrolone was used in the treatment of idiopathic short stature, anemia, hereditary angioedema, hypogonadism and alcoholic hepatitis.

Medical research established the effectiveness of oxandrolone in aiding the development of girls with Turner syndrome. Although oxandrolone had long been used to accelerate growth in children with idiopathic short stature, it is unlikely to increase adult height, and in some cases may even decrease it. As of 2015, oxandrolone had, therefore, largely been replaced by growth hormone for this use. However, a 2019 Cochrane review comparing effects of adding oxandrolone to growth hormone treatment to growth hormone alone found moderate-quality evidence that the addition of oxandrolone led to an increase in final adult height of girls with Turner syndrome, and low-quality evidence showed no increase in adverse effects. When the same review assessed the effects of adding oxandrolone to growth hormone treatment on speech, cognition and psychological status, the results were inconclusive due to very-low quality evidence. Children with idiopathic short stature or Turner syndrome were given doses of oxandrolone far smaller than those given to people with burns to minimize the likelihood of virilization and premature maturation.

Oxandrolone shows positive effects on cardiometabolic health and visual, motor, and psychosocial functions in adolescent males with preserved testosterone production, such as those with Klinefelter syndrome.

Non-medical uses
Oxandrolone has been used illicitly by bodybuilders and athletes for its muscle-building effects as doping agent in sports. Cases of doping with oxandrolone by professional athletes have been reported. Because it is more anabolic than androgenic, so women and those seeking less intense steroid regimens used it particularly often. In the past many valued oxandrolone's supposed low hepatotoxicity relative to most other orally active AASs.

Contraindications
Like other AASs, oxandrolone may worsen hypercalcemia by increasing osteolytic bone resorption. When taken by pregnant women, oxandrolone may have unintended effects such as masculinization on the fetus.

Side effects
As of 2004 it was thought that "uniquely" among 17α-alkylated AASs, oxandrolone showed little to no hepatotoxicity, even at high doses. However, elevated liver enzymes have been observed in some people, particularly with high doses and/or prolonged treatment, although sometimes returning to normal ranges following discontinuation. The lack of hepatotoxicity turned out not to be true in the long run: Severe cases of peliosis hepatis, sometimes associated with liver failure and intra-abdominal hemorrhage; liver tumors, sometimes fatal; and blood lipid changes associated with increased risk of atherosclerosis led FDA to remove approval in June 2023. Additional warnings include the risks associated with cholestatic hepatitis, hypercalcemia in patients with breast cancer, and increased risk for the development of prostatic hypertrophy and prostatic carcinoma in older patients.

Women who are administered oxandrolone may experience virilization, irreversible development of masculine features such as voice deepening, hirsutism, menstruation abnormalities, male-pattern hair loss, and clitoral enlargement. Because of these side effects, doses given to women and children are minimized and people are usually monitored for virilization and growth abnormalities. Like other androgens, oxandrolone can cause or worsen acne and priapism (unwanted or prolonged erections). Oxandrolone can also reduce males' fertility, another side effect common among androgens. In an attempt to compensate for the exogenous increase in androgens, the body may reduce testosterone production via testicular atrophy and inhibition of gonadotropic activity.

Unlike some AASs, oxandrolone does not generally cause gynecomastia because it is not aromatized into estrogenic metabolites. However, although no reports of gynecomastia were made in spite of widespread use, oxandrolone was reported in a publication in 1991 to have been associated with 33 cases of gynecomastia in adolescent boys treated with it for short stature. The gynecomastia developed during oxandrolone therapy in 19 of the boys and after the therapy was completed in 14 of the boys, and 10 of the boys had transient gynecomastia, while 23 had persistent gynecomastia that necessitated mastectomy. Though transient gynecomastia is a natural and common occurrence in pubertal boys, the gynecomastia associated with oxandrolone was of a late/delayed onset and was persistent in a high percentage of the cases. As such, the researchers stated, "although oxandrolone cannot be implicated as stimulatory [in] gynecomastia", a possible relationship should be considered in clinicians using oxandrolone in adolescents for growth stimulation.

Interactions
As of 2004 it was known that oxandrolone greatly increases warfarin's blood-thinning effect, sometimes dangerously so. In April 2004, Savient Pharmaceuticals published a safety alert through the FDA warning healthcare professionals of this. Oxandrolone also inhibits the metabolism of oral hypoglycemic agents. It may worsen edema when taken alongside corticosteroids or adrenocorticotropic hormone.

Pharmacodynamics
Like other AASs, oxandrolone is an agonist of the androgen receptor, similar to androgens such as testosterone and DHT. The relative binding affinity of oxandrolone for the androgen receptor is about 0.3% of that of metribolone. Activation of the androgen receptor stimulates protein synthesis, which increases muscle growth, lean body mass, and bone mineral density.

Compared to testosterone and many other AASs, oxandrolone is less androgenic relative to its strength as an anabolic. Oxandrolone has as much as 6 times the anabolic potency of testosterone. Still, and has significantly reduced androgenic potency in comparison: oxandrolone exhibits significantly lower virilizing androgenic properties compared to testosterone, with a relative potency of only 5%.

Compared to methyltestosterone, oxandrolone has about 322 to 633% of the anabolic potency and 24% of the androgenic potency.

The reduced ratio of anabolic to androgenic activity of oxandrolone often motivates its medical use in children and women because less androgenic effect implies less risk of virilization. The bodybuilding community also considers this fact when choosing between AASs.

As of 2003 and 2011 Oxandrolone was thought to be "uniquely" far less hepatotoxic than other 17α-alkylated AASs, which was thought to be due to differences in metabolism. This turned out not to be the case in the long run, which is why it was taken off the US market in 2023.

Steroid configuration

Oxandrolone is based on the tetracyclic steroid framework, which consists of three cyclohexane rings (A, B, and C) and one cyclopentane ring (D). This is a common structure shared by all steroids.

The oxygen atom in the lactone bridge replaces a carbon atom at position 2 of the steroid nucleus, classifying oxandrolone as an 2-oxa-steroid. There is a hydroxyl group (-OH) attached at stereo-direction β to carbon 17, which is a characteristic of 17β-hydroxy-steroids.

The overall structure of oxandrolone is distinguished by these modifications to the standard steroid skeleton, which contribute to its unique properties as an anabolic steroid. The presence of the lactone bridge, i.e., the 2-oxa-steroid classification, is particularly noteworthy, as it is not commonly found in the steroid family. This structural element is what gives oxandrolone its distinctive chemical identity within the class of anabolic steroids. Due to this lactone bridge, oxandrolone is resistant to inactivation by 3α-hydroxysteroid dehydrogenase in skeletal muscle. This is in contrast to DHT, and is thought to underlie the preserved anabolic potency with oxandrolone.

As oxandrolone is already 5α-reduced (have a single bond between carbons 4 and 5), it is not a substrate for the 5α-reductase enzyme, hence is not potentiated in androgenic tissues such as the skin, hair follicles, and prostate gland. This is involved in its reduced ratio of anabolic to androgenic activity. Because it is 5α-reduced, oxandrolone is not a substrate for aromatase, hence cannot be aromatized into metabolites with estrogenic activity. Oxandrolone similarly possesses no progestogenic activity.

Pharmacokinetics
The oral bioavailability of oxandrolone is 97%. Its plasma protein binding is 94 to 97%. The drug is metabolized primarily by the kidneys and to a lesser extent by the liver. Oxandrolone is the only AAS that is not primarily or extensively metabolized by the liver, and this is thought to be related to its diminished hepatotoxicity relative to other AASs. Its elimination half-life is reported as 9.4 to 10.4 hours, but is extended to 13.3 hours in the elderly. About 28% of an oral dose of oxandrolone is eliminated unchanged in the urine and 3% is excreted in the feces.

Chemistry
Oxandrolone is a synthetic androstane steroid and a 17α-alkylated derivative of DHT. It is also known as 2-oxa-17α-methyl-5α-dihydrotestosterone (2-oxa-17α-methyl-DHT) or as 2-oxa-17α-methyl-5α-androstan-17β-ol-3-one, and is DHT with a methyl group at the C17α position and the C2 carbon replaced with an oxygen atom. Closely related AASs include the marketed AAS mestanolone (17α-methyl-DHT), oxymetholone (2-hydroxymethylene-17α-methyl-DHT), and stanozolol (a 2,3-pyrazole A ring-fused derivative of 17α-methyl-DHT) and the never-marketed/designer AAS desoxymethyltestosterone (3-deketo-17α-methyl-δ2-DHT), methasterone (2α,17α-dimethyl-DHT), methyl-1-testosterone (17α-methyl-δ1-DHT), and methylstenbolone (2,17α-dimethyl-δ1-DHT).

History
Oxandrolone was first made by Raphael Pappo and Christopher J. Jung while at Searle Laboratories, now part of Pfizer and they first described the drug in 1962. They were immediately interested in oxandrolone's very weak androgenic effects relative to its anabolic effects. It was introduced as a pharmaceutical drug in the United States in 1964.

It was prescribed to promote muscle regrowth in disorders which cause involuntary weight loss, and is used as part of treatment for HIV/AIDS. It had also been shown to be partially successful in treating cases of osteoporosis. However, in 1989, in part due to bad publicity from its illicit use by bodybuilders, production of Anavar was discontinued by Searle Laboratories. It was picked up by Bio-Technology General Corporation, which changed its name to Savient Pharmaceuticals. In 1995, following successful clinical trials, Savient released it under the brand name Oxandrin. As of 2011 BTG subsequently had won approvals for orphan drug status by the Food and Drug Administration for treating alcoholic hepatitis, Turner syndrome, and HIV-induced weight loss and as an offset to protein catabolism caused by long-term administration of corticosteroids.

Generic names
Oxandrolone is the generic name of the drug and its INN, USAN, USP, BAN, DCF, DCIT, and JAN, while ossandrolone is or was formerly the DCIT.

Brand names
The original brand name of oxandrolone was Anavar, which was marketed in the United States and the Netherlands. This product was eventually discontinued and replaced in the United States with a new name of Oxandrin, which as of 2011 was the sole remaining brand name for oxandrolone in the United States. Oxandrolone has also been sold under the brand names Antitriol (Spain), Anatrophill (France), Lipidex (Brazil), Lonavar (Argentina, Australia, Italy), Protivar, and Vasorome (Japan), among others. As of 2016, among those using oxandrolone for nonmedical purposes, it has been referred to colloquially as "Var", a shortened form of the old brand name Anavar. Additional brand names existed for products that were manufactured for the steroid black market.

United States
As of 2017, Oxandrolone was one of the few AASs that remained available for medical use in the United States.

In June 2023, the FDA formally withdrew approval for oxandrolone for all indications, stating that possible adverse effects of the drug were sufficiently serious to warrant removal from the US market. The FDA decision was for reasons of safety or effectiveness, following a 2019 letter from Gemini, a drug manufacturer, stating that the product was no longer being marketed.

As of August 2023, the AASs that remained available for medical use in the US were testosterone, testosterone cypionate, testosterone enanthate, testosterone undecanoate, methyltestosterone, fluoxymesterone, and oxymetholone.

Other countries
Outside of the United States, the availability of oxandrolone is also quite limited. It is no longer available in Europe. Oxandrolone is available in some less-regulated markets in Asia such as Malaysia and in Mexico.

Historically, oxandrolone has been marketed in Argentina, Australia, Brazil, France, Italy, Japan, and Spain,  but it appears to no longer be available in these countries.

Legal status
In the United States, oxandrolone was categorized as a Schedule III controlled substance under the Controlled Substances Act along with many other AASs. In 2017, it was a Schedule IV controlled substance in Canada, and a Schedule 4 controlled drug in the United Kingdom.

title: Oxandrolone