the concentration gradient: 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: Putting the two together, we get the diffusion equation: Magnetization dynamics With no diffusion present, the change in nuclear magnetization over time is given by the classical Bloch equation 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 is a vector, there are 3 diffusion equations, one for each dimension. The Bloch-Torrey equation is: where is now the diffusion tensor. For the simplest case where the diffusion is isotropic the diffusion tensor is a multiple of the identity: then the Bloch-Torrey equation will have the solution The exponential term will be referred to as the attenuation . 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: where the terms incorporate the gradient fields , , and . 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