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## Three dimensional anisotropy contrast (3DAC)

Expansion of contrast from scalar to 3-dimensional vector introduces significantly higher contrast resolution in given images similar to the change of black and white photograph to color. Among various magnetic resonance imaging contrast mechanisms, apparent diffusion possesses the physical property of the 3-dimensional nature. This property can be used to gain 3-dimensional vectors, instead of a conventional scalar contrast for image reconstruction. Three dimensional anisotropy contrast (3DAC) is an algorithm introduced to clinical medicine at this venue. Three primary colors-red, green, and blue-were assigned to the gray scale of the three, x-, y-, and z-axes, anisotropic diffusion weighted images, respectively. These three primary color images were then combined pixel by pixel to form a single color image in full visible color spectrum. The final images were displayed negatively to obtain a one-to-one correlation between the red, green, and blue colors and the x-, y-, and z-axes, respectively. These images were generated using in-house software written in MATLAB language (MathWorks, Natick, MA, USA). For details of 3DAC processing and further mathematical formalism, the readers are referred to references. Figures are representative 3DAC 3.0 Tesla images of normal brain.

## Lambda Chart Analysis (LCA)

LCA incorporates biological characteristics into an algorithm, namely,

λ_{1} ≥ λ_{2} = λ_{3},

where λ_{1} represents the largest eigenvalue, and λ_{2} and λ_{3} signify the remaining smaller eigenvalues. Under this condition, a diffusion system under consideration can be fully characterized by the diffusion characteristic function, Ψ(Tr, θ), where Tr represents the trace and θ the anisotropic angle. In practice, a diffusion system in question is first expressed by 2 eigenvalues, lambda longitudinal (λ_{L}) and lambda transverse (λ_{T}), calculated using the actual determination of 3 eingenvalues as follows:

λ_{L} = λ_{1},

λ_{T} = (λ_{2} + λ_{3}) / 2

λ_{T} is so defined as to take into account the minor variation and potential estimation errors of the 2 small eigenvalues, λ_{2} and λ_{3}. Subsequently, λ_{L} of target pixels are plotted against λ_{T}, creating a 2-dimensional chart, lambda chart.

## Isotropic Component Trace Analysis (ICTA)

Pretreatment of a given diffusion tensor imaging data set with Lambda Chart, which effectively segregates isotropic and anisotropic components, allows for total removal of the anisotropic component from the diffusion tensor imaging data set. The remaining pure isotropic component can be subjected to further analysis similar to that applied in the trace histogram method. Deconvolution of the trace function yielded 3 Gaussian elements.

Trace function. The isotropic pixels are further divided into 3 subgroups based on their characteristic trace value. First, the pixels in the isotropic cluster are plotted against their trace value, creating a trace function. Subsequently, this histogram is deconvoluted into 3 Gaussian components by the chi-square curve-fitting process.

ICTA provides quantitative indices of certain parenchymal parameters with better clarity than currently available methods. A ready-to-use program, EZ-LCA, for this method is provided from our site.

## φ-MRA

Dynamic contrast enhanced MRI represents a MRI version of non-diffusible tracer methods, the main clinical use of which is the physiological construction of what is conventionally referred to as perfusion images. The raw data utilized for constructing MRI perfusion images are time series of pixel signal alterations associated with the passage of a gadolinium containing contrast agent. Such time series are highly compatible with independent component analysis (ICA), a novel statistical signal processing technique capable of effectively separating a single mixture of multiple signals into their original independent source signals (blind separation). Accordingly, we applied ICA to dynamic MRI time series. The technique, which we named as φ-MRA, was found to be capable of separating spatial patterns of arterial, venous, and capillary flows, allowing for hitherto unobtainable assessment of regional cerebral hemodynamics in vivo.

Suzuki, K., Matsuzawa, H., Igarashi, H., Watanabe, M., Nakayama N., Kwee, I.L., Nakada, T. All-phase MR angiography using independent component analysis of dynamic contrast enhanced MRI time series: φ-MRA. Magn Reson Med Sci 2003; 2:23–27.