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Diagnostic Imaging

Biomedical Signal Analysis: Contemporary Methods and by Fabian J. Theis

By Fabian J. Theis

A finished advent to cutting edge equipment within the box of biomedical sign research, overlaying either conception and perform.

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Extra resources for Biomedical Signal Analysis: Contemporary Methods and Applications

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At a given voxel, the value of an MR image is characterized by two important factors: the tissue properties and the scanner imaging protocol. The most relevant tissue properties are the relaxation parameters T1 and T2 and the proton density. The proton density is defined as the number of targeted nuclei per unit volume. The scanner software and hardware manipulate the magnetization vector M over time and space based on the so-called pulse sequence. In the following text, we will focus on a particular voxel and give the equations of motion for M(t) as a function of time t.

8) n=0 and the corresponding inverse transform is x(n) = 1 N N −1 2π y(k)ej N kn , k=0 n = 0, 1, . . 9) 34 Chapter 2 √ with j ≡ −1. All x(n) and y(k) can be concatenated in the form of two N × 1 vectors. 11) with ⎡ ⎢ ⎢ W=⎢ ⎢ ⎣ 1 1 .. 1 WN .. 1 WN2 .. 1 WNN −1 WN 2(N −1) ··· ··· .. 1 WNN −1 .. 12) · · · WN where W is an unitary and symmetric matrix. Let us choose as an example the case N = 2. 1. 1 Time and frequency resolution by window width. 15) We immediately see that the two-dimensional DFT represents a separable transformation with the basis images wi wjT , i, j = 0, 1, .

The two underlying characteristics of hemodynamic effects are spatial and temporal. While vasculature is mainly responsible for spatial Foundations of Medical Imaging and Signal Recording 23 effects, the temporal effects are responsible for the delay of the detected MR signal changes in response to neural activity and a longer duration of the dispersion of the hemodynamic changes. The temporal aspects impose two different types of fMRI experiments: “block” designs and “event-related” designs. The block designs are characterized by an experimental task performed in an alternating sequence of 20-60 sec blocks.

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