## Conclusions

Although IVUS is continuously gaining in use in practice due to its multiple clinical advantages, the technical process of IVUS image generation is not known to doctors and researchers developing IVUS image analysis. This fact leads to a simplified use, analysis, and interpretation of IVUS images based only on the gray-level values of image pixels. In this chapter we discuss a basic physical model to generate synthetic 2D IVUS images. The model has different utilities Firstly, an expert can...

## Discussion and Concluding Remarks

This chapter presented an overview of quantitative PET imaging, including the basic principles and instrumentation, methods of image reconstruction from projections, and some specific correction factors necessary to achieve quantitative images. Techniques for absolute physiologic parameters estimation based on the framework of tracer kinetic modeling are also introduced. Recent advances in instrumentation and detector technologies have partially resolved some of the challenges. Research is...

## Linearization Approaches

Linearization approaches reformulate the model equations so that (1) a linear relationship exists between the transformed data and the primary physiological parameter of interest, or (2) the reformulated model equations contain only linear parameters. In these circumstances, estimation of parameters can be accomplished by a simple linear regression or by linear least-squares (LLSs) techniques. A number of graphical techniques that aim at transforming the measured data into a plot which is...

## Inflow Method Time of Flight

This method belongs to a class of MR angiographic techniques known as time-of-flight. This technique gives rise to 3D information about the vessels in the volume of tissue being imaged with high contrast between the stationary tissue and the flowing blood. The INFLOW method relies on the flow related image enhancement caused by the movement of fresh, unsaturated blood into an already saturated slab of tissue. The INFLOW method has a number of advantages over other angiographic imaging methods....

## Wavelet Transform and Multiscale Analysis

One of the most fundamental problems in signal processing is to find a suitable representation of the data that will facilitate an analysis procedure. One way to achieve this goal is to use transformation, or decomposition of the signal on a set of basis functions prior to processing in the transform domain. Transform theory has played a key role in image processing for a number of years, and it continues to be a topic of interest in theoretical as well as applied work in this field. Image...

## Level Set Surface Deformation

The initialization should position the model near the desired solution while retaining certain properties such as smoothness, connectivity, etc. Given a rough initial estimate, the surface deformation process moves the surface model to ward specific features in the data. One must choose those properties of the input data to which the model will be attracted and what role the shape of the model will have in the deformation process. Typically, the deformation process combines a data term with a...

## Phase Contrast PC Technique

4D PC technique was demonstrated for its feasibility that permits spatial and temporal coverage of an entire 3D volume 26 . It validated quantitatively the accuracy against an established time resolved 2D PC technique to explore advantages of the approach with regard to the 4D nature of the data. Time-resolved, 3D anatomical images were generated simultaneously with registered three-directional velocity vector fields. Improvements were compared to prior methods for gated and respiratory...

## Image Registration Using Wavelets

In this section, we give a brief overview of another very important application of wavelets in image processing image registration. Readers interested in this topic are encouraged to read the references listed in the context. Image registration is required for many image processing applications. In medical imaging, co-registration problems are important for many clinical tasks 2. cross-subject normalization and template atlas analysis, 3. patient monitoring over time with tracking of the...

## Discussion on Related Mathematical Models

The level set equation (11.1) has great significance in axiomatization of image processing and computer vision 1 . It fulfills the so-called morphological principle If u is a solution then, for any nondecreasing function < , < (u) is a solution as well. It means that level sets of a solution u move independently of each other, or in other words, they diffuse only intrinsically (in tangential direction) and there is no diffusion across level sets in the normal direction. In that sense it...

## Semiimplicit CoVolume Scheme

We present our method in discretization of Eq. (11.8), although we always use its e-regularization (11.2) with a specific e > 0. The notation is simpler in the case of (11.8) and it will be clear where regularization appears in the numerical scheme. First we choose a uniform discrete time step t and a variance a of the smoothing kernel Ga. Then we replace time derivative in (11.8) by backward difference. The nonlinear terms of the equation are treated from the previous time step while the...

## Present Limitations of the IVUS Technique and the Need for a Generation Model of IVUS Data

The main function of the IVUS technique is to serve as a guide in the interventional procedures, allowing us to measure the cross section of the artery. The precision in the measurements of distance is subject to the following potential sources of error 9 (a) Incorrect identification of the surface and the sections to be measured. Although the vessel and the interface defining the wall vessel have sufficiently good acoustics in most of the cases, in several cases the identification of the...

## Further Reading

Deformable contour models are commonly used in image processing and computer vision, for example for shape description 21 , object localization 22 , and visual tracking 23 . A good starting point to learn about parametric active contours is 24 . These snakes have undergone significant improvements since their conception, for example see the GVF snake in 7,9 . Region-based parametric snake frameworks have also been reported in 25-27 The geometric model of active contours was simultaneously...

## Summary

The wavelet-based method we demonstrated in this section is based on the approximation of the objective function in V0. It should be pointed out that it did not use the multiscale structure possessed by the wavelet bases, nor the Mallat algorithm to speed up the computation. Since the selected wavelet bases are time-limited (therefore it is not band-limited), it may be not the best choice for approximating differential operators. At this point, we would like to mention the idea of...

## The Geometric Snake

Geometric active contours were introduced by Caselles et al. 1 and Malladi et al. 2 and are based on the theory of curve evolution. Using a reaction-diffusion model from mathematical physics, a planar contour is evolved with a velocity vector in the direction normal to the curve. The velocity contains two terms a constant (hyperbolic) motion term that leads to the formation of shocks3 from which more varied and precise representations of shapes can be derived, and a (parabolic) curvature term...

## Spectral Analysis

In compartmental model fitting, the number of compartments and their interconnection are defined a priori. This implies that the physiological or biochemical pathways are somewhat known. Yet, a priori knowledge about the behavior of novel anticancer drugs may not be available. Further, the compartmental modeling approach assumes well-mixed, homogeneous tracer distribution within the tissue or the ROI. This may not be true for tumor which normally has high degree of heterogeneity. Spectral...

## Quadruple Contrast Enhancement with MRA and MR Spectroscopic Imaging

This approach minimized the false tissue classifications by (1) improving the lesion-to-tissue contrast on MR images by developing a fast imaging pulse sequence that incorporated both cerebrospinal fluid signal attenuation and magnetization transfer contrast (see Fig. 3.33) and (2) including information from MR flow images 24 . In pathologically defined abnormalities in the cortical gray matter (GM) and normal volunteers, high resolution MRI and short echo Figure 3.33 An approach is represented...

## Phase Contrast Angiography

3D PC MRA technique relies on velocity-induced phase shifts to distinguish flowing blood from surrounding tissue. The phase contrast approach can be made sensitive to slow flow in small vessels. The reason for this can be attributed to the fact that the contrast between flowing blood and stationary-tissues is related to blood velocity, rather than stationary-tissue T1. PC angiography also permits excellent cancellation of stationary tissues and offers the potential for quantitative measurements...

## Principles of Magnetization and Flow

The vascular system experiences motion of blood due to continuous flow of blood inside. Precession frequency and gradient field vectors are related. These vectors are represented as spin isochromats. The behavior of the moving spin 1 Department of Medicine, Columbia University, New York, NY 10032, USA 2Electrical Engineering Department, Indian Institute of Technology, New Delhi 10016, India isochromats can be explained as follows S St 0 Y (B + xGx + yGy + zGz) (3.1) where y is gyromagnetic...

## Results

8.6.5.1 Transmission Electron Microscopy Transmission electron microscopy is the process of using transmission images of electron beams to reveal biological structures on very small dimensions. Typically transmission electron microscopy (TEM) datasets are produced using a dye that highlights regions of interest, e.g. the interior of a microscopic structure, such as a cell (see Fig. 8.22(a)). There are technical limits to the projection angles from which data can be measured. These limits are...

## Technical Aspects of the IVUS

The images of ultrasound 7 are based on the reception and transmission of high-frequency sound waves. The transmitted wave propagates through the material until it strikes the reflecting object. The reflected wave returns and is received by a transducer. The time interval between the transmission and the reception of the wave is directly related to the distance between the source and the reflector. The advantage of ultrasound is that it can travel through water smooth tissue. Additionally,...

## Tof

This approach is based on flow-related enhancement in which 2D or 3D GRE techniques are applied (see Fig. 3.6). Usually, FC (flow compensation) is used perpendicular to the lumen of the vessel. So, it relies primarily on flow-related Figure 3.6 Two-dimensional TOF MRA pulse sequence (left) and 3D TOF pulse sequence (right) are shown. Several gradient waveforms are combined to reduce TE. Figure 3.6 Two-dimensional TOF MRA pulse sequence (left) and 3D TOF pulse sequence (right) are shown. Several...

## Stateofthe Art and Applications

In this section, we review two examples of multiscale denoising. To illustrate the power of multiscale analysis, two extreme cases of medical imaging modalities (ultrasound and PET SPECT) with high noise level and complicated noise patterns were considered. A more detailed description of these clinical applications can be found in 59, 60 . 6.3.5.1 Spatial-Temporal Analysis of Real-Time 3D Cardiac Ultrasound Using Brushlet 59 Recent development of a real-time three-dimensional (RT3D) ultrasound...

## MRA Image Reformation

The MR data from MRA images is reformatted and this reformatting plays a major role in vascular anatomy observed in the MRA imaging. The common method for reformatting TOF-MRA uses the technique known as MIP. This technique also generates 3D images of blood vessels with blood motion. The other method for reformatting MRA images is shaded surface display. This method reformats image data in such a way that it appears as if a light is thrown onto structures to generate 3D appearance of...

## Phase Contrast MRA

Phase contrast PC MRA is based on the fact that the phase gain of flowing blood through a gradient is proportional to its velocity assuming constant velocity . Figure 3.14 Two-dimensional Phase contrast pulse sequence left and 3D phase contrast pulse sequence right are shown with velocity-induced phase shift to distinguish stationary and flowing spins. In both 2D 3D PC MRA, two or more acquisitions with opposite polarity of the bipolar flow-encoding gradients are subtracted to produce image of...

## Segmentation From Multiple Nonuniform Volume Datasets

Many of today's volumetric datasets are generated by medical MR, CT, and other scanners. A typical 3D scan has a relatively high resolution in the scanning X-Y plane, but much lower resolution in the axial Z direction. The difference in resolution between the in-plane and out-of-plane samplings can easily range between a factor of 5 and 10, see Fig. 8.9. This occurs both because of physical constraints on the thickness of the tissue to be excited during scanning MR , total tissue irradiation CT...

## Attenuation Correction

One of the most important data correction techniques for PET and also SPECT studies is the correction for attenuation. Although the basic principles of image reconstruction in emission computed tomography PET and SPECT are the same as transmission tomography X-ray CT , there is a distinct difference in these two modalities on the data to be reconstructed. In X-ray CT, image reconstruction gives attenuation coefficient distribution of a known source while scattering is usually ignored. In PET...

## Framework Results

Figure 8.4 presents one slice from an MRI scan of a mouse embryo, and an isosurface model of its liver extracted from the unprocessed dataset. Figure 8.5 presents 3D renderings of the sequence of steps performed on the mouse MRI data to segment the liver. The first step is the initialization, which includes smoothing the input data, thresholding followed by a a flood fill to remove isolated holes, and finally applying morphological operators to remove small gaps and protrusions on the surface....

## Multislice GRE Techniques

These techniques use longer decrease in repetition time TR. As a result, the saturation effects lead to signal loss with the use of larger flip angles. This approach using longer decrease in TR improves the SNR. Other ways are also used to decrease saturation effects. Common use of paramagnetic contrast agent such as gadolinium chelate causes spin-lattice relaxation time T1 shortening of blood see Fig. 3.25 . Consequently, the T1 recovery from short T1 to normal T1 values is faster with less...