Kluwer - Handbook of Biomedical Image Analysis Vol

improved blood suppression methods are promising for accurate imaging by dual-inversion 3D FSE imaging sequence with real-time navigator technology for high-resolution, free-breathing black-blood CMRA, delineation of coronary artery by echoplanar imaging. In general, in future, high-resolution MRA seems well suited to 3.0 T MR field strength since spatial resolution is often limited by S/N at 1.5 T. Initial feasibility of CMRA for intracranial and cervical studies is encouraging. 3.0 T and higher magnetic field scanners with superior field strength for 3DTOF and is extremely promising for 3DTOF and CMRA. The CMRA has advantages of shorter scan time and better depiction of slow flow hence it was the attention in last decade with combination of other modalities.

Questions

1.What do you understand by term MRA?

2.How spatial encoding, spatial resolution show relationship?

3.What are MRA k-space trajectories and how do they are applied?

4.What are the unique properties of blood and MRA contrast agents?

5.How ‘Black blood MRA’ is unique and significant?

6.What are newer approaches commonly known as Bright blood MRA with t extragenous contrast?

7.How both Cine MRI and PC MRA are comparable?

8.How contrast enhanced bright blood MRA is unique and better clinical imaging modality?

9.What is present state-of -art in quantitative analysis of MRA images?

10.What are advanced approaches in vessel detection and artery-vessel separation in MRA image data sets?

Bibliography

[1]Maki, J. H., Wilson, G. J., Eubank, W. B., and Hoogeveen, R. M., Utilizing SENSE to achieve lower station sub-millimeter isotropic resolution and minimal venous enhancement in peripheral MR angiography, J. Magn. Reson. Imaging, Vol. 15, No. 4, pp. 484–491, 2002.

[2]Hoffmann, U., Loewe, C., Bernhard, C., Weber, M., Cejna, M., Herold, C. J., and Schima, W., MRA of the lower extremities in patients with pulmonary embolism using a blood pool contrast agent: Initial experience, J. Magn. Reson. Imaging, Vol. 15, No. 4, pp. 429–437, 2002.

[3]Carriero, A., Maggialetti, A., Pinto, D., Salcuni, M., Mansour, M., Petronelli, S., and Bonomo, L., Contrast-enhanced magnetic resonance angiography MoBI-trak in the study of peripheral vascular disease, Cardiovasc. Intervent Radiol. Vol. 25, No. 1, pp. 42–47, 2002.

[4]Sutherland, G. R., Kaibara, T., Wallace, C., Tomanek, B., and Richter, M., Intraoperative assessment of aneurysm clipping using magnetic resonance angiography and diffusion-weighted imaging: Technical case report, Neurosurgery Vol. 50, No. 4, pp. 893–898, 2002.

[5]Kalden, P., Mohrs, O., Kreitner, K. F., Thelen, M., and Schreiber, W. G., Preliminary results of coronary artery examination using a 3D-navigator sequence on a high performance MR system, Rofo Fortschr Geb Rontgenstr Neuen Bildgeb Verfahr Vol. 174, No. 2, pp. 183–186, 2002.

[6]Sardanelli, F., Zandrino, F., Molinari, G., Iozzelli, A., Balbi, M., and Barsotti, A., MR evaluation of coronary stents with navigator echo and breath-hold cine gradient-echo techniques, Eur. Radiol., Vol. 12, No. 1, pp. 193–200, 2002.

[7]Ho, S. S., Chan, Y. L., Yeung, D. K., and Metreweli, C., Blood flow volume quantification of cerebral ischemia: comparison of three noninvasive imaging techniques of carotid and vertebral arteries, AJR Am. J. Roentgenol., Vol. 178, No. 3, pp. 551–556, 2002.

[8]Carr, J. C., Ma, J., Desphande, V., Pereles, S., Laub, G., and Finn, J. P., High-resolution breath-hold contrast-enhanced MR angiography of

the entire carotid circulation. AJR Am. J. Roentgenol., Vol. 178, No. 3,

pp.543–549, 2002.

[9]Huber, M. E., Oelhafen, M. E., Kozerke, S., Weber, O. M., and Boesiger, P., Single breath-hold extended free-breathing navigator-gated threedimensional coronary MRA, J. Magn. Reson. Imaging, Vol. 15, No. 2,

pp.210–214, 2002.

[10]Stuber, M., Bornert, P., Spuentrup, E., Botnar, R. M., and Manning, W. J., Selective three-dimensional visualization of the coronary arterial lumen using arterial spin tagging, Magn. Reson. Med., Vol. 47, No. 2, pp. 322– 329, 2002.

[11]Holmqvist, C., Stahlberg, F., Hanseus, K., Hochbergs, P., Sandstrom, S., Larsson, E. M., and Laurin, S., Collateral flow in coarctation of the aorta with magnetic resonance velocity mapping: correlation to morphological imaging of collateral vessels, J. Magn. Reson. Imaging, Vol. 15, No. 1,

pp.39–46, 2002.

[12]Greil, G. F., Powell, A. J., Gildein, H. P., and Geva, T., Gadoliniumenhanced three-dimensional magnetic resonance angiography of pulmonary and systemic venous anomalies, J. American Coll. Cardiol., Vol. 39, No. 2, pp. 335–341, 2002.

[13]Naganawa, S., Koshikawa, T., Fukatsu, H., Sakurai, Y., Ichinose, N., Ishiguchi, T., and Ishigaki, T., Contrast-enhanced MR angiography of the carotid artery using 3D time-resolved imaging of contrast kinetics: comparison with real-time fluoroscopic triggered 3D-elliptical centric view ordering, Radiat. Med., Vol. 19, No. 4, pp. 185–192, 2001.

[14]McGee, K. P., Felmlee, J. P., Jack, C. R. Jr., Manduca, A., Riederer, S. J., and Ehman, R. L., Autocorrection of three-dimensional time-of-flight MR angiography of the Circle of Willis, AJR Am. J. Roentgenol., Vol. 176 No. 2, pp. 513–518, 2001.

[15]Amann, M., Bock, M., Floemer, F., Schoenberg, S. O., Schad, L. R., Three-dimensional spiral MR imaging: Application to renal multiphase contrast-enhanced angiography, Magnetic Resonance in Medicine, Vol. 48, No. 2, pp. 290–296, 2002.

[16]Jeong, E. K., Parker, D. L., Tsuruda, J. S., and Won, J. Y., Reduction of flow-related signal loss in flow-compensated 3D TOF MR angiography, using variable echo time (3D TOF-VTE), Magn. Reson. Med., Vol. 48, No. 4, pp. 667–676, 2002.

[17]Spuentrup, E., Manning, W. J., Bornert, P., Kissinger, K. V., Botnar, R. M., and Stuber, M., Renal arteries: navigator-gated balanced fast field-echo projection MR angiography with aortic spin labeling: initial experience, Radiology, Vol. 225, No. 2, pp. 589–596, 2002.

[18]Bernstein, M. A., Huston, J., III, Lin, C., Gibbs, G. F., and Felmlee, J. P., High-resolution intracranial and cervical MRA at 3. 0 T: Technical considerations and initial experience, Magn. Reson. Med., Vol. 46, No. 5, 955–962, 2001.

[19]Azhari, H., McKenzie, C. A., and Edelman, R. R., MR angiography using spin-lock flow tagging, Magn. Reson. Med., Vol. 46, No. 5, pp. 1041–1044, 2001.

[20]Overall, W. R., Conolly, S. M., Nishimura, D. G., and Hu, B. S., Oscillating dual-equilibrium steady-state angiography, Magn. Reson. Med., Vol. 47, No. 3, pp. 513–522, 2002.

[21]Amano, Y., Amano, M., Matsuda, T., Tsuchihashi, T., Takahama, K., and Kumazaki, T., Fat-suppressed three-dimensional MR angiography technique with elliptical centric view order and no prolonged breathholding time, J. Magn. Reson. Imaging, Vol. 16, No. 6, pp. 707–715, 2002.

[22]Kim, J. H., Kim, T. K., Eun, H. W., Kim, B. S., Lee, M. G., Kim, P. N., and Ha, H. K., Preoperative evaluation of gall bladder carcinoma: Efficacy of combined use of MR imaging, MR cholangiography, and contrastenhanced dual-phase three-dimensional MR angiography, J. Magn. Reson. Imaging, Vol. 16, No. 6, pp. 676–684, 2002.

[23]Duran, M., Schoenberg, S. O., Yuh, W. T., Knopp, M. V., van Kaick, G., and Essig, M., Cerebral arteriovenous malformations: morphologic evaluation by ultrashort 3D gadolinium-enhanced MR angiography, Euro. Radiol., Vol. 12, No. 12, pp. 2957–2964, 2002.

[24]Sharma, R., Narayana, P. A., and Wolinsky, J. S., Grey matter abnormalities in multiple sclerosis: proton magnetic resonance spectroscopic imaging. Multiple Sclerosis, Vol. 7, No. 4, pp. 221–226, 2001.

[25]Danias, P. G., Stuber, M., Botnar, R. M., Kissinger, K. V., Yeon, S. B., Rofsky, N. M., and Manning, W. J. Coronary MR angiography clinical applications and potential for imaging coronary artery disease. Magn. Reson. Imaging Clini. North Am., Vol. 11, No. 1, pp. 81–99, 2003.

[26]Markl, M., Chan, F. P., Alley, M. T., Wedding, K. L., Draney, M. T., Elkins,

C.J., and Parker, D. W., Wicker, R., Taylor, C. A., Herfkens, R. J., Pelc, N. J. Time-resolved three-dimensional phase-contrast MRI. J. Magn. Reson. Imaging, Vol. 17, No. 4, pp. 499–506, 2003.

[27]Langerak, S. E., Vliegen, H. W., Jukema, J. W., Kunz, P., Zwinderman,

A.H., and Lamb, H. J., van der Wall, E. E., and de Roos, A. Value of magnetic resonance imaging for the noninvasive detection of stenosis in coronary artery bypass grafts and recipient coronary arteries. Circulation., Vol. 107, No. 11, pp. 1502–1508, 2003.

[28]Regenfus, M., Ropers, D., Achenbach, S., Schlundt, C., Kessler, W., Laub, G., Moshage, W., and Daniel, W. G. Diagnostic value of maximum intensity projections versus source images for assessment of contrastenhanced three-dimensional breath-hold magnetic resonance coronary angiography. Invest. Radiol., Vol. 38, No. 4, pp. 200–206, 2003.

[29]McCarthy, R. M., Shea, S. M., Deshpande, V. S., Green, J. D., Pereles,

F.S., Carr, J. C., Finn, J. P., and Li, D. Coronary MR angiography: true FISP imaging improved by prolonging breath holds with preoxygenation in healthy volunteers. Radiology., Vol. 227, No. 1, pp. 283–288, 2003.

[30]Bogaert, J., Kuzo, R., Dymarkowski, S., Beckers, R., Piessens, J., and Rademakers, F. E. Coronary artery imaging with real-time navigator three-dimensional turbo-field-echo MR coronary angiography: initial experience Radiology., Vol. 226, No. 3, pp. 707–16, 2003.

[31]Bunce, N. H., Lorenz, C. H., Keegan, J., Lesser, J., Reyes, E. M., Firmin,

D.N., and Pennell, D. J. Coronary artery anomalies: assessment with

free-breathing three-dimensional coronary MR angiography. Radiology., Vol. 227, No. 1, pp. 201–208, 2003.

[32]Hardy, C. J., Zhao, L., Zong, X., Saranathan, M., and Yucel, E. K. Coronary MR angiography: respiratory motion correction with BACSPIN. J. Magn. Reson. Imaging, Vol. 17, No. 2, pp. 170–176, 2003.

[33]Plein, S., Jones, T. R., Ridgway, J. P., and Sivananthan, M. U. Threedimensional coronary MR angiography performed with subject-specific cardiac acquisition windows and motion-adapted respiratory gating. AJR Am. J. Roentgen., Vol. 180, No. 2, pp. 505–512, 2003.

[34]Huber, M. E., Paetsch, I., Schnackenburg, B., Bornstedt, A., Nagel, E., Fleck, E., Boesiger, P., Maggioni, F., Cavagna, F. M., and Stuber, M. Performance of a new gadolinium-based intravascular contrast agent in free-breathing inversion-recovery 3D coronary MRA. Magn. Reson. Med., Vol. 49, No. 1, pp. 115–121, 2003.

The second fundamental idea was the adaptation of numerical methods developed for hyperbolic conservation laws. The field of numerical hyperbolic conservation laws is a mature field with a substantial body of research devoted to both the theory and practice of these methods. Much of this field is concerned with the construction of numerical flux functions, which approximate the physical flux function in a way which respects the propagating characteristics of the problem. The resulting numerical methods more accurately compute the speeds for propagating shocks, and find the unique entropy condition satisfying rarefaction fans. In [102], Sethian observed that the theory of hyperbolic conservation laws could be applied to the problem of propagating interfaces. This naturally led to [85], where the equation for propagating the interface using the implicit representation was formulated as the integral of a hyperbolic conservation law. In the context of moving interfaces, the shocks became corners in the interface, and the rarefaction fans became regions of interface expansion.

The coupling of the numerical hyperbolic conservation laws with the implicit representation led to the first level set method, which was demonstrated to be a powerful, robust method for solving the flame propagation problem.

Though the level set method, in its original form, was successful for the original application, it was soon observed by Chopp [19] that a fundamental problem in the method still existed. At that point, nearly all of the applications of the level set method involved interface speed functions which depended solely upon mean curvature. This class of problems is very special, as indicated in [39–42], because the embedding function maintained bounded gradients almost everywhere, giving the method additional stability properties. This property does not hold for a general interface speed function, and so for the level set method to be generalizable, one important modification was required in order to maintain a stable level set method.

The key modification to the level set method, proposed in [19], was to observe that forcing the embedding function to maintain bounded gradients was possible, without changing the underlying motion of the interface. This process was called reinitialization, and it essentially forced the embedding function to be the signed distance function, even if the level set evolution equation would not do it on its own. Once this piece was added to the level set method toolbox, the level set method exploded in popularity, being used in a wide array of interface motion applications.

In the remainder of this chapter, we will begin by giving a more detailed description of the basic level set method. Next, some of the recent modifications to the method will be explored, particularly those relevant to the medical imaging community. The chapter will conclude with a brief review of the myriad applications of the level set and fast marching methods that have been published over the last few years.

4.2 Basic Level Set Method

In this section, the necessary pieces for implementing the general level set method are presented. These include the implicit representation of the interface, the equation which describes interface motion, and the gradient control process. There are now two methods for gradient control: reinitialization and velocity extensions. Both of these methods will require some background information on the fast marching method for implementation. The fast marching method is an interesting method in its own right, and a description of this method will also be presented.

4.2.1 The Level Set Representation

At the heart of the level set method is the implicit representation of the interface. If the interface is given by , can then be represented by a function φ, called the level set function, defined by the signed distance function

Here d (x) is the distance from the point x to the interface , and the sign is determined so that it is negative on the inside and positive on the outside. At any time, the interface can be recovered by locating the set

For example, a circle interface and the corresponding level set function representation are shown in Fig. 4.1.

For most applications, this representation works well, but there are interfaces which cannot use it. For example, interfaces with triple junctions or any interface which does not have a clearly defined inside and outside cannot easily

graph of ϕ

level set ϕ = 0

Figure 4.1: Example of a level set representation of a circle.

be represented using a level set function. However, the level set method, with some modifications, can even be applied to these cases as well. These variations will be discussed in Section 4.3.

Once the level set function, φ, is constructed, the evolution equation for the interface must be rewritten in terms of φ. Given the interface , let F(x) be the speed of the interface in the direction of the normal (see Fig. 4.2). Let x(t) be a point on the interface which evolves with the interface, then φ(x(t), t) ≡ 0 for all t. Differentiating with respect to t gives

where n is the unit normal to the interface. Use the fact that the unit normal can also be computed to be n = φ/ φ , and substituting this with Eq. 4.4 into

ϕ

Fn = F || ϕ||

x(t)

ϕ = 0

Figure 4.2: Illustration of the relationship between φ(x, t), x, and F.