Abstract

We demonstrate the reconstruction of a 3D, time-varying bolus of radiotracer from first-pass data obtained by the dynamic SPECT imager, FASTSPECT, built by the University of Arizona. The object imaged is a CardioWest Total Artificial Heart. The bolus is entirely contained in one ventricle and its associated inlet and outlet tubes. The model for the radiotracer distribution is a time-varying closed surface parameterized by 162 vertices that are connected to make 960 triangles, with uniform intensity of radiotracer inside. The total curvature of the surface is minimized through the use of a weighted prior in the Bayesian framework. MAP estimates for the vertices, interior intensity and background count level are produced for diastolic and systolic frames, the only two frames analyzed. The strength of the prior is determined by finding the corner of the L-curve. The results indicate that qualitatively pleasing results are possible even with as few as 1780 counts per time frame (total after summing over all 24 detectors). Quantitative estimates of ejection fraction and wall motion should be possible if certain restrictions in the model are removed, e.g., the spatial homogeneity of the radiotracer intensity within the volume defined by the triangulated surface, and smoothness of the surface at the tube/ventricle join.

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References

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  1. W.P. Klein, H.H. Barrett, I. W. Pang, D.D. Patton, M.M. Rogulski, J.J. Sain, and W. Smith OFASTSPECT: Electrical and mechanical design of a high resolution dynamic SPECT imager,O Conference Record of the 1995 IEEE Nucl. Sci. Symp. & Med. Imaging Conf. (IEEE, Los Alamitos, 1996), Vol. 2, pp. 931-933.
    [CrossRef]
  2. K.M. Hanson, OBayesian reconstruction based on flexible prior models,O J. Opt Soc. Amer. A 10, pp. 997- 1004 (1993).
    [CrossRef]
  3. Y. Bresler, J.A. Fessler, and A. Macovski, OA Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,O IEEE Trans. Pattern Anal. Mach. Intell. 11, pp. 840-858 (1989).
    [CrossRef]
  4. P.C. Chiao, W.L. Rogers, N.H. Clinthorne, J.A. Fessler, and A.O. Hero, OModel-based estimation for dynamic cardiac studies using ECT,O IEEE Trans. Med. Imaging 13, pp. 217-226 (1994).
    [CrossRef] [PubMed]
  5. X.L. Battle, G.S. Cunningham, and K.M. Hanson, OTomographic reconstruction using 3D deformable models,O to appear in Phys. Med. Biol., 1998.
    [CrossRef] [PubMed]
  6. http://www.radiology.arizona.edu/~fastspec/detectors.html
  7. M. Kass, A. Witkin, and D. Terzopolous, OSnakes: active contour models,O Int. J. Comput. Vis., pp. 321- 331 (1988).
    [CrossRef]
  8. K.M. Hanson and G.S. Cunningham, OA computational approach to Bayesian inference,O M.M. Meyer and
  9. K.M. Hanson, R.L. Bilisoly, and G.S. Cunningham, OKinky tomographic reconstruction,O Proc. SPIE (SPIE, Bellingham, 1996), Vol. 2710, pp. 156-166.
    [CrossRef]
  10. D.J.C. MacKay, OBayesian interpolation,O Neural Comput. 4, pp. 415-447 (1992).
    [CrossRef]
  11. P.C. Hansen and D.P. OOLeary, OThe use of the L-curve in the regularization of discrete ill-posed problems,O SIAM J. Sci. Comput. 14, pp. 1487-1503 (1993).
    [CrossRef]
  12. Y. Bresler, J.A. Fessler, and A. Macovski, OA Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,O IEEE Trans. Pattern Anal. Mach. Intell. 11, pp. 840-858 (1989).

Other (12)

W.P. Klein, H.H. Barrett, I. W. Pang, D.D. Patton, M.M. Rogulski, J.J. Sain, and W. Smith OFASTSPECT: Electrical and mechanical design of a high resolution dynamic SPECT imager,O Conference Record of the 1995 IEEE Nucl. Sci. Symp. & Med. Imaging Conf. (IEEE, Los Alamitos, 1996), Vol. 2, pp. 931-933.
[CrossRef]

K.M. Hanson, OBayesian reconstruction based on flexible prior models,O J. Opt Soc. Amer. A 10, pp. 997- 1004 (1993).
[CrossRef]

Y. Bresler, J.A. Fessler, and A. Macovski, OA Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,O IEEE Trans. Pattern Anal. Mach. Intell. 11, pp. 840-858 (1989).
[CrossRef]

P.C. Chiao, W.L. Rogers, N.H. Clinthorne, J.A. Fessler, and A.O. Hero, OModel-based estimation for dynamic cardiac studies using ECT,O IEEE Trans. Med. Imaging 13, pp. 217-226 (1994).
[CrossRef] [PubMed]

X.L. Battle, G.S. Cunningham, and K.M. Hanson, OTomographic reconstruction using 3D deformable models,O to appear in Phys. Med. Biol., 1998.
[CrossRef] [PubMed]

http://www.radiology.arizona.edu/~fastspec/detectors.html

M. Kass, A. Witkin, and D. Terzopolous, OSnakes: active contour models,O Int. J. Comput. Vis., pp. 321- 331 (1988).
[CrossRef]

K.M. Hanson and G.S. Cunningham, OA computational approach to Bayesian inference,O M.M. Meyer and

K.M. Hanson, R.L. Bilisoly, and G.S. Cunningham, OKinky tomographic reconstruction,O Proc. SPIE (SPIE, Bellingham, 1996), Vol. 2710, pp. 156-166.
[CrossRef]

D.J.C. MacKay, OBayesian interpolation,O Neural Comput. 4, pp. 415-447 (1992).
[CrossRef]

P.C. Hansen and D.P. OOLeary, OThe use of the L-curve in the regularization of discrete ill-posed problems,O SIAM J. Sci. Comput. 14, pp. 1487-1503 (1993).
[CrossRef]

Y. Bresler, J.A. Fessler, and A. Macovski, OA Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,O IEEE Trans. Pattern Anal. Mach. Intell. 11, pp. 840-858 (1989).

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Figures (6)

Fig. 1.
Fig. 1.

Raw data for a) diastolic frame and c) systolic frame. Predicted detector Poisson rates for b) diastolic frame and d) systolic frame using MAP solution with α=0.2.

Fig. 2.
Fig. 2.

BIE canvas used to analyze SPECT data. The triangulated surface box at the far left contains x. It is transformed into a voxellated grid, f, and then by the matrix, H, to produce Hf(x). Finally it is multplied by the intensity, I, and the additive background constant, s, is added, to produce the predicted detector pixel rates g=IHf(x)+s.

Fig. 3.
Fig. 3.

The L-curve for the diastolic frame.

Fig. 4.
Fig. 4.

MAP reconstructions of the bolus boundary surface using a) α=3.2, b) α=0.2, and c) α=0.1.

Fig. 5.
Fig. 5.

Comparison between diastolic and systolic frame reconstructions: a) diastolic frame is wireframe and systolic frame is solid surface, b) diastolic frame is solid surface and systolic frame is wireframe. See http://planck.lanl.gov/~cunning/3D for an interactive Java display of the reconstructions. [Media 1]

Fig. 6.
Fig. 6.

Cut planes through the reconstructions in Fig. 5. Red lines are for diastolic frame and green lines are for systolic frame. Z-slices are a) -8 mm, b) -4 mm, c) 0 mm, d) 4 mm, e) 8 mm, and f) 12 mm.

Equations (5)

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π ( x ) = i A i ( j [ tan ( θ ij 2 ) l ij ] 2 ) ,
ϕ x I s = ln Prob [ data predicted data ]
= i [ k i ln g i + g i ] ,
x MAP ( α ) = arg min x [ ϕ x I s + α π ( x ) ] ,
( ϕ ( x MAP ( α ) ) , π ( x MAP ( α ) ) ) ,

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