Motion Estimation - Motion Correction in Thoracic Positron Emission Tomography - page 60

Validation

We perform a validation of the patient data based on the range of the Jacobian
determinant and the NCC defined in Eqs. ( 2.91 ) and ( 2.92 ). The minimum of
all Jacobian maps (for all patients and all gates) is 0

. 340 and the maximum is

2 375. As no negative or too large values appear we can ensure that no unwanted

foldings occur in the estimated transformations. For the NCC we can observe an
improvement from 0

.

002 on average across all patients. For the
most challenging gates in relation to the reference gate, i.e., heart in systole and heart
in maximum inspiration, we found an increase from 0

. 88 ± 0 . 07 to 0 . 97 ± 0 .

. 80 ± 0 . 06 to 0 . 97 ± 0 . 001 and

0 002, respectively. Figure 2.12 illustrates the average NCC

values for the cardiac and respiratory phases individually. The two most challenging
phases are gate two in Fig. 2.12 a, representing the systole, and gate five in Fig. 2.12 b,
representing the gate in maximum inspiration.

. 79 ± 0 . 06 to 0 . 97 ± 0 .

a b

1 1

0.9 0.9

uncorrected
corrected

uncorrected
corrected 0.8 0.8

1 2 3 4 5 1 2 3 4 5

Gates Gates

Fig. 2.12 The average NCC before and after motion correction is plotted for all cardiac ( a )and
respiratory ( b ) gates for the patient data (The plots are taken from [ 51 ]. c 2011 IEEE)

Attenuation Correction

Additional corrections like scatter and attenuation correction are necessary to make
the presented results quantitative [ 38 ]. As attenuation correction is not the focus
of this chapter we give only a short outlook. According to the method proposed
by Bai and Brady [ 8 ] we perform an image-based attenuation correction. The idea
of their attenuation correction approach is to reconstruct the PET reference gate R

AC ,AC

twice - once with attenuation correction ( R = Attenuation Corrected) and

NAC ,NAC

once without ( Non-Attenuation Corrected). Hence, an additional CT

scan that matches the reference PET gate

R =

R is required. The Attenuation Coefficient

AC

= R

ACF

Factor (ACF) image I

NAC of the two reference images is computed. For the

R

reference gate it holds