**5.1** *Cr*ð Þ*<sup>t</sup>* **for [11***C***]***PIB* **radiotracer**

For [11*C*]*PIB* tracer is chosen as reference region the left and right cerebellum, known to be amyloid free illustrated in **Figure 4**. The left and right cerebellum are

**Figure 4.** *Region of reference outlined in both cerebellar gray matter in a sagittal (left) and coronal (right) slices.*

**Figure 5.** *Discrete and fitted rational cerebellum TAC (Cr(t)): the best model.*

clearly visible, defined as the discrete left TAC and right TAC, and then the discrete average TAC is generated.

Nonlinear regression is applied to determine the parameters of the model chosen to approximate *Cr*ð Þ*t* , from a discrete TAC curve.

The rational model (**Figure 5**) showed to be adequate for those seven patients (**Figure 6**), only differentiating by the values of the parameters *a*, *b*,*c*, *d*.

$$C\_r(t) = \frac{at + b}{ct^2 + dt + 1} \tag{30}$$

**5.2** *Cr*ð Þ*<sup>t</sup>* **for [18***F***]***FDG* **radiotracer**

*Biomechanical Model Improving Alzheimer's Disease DOI: http://dx.doi.org/10.5772/intechopen.92047*

stage.

**Figure 8.**

**87**

*Discrete TACs (P1–P4) and average logistic fitted carotid TAC (Crm(t)) [21].*

In order to obtain *Cr*ð Þ*<sup>t</sup>* for [18*F*]*FDG* radiotracer, the carotids are chosen as reference region. Manually, it is defined as volumes-of-interests (VOIs), illustrated in **Figure 7**, using a biomedical image quantification software PMOD. Over which the left and right carotid arteries where clearly visible, is defined discrete TAC. Then, it may be appropriate to estimate the *Cr*ð Þ*t* considering the fast and slow

After this, we apply regression techniques, and in two stages of the time, a good option that came up was the piecewise function logistical to describe the behavior of

The technique was applied for 7 patients considering the activity for the reference regions: right cerebellum, left cerebellum, and also for the mean of both (total of 24 simulations). The minor *R*<sup>2</sup> was 0.96421. The attempt to use an average of all discrete TAC was not to be adequate.

**Figure 6.** *Average (MdM) and rational fitted cerebellum time active (P1,P3-P8) curve (Cr(t)).*

**Figure 7.** *Region of reference outlined in the left carotid artery region in a coronal slice in both PET (left) and MIP (right) images.*
