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

clearly visible, defined as the discrete left TAC and right TAC, and then the discrete

Nonlinear regression is applied to determine the parameters of the model chosen

*at* þ *b*

*ct*<sup>2</sup> <sup>þ</sup> *dt* <sup>þ</sup> <sup>1</sup> (30)

The rational model (**Figure 5**) showed to be adequate for those seven patients

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

(**Figure 6**), only differentiating by the values of the parameters *a*, *b*,*c*, *d*.

*Cr*ðÞ¼ *t*

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

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

average TAC is generated.

*Recent Advances in Biomechanics*

to approximate *Cr*ð Þ*t* , from a discrete TAC curve.

discrete TAC was not to be adequate.

**Figure 6.**

**Figure 7.**

*images.*

**86**

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 stage.

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

**Figure 8.** *Discrete TACs (P1–P4) and average logistic fitted carotid TAC (Crm(t)) [21].*

the mean of the discrete TACs of four patients (considering left volume), **Figure 8**, with correlation coefficient of 0.9947 (at least) is

PET positron emission tomography

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

ROI region of interest TAC time activity curve VOI volume of Interest

**Author details**

**89**

Jaderson Costa da Costa<sup>2</sup>

Eliete Biasotto Hauser1,2\*, Wyllians Vendramini Borelli2 and

2 Brain Institute of Rio Grande do Sul (BraIns), PUCRS, Porto Alegre, Brazil

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 School of Technology, PUCRS, Porto Alegre, Brazil

\*Address all correspondence to: eliete@pucrs.br

provided the original work is properly cited.

$$C\_r(t) = \frac{[H(t) - H(t - 37.5)]21088.3809}{1 + 1861.3158e^{0.2801t}} + \frac{[H(t - 37.5) - H(t - 3750)]8921.3809}{1 - 1.7712e^{0.03t}}\tag{31}$$

It may be convenient in the diagnosis of Alzheimer's disease to consider the specific time interval seconds, [22, 23]. In this time interval, the graphs in **Figure 8** show the comparison between the values estimated by the function and the concentration of the FDG radiotracer in the left VOI. As we can see, the estimated values between 1170 and 2970 s were close to the original values, with the lowest average relative error is 0.0582 and the highest is 0.1096.

## **6. Conclusion**

The aim this study was described the algorithms of kinetic modeling to analyze the pattern of deposition of amyloid plaques and glucose metabolism in Alzheimer's dementia, obtaining the exact solution of the [11*C*]*PIB* two-tissue reversible compartment model and a [18*F*]*FDG* two-tissue irreversible compartment model. Was solved a system of two first-order differential equations, applying the Laplace transform technique. Many sources of errors are involved in this problem. For example, the gathering data in image processing and the input function construction. With the exception of these errors, is assuring by using Laplace method proposed, there will not be error accumulation.

Longitudinal studies, without arterial blood samples, can assist in the calculation of the dose of medicine, providing the stabilization of cognitive impairment, behavior and the performance of activities of daily living. The technique here described can be used to analyze the pattern of deposition of amyloid plaques, glucose metabolism, the cortical and functional structure of the brain of SuperAgers in relation to cognitively normal elderly and individuals with Alzheimer's dementia. Older adults with exceptional memory ability are coined SuperAgers. Their preserved cognitive capacities with aging may help uncover neuromechanisms of dementia. These individuals showed whole-brain volume similar to middle-aged individuals and some areas thicker than usual agers. Intriguingly, they also exhibited decreased atrophy rate when compared to normal older adults. To our knowledge, their brain functional integrity is yet to be uncovered.

#### **Thanks**

This study was made possible by a team work from all members of the SuperAgers project: Lucas Porcello Schilling, Louise Mross Hartmann, Ana Maria Marques da Silva, Cristina Sebastiao Matushita, Mirna Wetters Portuguez, Alexandre Rosa Franco, and Ricardo Bernardi Soder. This research was partially supported by CNPq, project number 403029/2016-3 FAPERGS, project number 27971.414.15498.22062017.

#### **Nomenclature**


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


the mean of the discrete TACs of four patients (considering left volume), **Figure 8**,

It may be convenient in the diagnosis of Alzheimer's disease to consider the specific time interval seconds, [22, 23]. In this time interval, the graphs in **Figure 8** show the comparison between the values estimated by the function and the concentration of the FDG radiotracer in the left VOI. As we can see, the estimated values between 1170 and 2970 s were close to the original values, with the lowest

The aim this study was described the algorithms of kinetic modeling to analyze the pattern of deposition of amyloid plaques and glucose metabolism in Alzheimer's dementia, obtaining the exact solution of the [11*C*]*PIB* two-tissue reversible compartment model and a [18*F*]*FDG* two-tissue irreversible compartment model. Was solved a system of two first-order differential equations, applying the Laplace transform technique. Many sources of errors are involved in this problem. For example, the gathering data in image processing and the input function construction. With the exception of these errors, is assuring by using Laplace method

Longitudinal studies, without arterial blood samples, can assist in the calculation

This study was made possible by a team work from all members of the SuperAgers project: Lucas Porcello Schilling, Louise Mross Hartmann, Ana Maria Marques da Silva, Cristina Sebastiao Matushita, Mirna Wetters Portuguez, Alexandre Rosa Franco, and Ricardo Bernardi Soder. This research was partially supported by CNPq, project num-

of the dose of medicine, providing the stabilization of cognitive impairment, behavior and the performance of activities of daily living. The technique here described can be used to analyze the pattern of deposition of amyloid plaques, glucose metabolism, the cortical and functional structure of the brain of SuperAgers in relation to cognitively normal elderly and individuals with Alzheimer's dementia. Older adults with exceptional memory ability are coined SuperAgers. Their preserved cognitive capacities with aging may help uncover neuromechanisms of dementia. These individuals showed whole-brain volume similar to middle-aged individuals and some areas thicker than usual agers. Intriguingly, they also exhibited decreased atrophy rate when compared to normal older adults. To our

knowledge, their brain functional integrity is yet to be uncovered.

ber 403029/2016-3 FAPERGS, project number 27971.414.15498.22062017.

<sup>1</sup> <sup>þ</sup> <sup>1861</sup>*:*3158*e*0*:*2801*<sup>t</sup>* <sup>þ</sup> ½ � *H t*ð Þ� � <sup>37</sup>*:*<sup>5</sup> *H t*ð Þ � <sup>3750</sup> <sup>8921</sup>*:*<sup>3</sup>

1 � 1*:*7712*e*0*:*03*<sup>t</sup>*

(31)

with correlation coefficient of 0.9947 (at least) is

*Recent Advances in Biomechanics*

*Cr*ðÞ¼ *<sup>t</sup>* ½ � *H t*ðÞ� *H t*ð Þ � <sup>37</sup>*:*<sup>5</sup> <sup>21088</sup>*:*<sup>3809</sup>

proposed, there will not be error accumulation.

**6. Conclusion**

**Thanks**

**Nomenclature**

**88**

AIF arterial input function CT computed tomography EDI effective dose injected

MIP maximum intensity projection

average relative error is 0.0582 and the highest is 0.1096.

