Quantitation, regional vulnerability, and kinetic modeling of brain glucose metabolism in mild Alzheimer’s disease

Abstract

Purpose

To examine CMRglc measures and corresponding glucose transport (K ₁ and k ₂) and phosphorylation (k ₃) rates in the medial temporal lobe (MTL, comprising the hippocampus and amygdala) and posterior cingulate cortex (PCC) in mild Alzheimer’s disease (AD).

Methods

Dynamic FDG PET with arterial blood sampling was performed in seven mild AD patients (age 68 ± 8 years, four females, median MMSE 23) and six normal (NL) elderly (age 69 ± 9 years, three females, median MMSE 30). Absolute CMRglc (μmol/100 g/min) was calculated from MRI-defined regions of interest using multiparametric analysis with individually fitted kinetic rate constants, Gjedde-Patlak plot, and Sokoloff’s autoradiographic method with population-based rate constants. Relative ROI/pons CMRglc (unitless) was also examined.

Results

With all methods, AD patients showed significant CMRglc reductions in the hippocampus and PCC, and a trend towards reduced parietotemporal CMRglc, as compared with NL. Significant k ₃ reductions were found in the hippocampus, PCC and amygdala. K ₁ reductions were restricted to the hippocampus. Relative CMRglc had the largest effect sizes in separating AD from NL. However, the magnitude of CMRglc reductions was 1.2- to 1.9-fold greater with absolute than with relative measures.

Conclusion

CMRglc reductions are most prominent in the MTL and PCC in mild AD, as detected with both absolute and relative CMRglc measures. Results are discussed in terms of clinical and pharmaceutical applicability.

Appendix

a) Multiparametric method with individually derived kinetic rate constants (KIN)

The three-compartment FDG model is described by the differential equations [14, 16]:

$$ \begin{array}{*{20}c} {\frac{{dC_{E} }} {{dt}} = k_{1} C_{P} - {\left( {k_{2} + k_{3} } \right)}C_{E} + k_{4} C_{M} } \\ {\frac{{dC_{M} }} {{dt}} = k_{3} C_{E} - k_{4} C_{M} } \\ {C_{i} = C_{E} + C_{M} } \\ \end{array} $$

where

C _p is the concentration of FDG in plasma, C _E is the concentration of free FDG in tissue, C _M is the concentration of phosphorylated FDG in tissue, and C _i is the total concentration of FDG in tissue. With t <60 min, k ₄ is negligibly small.

The solution of the differential equations becomes:

$$ C_{i} {\left( t \right)} = \frac{{k_{1} }} {{k_{2} + k_{3} }}{\left( {k_{3} + k_{2} e^{{ - {\left( {k_{2} + k_{3} } \right)}t}} } \right)} \otimes C_{p} {\left( t \right)} $$

where ⊗ denotes the convolution:

$$ f{\left( t \right)} \otimes g{\left( t \right)} = {\int_0^t {f{\left( s \right)}g{\left( {t - s} \right)}ds} } $$

The kinetic constants K ₁–k ₃ are estimated by fitting the measured values of C _P and C _i in the equation using a non-linear least-square iterative method. The glucose metabolic rate R _i is then computed as:

$$ R_{i} = \frac{{C^{'}_{P} }} {{LC}} \times \frac{{k_{1} k_{3} }} {{k_{2} + k_{3} }} $$

where$C^{\prime }_{P}$ is the concentration of glucose in plasma and LC is the lumped constant=0.52 [17].

b) Gjedde-Patlak method with plasma sampling (PAT)]

In the graphic PAT method [15], R _i is computed as in a) by using the dynamic PET images and the input function C _p , and $K_{i} = \frac{{k_{1} k_{3} }} {{k_{2} + k_{3} }}$ is estimated as the slope of a Patlak plot:

$$ y{\left( t \right)} = K_{i} x{\left( t \right)} + b $$

where

$$ \begin{array}{*{20}c} {y{\left( t \right)} = \frac{{C_{i} {\left( t \right)}}} {{C_{P} {\left( t \right)}}}} \\ {x{\left( t \right)} = \frac{{{\int_0^t {C_{P} {\left( s \right)}ds} }}} {{C_{P} {\left( t \right)}}}} \\ \end{array} $$

c) Sokoloff’s autoradiographic method with population-based rate constants (ARG)

In the ARG method [16, 17], C _i is measured at only one time point from the PET_sum image, and R _i is computed with a correction factor:

$$ R_{i} = \frac{{C^{\prime }_{P} }} {{LC}} \times \frac{{k_{1} k_{3} }} {{k_{2} + k_{3} }} \times \frac{{C_{i} - C_{E} }} {{C_{M} }} $$

where

C _E and C _M are computed from the standard kinetic constants k’s derived from a normative population: K ₁=0.095 ml/min/100 g, k ₂=0.125 1/min, k ₃=0.069 1/min [17], $C^{\prime }_{P}$ is the concentration of glucose in plasma, and LC is the lumped constant=0.52 [17].