Variance in brain volume with advancing age: implications for defining the limits of normality

Abstract

Background: Statistical models of normal ageing brain tissue volumes may support earlier diagnosis of increasingly common, yet still fatal, neurodegenerative diseases. For example, the statistically defined distribution of normal ageing brain tissue volumes may be used as a reference to assess patient volumes. To date, such models were often derived from mean values which were assumed to represent the distributions and boundaries, i.e. percentile ranks, of brain tissue volume. Since it was previously unknown, the objective of the present study was to determine if this assumption was robust, i.e. whether regression models derived from mean values accurately represented the distributions and boundaries of brain tissue volume at older ages.

Materials and methods: We acquired T1-w magnetic resonance (MR) brain images of 227 normal and 219 Alzheimer's disease (AD) subjects (aged 55-89 years) from publicly available databanks. Using nonlinear regression within both samples, we compared mean and percentile rank estimates of whole brain tissue volume by age.

Results: In both the normal and AD sample, mean regression estimates of brain tissue volume often did not accurately represent percentile rank estimates (errors=-74% to 75%). In the normal sample, mean estimates generally underestimated differences in brain volume at percentile ranks below the mean. Conversely, in the AD sample, mean estimates generally underestimated differences in brain volume at percentile ranks above the mean. Differences between ages at the 5(th) percentile rank of normal subjects were ~39% greater than mean differences in the AD subjects.

Conclusions: While more data are required to make true population inferences, our results indicate that mean regression estimates may not accurately represent the distributions of ageing brain tissue volumes. This suggests that percentile rank estimates will be required to robustly define the limits of brain tissue volume in normal ageing and neurodegenerative disease.

Figure 1. Residual plots (actual minus mean linear regression predicted brain volumes by age) from the normal (top panel; n=227) and AD (bottom panel; n=219) samples.

There are skewed residuals at 70 years in the normal sample (top) and a similar pattern at 85-89 years in the AD sample (bottom). This means that the linearity assumption was in question.

Figure 2. Mean (top panel) and percentile rank (bottom panel) regression estimates of brain tissue volume across age in the normal sample (n=227).

The slopes of these lines represent the beta coefficients in table 4. The mean-based model expects all percentile ranks to change at the same rate, i.e. be parallel. The diverging percentile ranks show that this is not the case and that variance in brain volume generally increased with age in the normal subjects. Although some may appear linear, each line is the result of nonlinear regression (table 4).

Figure 3. Illustration of the varying differences in normal ageing brain tissue volume, according to percentile rank.

There were much greater differences between ages at the 5th percentile of brain tissue volume (bottom panel) than between ages at the 95th percentile (top panel) of normal subjects.

Figure 4. Mean (top panel) and percentile rank (bottom panel) regression estimates of brain tissue volume across age in the AD sample (n=219).

The slopes of these lines represent the beta coefficients in table 5. The mean-based model expects all percentile ranks to change at the same rate, i.e. be parallel. The converging percentile ranks show that this is not the case and variance in brain volume generally decreased with age in the AD subjects. Although some may appear linear, each line is the result of nonlinear regression (table 5).