fMRI‐based method to describe human brain size as a function of age and height
Authors: Obatusin Mosadoluwa O. , Reyes Levy A. , Serrador Jorge M , Wylie Glenn D 
Published: November 2023

Brain size may not matter, but proportions sure do. Haller's Rule, which holds that brains of smaller animals must take up more room to function, has been a landmark principle for all who have considered brain size. Since, the brain is part of the body, it is important to know the relationships of brain size to body size. To date, there has not been a method that assesses brain size using functional magnetic resonance imaging (fMRI). all other methods described in literature are based on autopsy and MRI [Filipek et al. (1994), Caviness et al. (1996), Courchesne et al. (2000), Dekaban and Sadowsky (1978), Dobbing and Sands (1973), Giedd et al. (1996), Kretschmann et al. (1979)].We reviewed literature comparing brain size to body height and body size. An equation commonly found in literate states that brain size can be computed based on the total amount of energy available to sustain it. This basis is used to derive the equation BM (e) = 1.77 * (W0.76) where BM (e) predicts brain mass, in grams, and W = body mass, in grams [Martin 1981]. The most recent equation in literature characterizing brain size is based on an adjustment to equations proposed by Birch [Birch 1999] and another proposed by Riddle [Riddle et al. (2010)] is Y = y1 * (1 + P4*X+P5*X2) where Y is the brain size in the modified equation, X is age, y1 is the brain size for the original unmodified Birch equation, P1–5 are parameters. The equations demonstrate that the size of the human brain at different development stages can be predicted both gender and age.The aforementioned equations chosen from literature, and the equation developed by us were fit to the subset of data obtained from volunteers in the study examining cognitive fatigue in Gulf War Illness using fMRI. These participants included 9 healthy male volunteer subjects, between the age of 42 and 64 years old, average age of 49 years old. Brain tissue volume, normalized for subject head size, was estimated with SIENAX [Smith 2001, Smith 2002], part of FSL [Smith 2004]. The conversion of volume in cubic millimeter to Kilogram (kg) was computed by multiplying the volume by the human brain density of 1.01 × 10^‐6 Kg/cubic millimeter (Brain size range: 1.42Kg – 1.56 Kg), average: 1.48 Kg, Standard deviation: 0.041, SEM: 0.013). The average body mass is 99.38 Kg, average height is 1.79 m. We calculated the percent difference between the models and the percent difference between the brain sizes computed using the models and the actual brain size obtained from fMRI. The estimated brain sizes from both models were vastly different. We calculated over 100% error using Martins equation, whereas we calculated a 4.1% error using the equation proposed by Riddle. Martins use of an allometric exponent value a = 0.76 as suggested for placental mammals vastly overestimates brain sizes for humans. This is directly relevant to accurately determining brain size based not just on body weight but taking into consideration age and height. Furthermore, this finding suggests the need for a new empirical formula predicting brain size using a modern method such as fMRI. fMRI would serve as a better model to empirically derive an accurate equation since it would take into account deviations in regional brain size in clinical samples, which is often the limitation of other methods utilizing autopsy and MRI.