Quantifying Brain Volume Changes

The presentation of the brain, and peripheral veins (azygos, superior mesenteric and inferior caval) was recorded in deeply anaesthetized rats, with a camera attached to a VMS-004 Discovery Deluxe USB microscope (Veho, USA), before procedure in normal, and then, in rats with ligated superior sagittal sinus 15 min after procedure, before and after therapy as well as at the 15 min, 24 h and 48 h ligation-time before sacrifice. The border of the brain or veins were photographed and marked using ImageJ computer software and then, the surface area (in pixels) of the brain or veins was measured using a measuring function. This was performed with brain photographs before the application and at intervals after the application for both control and treated animals. The brain or veins area before the procedure and application was marked as 100% and the ratio of each subsequent brain area to the first area was calculated ( $\frac{A_2}{A_1}$ ). Starting from square-cube law Equations (1) and (2), an equation for change of brain volume proportional with the change of the brain surface area (6) was derived. In Expressions (1)–(5) l is defined as any arbitrary one-dimensional length of brain (for example rostro-caudal length of the brain); used only for defining one dimensional proportion (l₂/l₁) between two observed brains and as an inter-factor (and because of that not measured (6)) for deriving the final expression [6 (link)]. The procedure was as follows: $A_2=A_1\times {\left(\frac{l_2}{l_1}\right)}^2$ (1) (square-cube law), $V_2=V_1\times {\left(\frac{l_2}{l_1}\right)}^3$ (2) (square-cube law), $\frac{A_2}{A_1}={\left(\frac{l_2}{l_1}\right)}^2$ (3) (from (1), after dividing both sides by A₁), $\frac{l_2}{l_1}=\sqrt{\frac{A_2}{A_1}}$ (4) (from (3), after taking square root of both sides), $\frac{V_2}{V_1}={\left(\frac{l_2}{l_1}\right)}^3$ [5 (link)] (from (2), after dividing both sides by V₁), $\frac{V_2}{V_1}={\left(\sqrt{\frac{A_2}{A_1}}\right)}^3$ (6) (after incorporating expression (4) into Equation (5)).