A Theoretical Model of Benign External Hydrocephalus That Predicts a Predisposition towards Extra-Axial Hemorrhage after Minor Head Trauma

Abstract

Introduction: There is controversy over whether there exists a predisposition towards bleeding into the subdural space in infants with benign external hydrocephalus (BEH) or other enlargement of the extra-axial space (e.g. subdural hygroma). The presumed etiology implicates shear forces in over-stretching the extra-axial blood vessels. We have created a model of the intracranial space that approximates certain aspects of BEH. Using this model, we predict situations where children with BEH will bleed into the extra-axial space when normal infants will not. Methods: The cranial model consists of two spheres representing the brain and the skull. The distance between them represents the width of the extra-axial space. The spheres are concentric (with interspheric distance equal to N) in the normal condition and nonconcentric in BEH. In BEH, the distance between the two spheres varies from N to Q (0 < N ≤ Q) over a 906 M ≤ Q, with the translation orthogonal to the vector of N and parallel to that of M or vice versa), then the final length V_f of a vein V is V_f = (N² + M)^1/2, and the stretch ratio V_f/V_i is: V_f/V_i = (N² + M²)^1/2/N·S_i, with S_i the slack factor, where i represents either n for normal or b for BEH and M = N in the normal condition. Results: Given an equivalent capacity of veins to resist stretch injury (based on the proportion of change in length), for brain translations after a low-impact head injury, stretch ratios for BEH veins range from 1.677 to 3.436, whereas in the normal condition they range from 1.061 to 1.179. Therefore, for an increase in subarachnoid space from 3 (normal) to 6 mm (BEH), brain translocation in BEH will stretch veins beyond an average breaking point when the translation for the normal condition will not. Conclusions: Mathematical modeling of the cranial vault produces a relationship between venous stretch and the width of the extra-axial space. These equations predict an increased frequency of venous stretch injury in the situation of widened extra-axial space. Such venous injury is consistent with forces generated by minor trauma. This relationship, as predicted by our model, could underlie a predisposition towards extra-axial bleeding after minor head trauma in infants with BEH.