Papasian N C, Frim D M
Section of Pediatric Neurosurgery, University of Chicago Children's Hospital, Chicago, Ill 60637, USA.
Pediatr Neurosurg. 2000 Oct;33(4):188-93. doi: 10.1159/000055951.
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.
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) = (N(2) + M)(1/2), and the stretch ratio V(f)/V(i) is: V(f)/V(i) = (N(2) + M(2))(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.
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.
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.
对于患有良性外部脑积水（BEH）或其他轴外间隙扩大（如硬膜下积液）的婴儿是否存在硬膜下间隙出血的易感性存在争议。推测的病因涉及剪切力过度拉伸轴外血管。我们创建了一个颅内空间模型，该模型近似于BEH的某些方面。使用这个模型，我们预测了BEH患儿在正常婴儿不会出血的情况下轴外间隙出血的情况。
颅骨模型由代表大脑和颅骨的两个球体组成。它们之间的距离代表轴外间隙的宽度。在正常情况下，球体是同心的（球间距离等于N），而在BEH中是非同心的。在BEH中，两个球体之间的距离在906 M≤Q的范围内从N变化到Q（0 < N≤Q），平移方向与N向量正交且与M向量平行，或者反之亦然），那么静脉V的最终长度V(f)为V(f) = (N(2) + M)(1/2)，拉伸比V(f)/V(i)为：V(f)/V(i) = (N(2) + M(2))(1/2)/N.S(i)，其中S(i)为松弛因子，i代表正常情况的n或BEH的b，且在正常情况下M = N。
假设静脉抵抗拉伸损伤的能力相同（基于长度变化的比例），对于低冲击性头部损伤后的脑平移情况，BEH静脉的拉伸比范围为1.677至3.436，而在正常情况下范围为1.061至1.179。因此，对于蛛网膜下腔从3（正常）增加到6毫米（BEH）的情况，BEH中的脑移位将使静脉拉伸超过平均断裂点，而正常情况下的平移不会。
颅穹窿的数学建模产生了静脉拉伸与轴外间隙宽度之间的关系。这些方程预测在轴外间隙增宽的情况下静脉拉伸损伤的频率会增加。这种静脉损伤与轻微创伤产生的力一致。正如我们的模型所预测的，这种关系可能是BEH婴儿在轻微头部创伤后轴外出血易感性的基础。
