Intrinsic Geometry of Biological Surface Growth

1. Front Matter

   Pages I-IV

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2. Introduction

   • Philip H. Todd

   Pages 1-14

3. Some Geometrical Models in Biology

   • Philip H. Todd

   Pages 15-63

4. Minimum Dirichlet Integral of Growth Rate as a Metric for Intrinsic Shape Difference

   • Philip H. Todd

   Pages 64-82

5. Curvature of the Ferret Brain

   • Philip H. Todd

   Pages 83-105

6. Back Matter

   Pages 106-132

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1.1 General Introduction The work which comprises this essay formed part of a multidiscip­ linary project investigating the folding of the developing cerebral cortex in the ferret. The project as a whole combined a study, at the histological level, of the cytoarchitectural development concom­ itant with folding and a mathematical study of folding viewed from the perspective of differential geometry. We here concentrate on the differential geometry of brain folding. Histological results which have some significance to the geometry of the cortex are re­ ferred to, but are not discussed in any depth. As with any truly multidisciplinary work, this essay has objectives which lie in each of its constituent disciplines. From a neuroana­ tomical point of view, the work explores the use of the surface geo­ metry of the developing cortex as a parameter for the underlying growth process. Geometrical parameters of particular interest and theoretical importance are surface curvatures. Our experimental portion reports the measurement of the surface curvature of the ferret brain during the early stages of folding. The use of sur­ face curvatures and other parameters of differential geometry in the formulation of theoretical models of cortical folding is dis­ cussed.

• biological
• biology
• biomathematics
• brain
• cortex
• development
• differential geometry
• experiment
• geometry
• growth
• mathematical biology

• Department of Anatomy, Dundee University, Dundee, Scotland

  Philip H. Todd

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