Overview
Both spina bifida and anencephaly result from the failure of the neural tube to close. The neural tube is formed by the process called neurulation. This starts at the midbrain and proceeds to the anterior and posterior. The neural tube will give rise to the central nervous system thus the brain and spinal cord.
Here is a brief overview of the process of neurulation.
Firstly the notochord is necessary to induce the formation of the neural plate. The neural tube initially starts as a flat sheet of tissue called the neural plate which thickens after mesoderm induction. The anterior neural tube gives rise to the brain and CNS in the trunk. During neurulation the edges of the neural plate fold rise giving a depression in the midline called the neural groove. The edges continue to rise and fuse forming a tube in the dorsal midline of the embryo. This tube then separates from the adjacent ectoderm giving a sheet above it becoming epidermis. The posterior neural tube in the lumbar region develops in a different way to the anterior neural tube. It starts as a solid rod of cells which then forms a lumen to give a hollow tube.
Neurulation also creates the neural crest cells. These migrate away from the dorsal surface of the neural tube. The neural crest cells give rise to a diverse set of cells for example pigment cells and neurons.
Cell shape changes and cell migration drives neural tube formation. Neural plate cells get longer and thinner in gastrulation in comparison to adjacent ectoderm cells. Cells at the edge of the neural plate which roll upwards are constricted at the apical surface therefore becoming wedge shaped. This change in shape may be the driving force for folding. Constriction is caused by shroom, an actin binding protein. In the posterior neural tube the lumen is still filled with cells, producing a hollow tube involves intercalation of ventral neural cells and migration of the neural crest cells. The separation of the neural tube from what will become epidermis is due to changes in cell adhesiveness.
Article image - The process of neurulation courtesy of Wiki Commons: commons.wikimedia.org/wiki/File:Neural_Crest.png?uselang=en-gb