In my article on obesity, I argued that calcium deficiency plays an important role because calcium is necessary for the release of insulin from the pancreas and for the uptake of glucose by the muscles. Obesity is strongly associated with both calcium deficiency and insulin resistance, and I argue that the fat cells compensate by inserting themselves into the energy chain. They take upon themselves the task of converting glucose to fat, and they program the muscles to strongly prefer fat over glucose as an energy source. In the process, they hoard calcium and vitamin D, and cause measurable deficiencies in these important nutrients in the blood serum.
It is likely that some ADHD children may suffer from calcium deficiency as well, mainly as a consequence of vitamin D deficiency, a syndrome that is at epidemic proportions in the U.S (Vitamin D Deficiency Epidmemic). Probably the most significant nutritional role of vitamin D is its ability to promote both the absorption of calcium from the gut and the transport of calcium across membranes, a process that is extremely important in many aspects of metabolism and brain function. ADHD children tend to be stunted in growth, and their levels of growth hormone are abnormally low. Extending the length of a bone requires an enormous amount of calcium. Thus, by keeping the bones short, the calcium that would have gone into bone growth can be diverted to assure an adequate supply of insulin and an efficient glucose uptake mechanism in the muscle and fat cells.
It could be that ADHD children also sacrifice calcium levels in the brain in order to assure enough calcium for the efficient metabolism of glucose, which is extremely essential when the body is relying mainly on glucose as an energy source. Evidence that calcium channels in the brain are important for memory comes from the surprising result from a study involving 1,268 people who were being treated for high blood pressure (Calcium Blockers and Memory). The study found that people who take calcium blockers to lower blood pressure score less well on memory tests than people who use other medicines to lower blood pressure. Studies using Magnetic resonance Imaging (MRI) verified brain damage in the white matter of the brains of the people who used calcium blockers.
If ADHD children are deficient in calcium in their brains, they are also likely less able to utilize ketone bodies as an energy source in the brain. This conclusion comes indirectly from studies involving alzheimer's patients. It has been found that alzheimer's patients' brains are deficient in the ability to utilize glucose for fuel, and, as a result, regulatory control mechanisms have led to an increased supply of calcium in the brain, which plays an essential role in the metabolism of ketone bodies . This allows them to efficiently use ketone bodies instead of glucose as a fuel source. The converse of this observation is that reduced calcium in the brain would interfere with ketone body metabolism, leaving the brain even more vulnerable to situations of reduced blood glucose levels.
Vitamin D itself plays an important role in brain function, in addition to its influence on calcium, as implied by the existence of a wide distribution of vitamin D receptors throughout the brain  (Vitamin D and the Brain) . Vitamin D also affects proteins in the brain that are directly involved in learning and memory, as well as motor control. It may be that, for some ADHD children, insufficient vitamin D is even the main cause of their symptoms.