The neurons in our body works as proximity with other elements in the brain which means not only skull and cerebrum with neurons etc. rather whole set of head - physical as well as psychical, covers under the brains purview. Thus, all complex elements - sensory neuron and motor neurons are the parts of head. In addition, the mind is passed between head and palate.

The mathematical relationship between the input and output signals of a neuron is based on physiological facts. Method focus on the currents across the postsynaptic membrane of each synapse, and the key is to recognize that the net charge across the whole membrane of a neuron over each action potential cycle must equal to zero. By analyzing the relationship between the input of a synapse and the currents across the postsynaptic membranes, a dynamic pulse frequency model of the neuron can be obtained.

The attached paper may help you, entitled 'A Mathematical Model of a Neuron with Synapses based on Physiology'. (http://precedings.nature.com/documents/1703/version/1)

Dear Philip

The mathematical relationship between the input and output signals of a neuron is based on physiological facts. But what about psychical l facts.

Dear Philip and Ramanath,

Historical account:

Mathematical theory of nerve or neural conductions is based on both integral and differential functions confounded on diverse theories, i.e., Cable theory of the 1920-30s, Nernst Equation, Nernst–Planck equation besides the common Hodgkin-Huxley model and Fitz Hugh’s simplification of HH-model (1960). In fact, the HH-Model was simplified using Fitz Hugh-Nagumo nerve conduction equation with known traveling wave solutions (for a historical account, See John Rinzel’s paper in Biophysical Journal Vol.15 1975). Deriving formula for conduction propagation in a lab requires one to isolate single neuron study and measure the action potential differences across the cell. The electrical properties are further subdivided based on inorganic and organic elements within the nerve cell. The Physico-mathematical aspects of nerve conduction are based on ionic conductivity across the nerve cell membrane and signal attenuation-decay theory. The stimulus threshold and the intensity of the stimulus also modify conduction velocity and propagation of impulses across the gated channels as ionic conduction (i.e., the gradient pumps).

Recent studies indicate that since it is based on electro-physiological aspects, the Hodgkin-Huxley model is still indispensable to study such phenomenon. I have read somewhere that neural conduction is a bit slower than the propagation of light waves yet the brain thinks faster due to parallel processing but need further verification on this.