Gradient and Body Electric

gradient Gradient is a mathematical concept to measure the change of a scalar function over a specified distance and along a given direction. In physical applications, the scalar function can be chemical concentration (as shown in Figure 01), temperature, pressure, heat, gravitational potential, electrical potential, ... etc. The mathematical formula for change of the scalar function in a particular direction is just the slope of the curve:

where n indicates the direction of change.

Figure 01 Chemical Gradient [view large image]

In general the formula for change of a scalar function in any direction can be expressed as:


where i, j, and k are unit vectors along the x, y, and z axis respectively.

The gradient is positive if the scalar function increases toward the direction of change, and is negative for the reverse. Thus the bacteria in Figure 01 must have equiped with sensor that can discern the positive or negative of the chemical gradient.

The gradient of the gravitational or electrical potential is the field, which is equal to the force by multiplying an appropriate coupling conatant. A magnetic gradiometer detects the magnetic gradient; it can be used to locate object under the Earth's surface. While a gravity gradiometer measures gravitational gradient; it can be used as verification tool to check the load inside a container or the war head of a missile etc. The dotted curves around the salamander body in Figure 01 represents the equi-potential contours. The voltage is defined as the difference in the values of the potential between two points. Current will flow across these two points (if the medium is conductive or semi-conductive) until there is no more potential difference. That's why we need to replace battery every now and then.

Body Electric The gradient of the electric potential defines the electric field: E = -dV/dr n. Biologists have known for more than 200 years that nerve impulses are transmitted electrically. Research on body electric has been revived only recently in the past two decades. Countless studies have since confirmed that externally applied electric fields can affect the behaviour of cultured cells, influencing the way they migrate, develop and grow. Internally generated electric fields (typically between 10 and 100 millivolts per millimetre) are an inevitable product of biological systems. Cell membranes and epithelia routinely pump ions from one side to the other, creating gradients in electrical potential. It is found that the electric fields play a vital role in wound healing and regeneration of body parts in lower animals (Figure 02). It also provides a "spatial cues" to establish the left-right asymmetry in embryonic development.

Figure 02 Body Electric [view large image]

Regeneration of Body Parts On the molecular level, the retinoblastoma protein (Rb) has been identified as a key factor in getting muscle cells to differentiate, or specialize. Suppression of the Rb gene in salamander muscle cells sends the cells back into the cell cycle, which provides the salamander with a new limb. However, this mechanism does not work in mammalian cells, which have evolved to possess an extra tumour-suppressor gene called Arf. Using a gene-silencing technique to temporarily knock down both Arf and Rb in cultured mouse muscle cells, it is found that the treated cells re-entered the cell cycle and began proliferating. Meanwhile experiments had already shown that application of micro-ampere current to the cell has a profound effect on its chemical properties. In particular, it has been documented that immature red blood cells, fibroblasts, and white blood cells can de-differentiate when they are stimulated with very low levels of electric current. It is this kind of de-differentiation, which endows the animals with regenerative ability. Further study is required to demonstrate the link between electric current and the suppression of the Arf and Rb genes.

Figure 03 Regeneration of Body Parts

Qigang Myelin Sheath The concept of acupuncture points and meridians in Qigong has been explored in China for two thousand years (see a collection of modern researches on the subjects). Figure 04 depicts the 12 meridians and the acupuncture points along the pathways (see "The Meridians of Acupuncture" for details). The physical base has not been identified until some measurements were conducted in the 1970s. It indicates that current is carried in the myelin sheath laid down by specialized cells called Schwann cells (see Figure 05). The cells that biologists had considered merely as insulation turned out to be the real wires to conduct DC current. It is thought that the acupuncture points along the meridians may act as amplifiers to maintain the strength of the current, similar to the booster amplifiers along a transmission line used to keep the signal from getting weaker with distance. Unfortunately, further study ceased abruptly when NIH canceled

Figure 04 Meridians
[view large image]

Figure 05 Myelin Sheath [view large image]

the research grant.


Dog Acupuncture Since then Western medical experts have used high-tech tools to unravel the ancient mysteries. Neuroimaging studies show that it seems to calm areas of the brain that register pain and activate those involved in rest and recuperation. Doppler ultrasound shows that acupuncture increases blood flow in treated areas. Thermal imaging shows that it can make inflammation subside. Scientists are also finding parallels between the ancient concepts and modern anatomy. Many of the 365 acupuncture points correspond to nerve bundles or muscle trigger points. Several meridians track major arteries and nerves. Many medical experts remain deeply skeptical about acupuncture. The fact that many patients get some relief and register some brain changes from fake acupuncture has caused controversy in the effectiveness of acupuncture. Some critics say that proves the benefit from acupuncture is mainly a placebo effect. While

Figure 06 Dog Acupuncture [view large image]

acupuncture proponents have some explanation to do on this kind of clinical trials. There should not be any placebo effect on healing the dog with acupuncture (Figure 06).