Biomedical Engineering Reference
In-Depth Information
or succeed. The ancients had no such method based on intellectual
and experimental results, though a few did foresee such a scientific
need.
Before Newton and Leibniz both independently invented dif-
ferential and integral calculus in the 1670s mathematical abilities
were restricted mainly to solutions of simultaneous linear and
quadratic equations. The discovery of calculus by Newton and
Leibniz demanded a new notation, and today we generally use
Leibniz's method of indicating a differential and an integral,
althoughNewton'snotationissometimesusedasneedsdictate.Now
the mathematics was in place, the following century provided the
othernecessaryingredientstoenablethemathematicalformulation
of electrostatics and magnetostatics by Coulomb and Ampere.
Advances in mechanical engineering were made, including the
torsion spring and the marine chronometer. Coulomb is credited
with the invention of the torsion balance that enabled his experi-
ments concerning weak electrostatic charges. A decade or so later
Cavendishwasabletoinvestigatethegravitationforcesbetweentwo
spherical masses that attracted each other in a horizontal plane.
Like the 1920s, the period just prior to the French Revolution
was a period of great change in human affairs. The introduction of
Western science to bioelectricity came peremptorily in 1771, when
Galvani discovered that the legs of frogs twitched when exposed to
sources of electricity. At that time electrical energy was stored in
Leyden jars (Fig. 2.1), whose design had been improved by many,
includingPresidentFranklinoftheU.S.WhileGalvanicouldreplicate
his experiments it took 200 more years for these experiments of
electric excitation of living nerves to be understood quantitatively
at the electronic level.
During this time several important mathematical levels of
understanding, of the electrons, ions and finally the fields have
been uncovered. Biophotons, the most recent level of knowledge,
are basically dipolar particles that interact forming streams of field
particles. Their recent mathematical understanding has emerged
intothespotlightofcurrentresearchinanumberofareas,including
bioelectromagnetics(BEM),whereclassicalelectromagnetics(CEM)
has been used since the end of World War II (WWII). That photons
have a tiny but non-zero mass and therefore weakly attract one
