|Year : 2007 | Volume
| Issue : 2 | Page : 77-78
The role of mathematics on human structure: By Swapan Kumar Adhikari
Formerly, Professor of Radiological Physics, Christian Medical College, Vellore - 632 004, India
C A Jayachandran
Formerly, Professor of Radiological Physics, Christian Medical College, Vellore - 632 004
Source of Support: None, Conflict of Interest: None
|How to cite this article:|
Jayachandran C A. The role of mathematics on human structure: By Swapan Kumar Adhikari. J Med Phys 2007;32:77-8
(Dipali Publication, 35/1 Krshnatraran Naskar Lane, Ghusuri, Howrah, West Bengal - 711 107 India, pp156, US$10.95 ISBN 81-901643-0-9)
The role of mathematics on human structure is a useful book introducing a mathematical approach to understand the nature of the structure of the organs of the human body and the derivation and the formulations by analysis of the normal and the abnormal functions of the organs. As explained by the author, the correct inevitable concept to understand anatomy of organs of the human body is that quantification of the related parameters is essential to understand the physical basis of the various physiological principles that govern their function. This approach enables one to study the functions of the supporting structures like bone, muscle, tendon, etc., and their interrelationship in the overall function of the human body.
In the introductory chapters, the author has traced the history of the works of Leonardo da Vinci, the pioneering anatomist in the field of anatomy dating back to as early as the sixth century B.C. He has stated that the Egyptian surgeons investigated the nature of the organs of the human body as early as the sixth dynasty (2625-2475 B.C.), which is found in the sculpture on the wall of a tomb. His literature review confirms that the Egyptians were the pioneers in performing simple surgical procedures such as circumcision using knives carved out of stone. The author has brought out the fact that the first dissection of the human body was performed in Italy as early as 1286 A.D., which, he asserts, was mentioned in a book titled Anathomia of Mundius published as early as 1316 A.D.
Leonardo's remark that 'the bodies of those hanged, of which I have seen the depth of` anatomy' is history . Historical evidence shows that Leonardo studied anatomy from the body of Bandino Barocelli, who was hanged after the failure of the Pazzi revolt as early as 1477 A.D. He is the forerunner of dissection of the human body and had `witnessed the dissections and made anatomical studies in the hospital of Santa Maria Nova in Florence in Italy. In his book on anatomy, Leonardo has stressed the need for performing dissection of the human body for a correct analytical understanding of the organs of the human body.
The author sites quotations from eminent scientist Rene Descartes (1596-1650 A.D.), a geometer and a philosopher who said, 'Science may be compared to a tree of which metaphysics is the root, physics is the trunk and the three chief branches are mechanics, medicine and morals.'
The section on the pineal gland regarding mathematical approach and the treatment of early stages of the thalamus simulating an ellipsoid containing the pineal gland and subsequent growth of the gland under the constraints of absence of forces, justifies the application of the laws of inertia of a body at rest and their moments and angular moments with respect to the base of the skull to make a conclusion that the thalamus due to its formation and deformation ends up in the spiral form due to aging.
In the next chapter on mathematical concept of the movement in the heart, the treatment regards the heart as an organ with two chambers at the embryonic stage, which develops into a four-chamber unit. The author's contention is that in the heart, heat exchanges take place because of the movement of the flow of blood, its course during oxygenating and deoxygenating mechanisms or its structure, and expansion and contraction of the heart during the pumping cycle could be considered as a thermodynamical process. The author has introduced fundamental laws of physics in describing the physiological function of the heart. The author has introduced fundamental laws of physics in describing the physiological function of the heart. The author states that oxygen dissociation curves with increase in the pressure of oxygen, in terms of pO 2 consisting of saturation of myoglobin and the non-linear increase in Hemoglobin. The author summarizes that the essential features of the transportation of oxygen by the heart and related organs and tissues could be traced to the high affinity of oxygen by the lungs and low affinity for oxygen in tissues. Myoglobin has higher affinity for oxygen than hemoglobin at low concentration, and hemoglobin transports carbon dioxide back to the lungs, where it is expelled. The flow chart depicts the course of food in terms of transformation of energy to explain the physiology of the heart, related organs and tissues of the human body in very simple terms; useful energy and its waste implying the thermodynamical process that governs the function of the heart. After an extensive treatment of the flow of blood and biochemical changes that take place, the author has applied a simple mathematical expression for deducing the change in the flow rate of blood in an artery. According to that, if the blood flow in an artery is reduced by 30%, the flow rate will be reduced to just 20% on the clearance of two-thirds part of the radial space of the vessel.
The section on the skeletal system is in great depth- deriving mathematical equations that could throw more light on what would take place due to stress and the associated deformation in the structure and their function. The sketches of the humerus illustrate the results of flexion, extension and rotation of the head and the consequent changes that would take place in the shoulder joint. The discussion on clavicle deformations would be useful to the orthopedic surgeons and the physical medicine clinicians in the management of the changes that would occur due to trauma. The simple and the complicated formulations developed by the author are commendable.
The mathematical analyses of the various interrelated movements of the scapula, the humerus and the clavicle and their deformation due to stress have been discussed very vividly to enable the reader to understand the equations and formulations developed by the author. These reveal the depth of the knowledge the author has acquired to elucidate the changes mathematically. The illustrations and sketches showing the effect of stress and the strain in the ligaments on the movement of femur during flexion, extension, abduction, adduction and circumflexion are quite extensive and have been explained in simple terms with the formulation in terms of mathematical equations. The mathematical expression derived by the author to explain the physical properties such as viscosity and elasticity of cartilage is unique. If selected examples of the equations derived by the author in each section were solved and included by the author to enable the anatomist, the physiologist and the clinicians to have a better understanding, it would have been very useful
In conclusion, this book, which presents a rare but useful approach, might be an asset to the teachers of physiology to explain accurately the anatomical and physiological changes that take place in a human body. This could in turn lead to research in order to gain more knowledge of the fundamental nature of the structure of the organs and their functions. Particularly, the understanding of the flow of blood and the application of the first law of thermodynamics could help in improving the assessment of the anatomical defects that may develop in various parts of the heart, the blood vessels, and to quantify the related parameters leading to prediction of the various anatomical and physiological changes that would take place in the course of time. Besides, this book may also be useful to physicians who take care of the physically handicapped patients. It may also benefit orthopedic surgeons who perform replacement of the knee and the hip in inferring quantitatively the prognosis of the patients who have undergone these operations. The author has provided an analytical approach to study and gain knowledge of not only the anatomy and physiology of the human body but also of their changes; and with a high degree of competence, he has formulated and analyzed the mathematical equations that have been presented in this book. Selected examples of the derivations could have been solved and provided to enable the non-mathematically oriented clinicians to understand the concepts better. Of course, it is up to the readers who are experts in the field to decide the authenticity of the approach and the value of the contents of the book.