Math-Physical Medicine

NO. 265

How an engineer investigates his expected lifespan based on his metabolic conditions and lifestyle management program

Corresponding Author: Gerald C. Hsu, eclaireMD Foundation, USA.

In this paper, the author described how to apply his engineering background, including mathematics, physics, and computer science to conduct his medical research on the subject of “effective health age” (i.e. expected lifespan).  He reviewed his past 8-years of data from 2012 through 2019, focusing on both of his metabolic conditions and health lifestyle details.  He then created a simple model of “Effective Health Age” in comparison with the “Real Biological Age” using the GH-Method: math-physical medicine approach.

As a part of his research, he applied his acquired mechanical and structural engineering knowledge to develop several biomedical models to control his severe diabetes and estimate his risk probability % of having chronic diseases induced complications, including but not limited to heart disease, stroke, kidney complications, retinopathy, and more.  He also applied the concept of elastic and plastic structural behaviors to investigate his diabetes due to pancreatic beta cells insulin regeneration capability.

The engineering analogy of expected lifespan can be explained simply by using an example of new machine or new bridge.  If we develop a monitoring system to continuously measure, record, and analyze the strength of material, as well as the relationship between stress (lifestyle details) and strain (medical conditions), we can then have a clear idea how long this machine or bridge is going to last which is their usage life or expected lifespan.

As shown in Figure 1, approximately 2.1 million people died in 2017 from multiple causes of death in the United States.  Among them, the first and largest group, ~1.1 million deaths or 50% of the total were directly related to metabolic disorders and their various complications. The second group, ~600,000 deaths or 29% were caused by a variety of cancer diseases.  Furthermore, within the cancer cases, about 45% of them were related to metabolism conditions. The third group, ~215,000 deaths or 11% of the total were caused by various infectious diseases.  This last group requires excellent medical treatments and a strong immunity to fight against infection from these different virus or bacteria.  The medical community has already proven that immunity and metabolism are closely related to each other, like two sides of the same coin (Reference 1).  In summary, 90% of the total death cases are related, either directly or indirectly, to metabolism.  The final remaining 10% of death cases are not disease related.

Figure 1: US leading death causes

Topology is a newer branch of mathematics which was created around 1900.  It studies key properties of “spaces”, such as metabolism of the human body space, that are invariant under any continuous deformation happened during the lifespan.  Those few key properties or characteristics are not going to change as long as the space itself is not encountering a “break” situation, such as a discontinuity by death.  Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system.  As a matter of fact, topology optimization has been applied by some engineers on obtaining the best layout design of some automotive components (Reference 2).  When we look into the human organs and try to figure out how to achieve some predetermined health goals, we can recognize that it is also a form of topology optimization problem.  This problem can then be solved by using some available mathematical programming method in combination with finite element modeling method from both structural and mechanical engineering disciplines to conduct the targeted analysis to obtain an optimized organ performance or response.

Based on the above learned academic knowledge and acquired professional experience, the author spent the entire year of 2014 to develop a mathematical metabolic model.  This human metabolism model consists of a total of 10 categories, including 4-categories of disease (body outputs, like strain) and 6-categories of lifestyle details (body inputs, like stress).  Similar to a finite element model, these 10 categories further consist of about 500 detailed elements.  Finally, utilizing complicated mathematical programming techniques, he was able to proceed his topological response analysis and obtained 14-pages of long output which was used in his programming tasks for a rather sophisticated metabolism software.

After developing software for his iPhone, he began collecting his own data of weight and glucose beginning on 1/1/2012.  He then started category by category to enter his detailed lifestyle data for the period of 2013 to 2014.  Thus far, he has already collected nearly 2 million data regarding his body health and lifestyle details.  Finally, by the end of 2014, he compiled all the big data together and expressed them in terms of two newly defined biomedical terms: the metabolism index (MI), which is a combined daily score to show the body health situation, and general health status unit (GHSU), which is the 90-days moving average number to show the health trend.  He has also identified a break-even line” at 0.735 or 73.5% to separate his metabolic conditions between the healthy state (below 0.735) and unhealthy state (above 0.735).

Figures 2 and 3 demonstrate the details mentioned above for his metabolism index (MI) and medical conditions with lifestyle details for the past 8 years (2012-2019).

Figure 2: Metabolism Index (MI) model of inputs and outputs
Figure 3: MI & GHSU, medical conditions, lifestyle details (2012-2019)

With those 2 million data, initially, he focused on weight and glucose to conduct further analysis in order to put his severe diabetes under control which was his top priority.  Like engineers looking at a project’s design data or cardiologists reviewing a patient’s EKG chart, he adopted the traditional time-series analysis approach.  He then quickly realized that he could easily obtain a different conclusion dependent upon a specific time window he chose.  On the other hand, if he analyzed all data using the entire long period of time with big data, he could easily see a bigger picture, such as the data’s relationship and trend from spatial analysis.  Sometimes, the conclusion derived from a global view via spatial analysis might not be consistent with certain local views via time series analysis from a shorter time period.  One day, as he studied the history of medicine, he found a story about how Dr. John Snow from the UK discovered the cholera outbreak, which spread in the Broad Street area of London in 1854 (Figure 4).  He decided to adopt this similar concept, i.e. spatial analysis, from statistics as an additional tool to analyze his big and complicated medical data.  An example of the tight relationship between body weight and fasting glucose in the morning via spatial analysis is shown in Figure 5.  Spatial analysis is powerful to provide a rather clear view of the relationship and trend provided that data size is large enough.

Figure 4: Dr. John Snow’s study of cholera outbreak
(Broad Street, London, 1854)
Figure 5: Spatial analysis between body weight and fasting glucose

He also applied Fourier transform to convert a time domain data into frequency domain in order to calculate and compare associated energy between high frequency with lower amplitude glucose components versus low frequency with higher amplitude glucose components.  Here, energy theory from mechanical engineering is frequently applied to calculate different degrees of damage on the internal organs by different glucose components which carry different amounts of energy.

Sometimes, he utilized signal processing techniques from wave theory (electronic engineering, radio-wave communication, and geophysics) to decompose a glucose waveform into many component-based sub-waveforms to study impact on glucose by food, exercise, etc.  He even applied a simplified formula from perturbation theory (one variable and first-order only) of quantum mechanics to build an approximate postprandial glucose waveform before the patients eat their meals.  Remarkably, it achieved a greater than 95% of accuracy (Reference 3).

The author has suffered many complications resulting from his obesity, diabetes, hypertension, and hyperlipidemia, including five cardiac episodes, critical kidney condition, bladder infection, foot ulcer, diabetes retinopathy, and more.  By using metabolism as the foundation, he built up three mathematical simulation models to calculate his risk probability percentages of having heart attack, stroke, kidney failure, and even cancer.  In those extended study of disease complication risks, genetic factors were included.

Among these three chronic disorder diseases such as diabetes, hypertension, and hyperlipidemia, diabetes causes the most fundamental damage to our blood system.  The blood cells carry both nutrition via glucose and oxygen from the lungs then circulate through the blood vessels.  When elevated glucose flows through the arteries, it would alert the immune cells within the artery wall; therefore, these cells will treat them as an “invader” and start to fight against them.  This fight will result in a situation similar to the inflammation on the artery wall, causing the blood vessel wall to thicken with a non-smooth surface.  This rough surface allows the build up of lipids in the blood with the formation of plaque.  As a result, the combination of high glucose and high lipids will create an artery blockage (~70% cases).  When high blood pressure is added into the picture, an artery rupture becomes a possibility (~30% cases).  These two situations can lead to a heart attack or stroke.  For micro blood vessels, elevated glucose causes many microscopic leakages instead.  The kidney’s normal functions are to discharge body waste and recycle protein back into the body.  These microscopic leaking holes will reverse these two functions, which means the leaking of protein out of the body via urination and recycling body waste back into the body can be toxic.  This is why dialysis is utilized to mechanically perform the kidney’s normal expected functions.  Other complications, such as erectile dysfunction, bladder complications, peripheral nervous damage, and retina damage are also based on similar interpretations and reasons.

As an engineer, the author visualizes an image in his mind with the analogy of acid (glucose), water pipe (blood vessel), water pressure (blood pressure), and butter flowing through the pipe (lipids in blood).  This mechanical scenario of pipes is quite similar to the biomedical scenario inside the blood vessels.

In addition, if the damage is not too severe and only lasts for a shorter period of time, the body and organs are still in an “elastic state”, which is similar to pre-diabetes conditions that can be reversed.  However, when diabetes becomes extremely severe and lasts for a much longer period of time, then the body and organs are entering into a “plastic state”, i.e. never fully recovers back to its original healthy state.  By applying this structural engineering concept and using other math-physical techniques, the author can provide a guesstimate on his self-repair rate for his damaged pancreatic beta cells.

After the author compiled a large amount of data over the past 10 years, he built up some mathematical models to understand the progression stages of his diseases and also predict the projection of development in the future.  Therefore, his various disease risk probabilities can then be estimated with a reasonably high degree of accuracy.

The information mentioned above depicts how a mechanical and structural engineer, physicist, computer scientist, and mathematician learned about chronic diseases and various complications and is able to conduct all related medical research work.

With all of the math-physical and engineering-based research, his final goal is to fight against different diseases in order to survive by avoiding “pre-mature” death (at least 90% of death cases).  Living a healthier and longer life is his ultimate objective at this stage.  This is also his driving force in dedicating his entire efforts on medical research since 2010.  After 10-years of study and investigation, he has finally defined an “Effective Health Age” based on the evaluation of his multiple medical examination reports and his ~2 million data of his lifestyle, metabolism, and medical conditions over an 8-year period. This is different from the “Real Biological Age” or “Chronological Age” defined as the actual amount of time a person has been alive.  It should be pointed out that genetic factors are not explicitly expressed through his life expectancy formula.  However, those genetic factors were already implicitly included in his. Sin factor of metabolism.

His simple equation to calculate this effective health age is listed below:

Effective Health Age= Real Biological Age *(1+((MI-0.735)/0.735)/2)

He then utilized his annualized MI data to calculate his effective health age in order to compare against his real biological age.

As shown in Figures 2 and 3, both of his MI and GHSU were >73.5% from 2012 to 2014 (unhealthy) and <73.5% from 2014 to 2019 (healthy).  During 2014, his overall health condition improved significantly.  It should be noted that his MI and GHSU during the years 2018 and 2019 were slightly increased due to his heavy travel schedule to attend more than 60 medical conferences worldwide.  As a result, his risk probability of having a heart attack or stroke also increased by approximately 2-3%, whereas his kidney risk increased by 1% (Figure 6).

Figure 7 and 8 depict the comparison between his real biological age and effective health age.  Of course, the real biological age increases annually, while the effective health age was higher than his real biological age during 2012-2014 and lower than his real biological age during 2015-2019.  These changes are results of improvements on his metabolic conditions and lifestyle habits.  These factors were significantly improved during 2015 and then maintained through 2019.  Figure 8 also shows the two age differences between effective health age and real biological age.  The age difference has changed from +8 years in 2012 to -7 years in 2019 (here, + means getting worse and – means getting better).  This means that his effective health age was 73 when his biological age was 65 and his effective health age is 65 when his biological age is 72.

Figure 6: Risk probabilities of having heart attack, stroke, kidney diseases, cancer.
Figure 8: Differences between Real & Effective Ages
Figure 7: Annualized MI & GHSU

An interesting fact from the past decade is that his physician indicated his age was about 10 years older after reviewing his medical examination reports when he was 63 years old.  However, the same physician told him during 2016-2019 that he was about 10 younger when he reached ~70 years old.  This range of +10 years to -10 years was an empirical judgement based on their many years of clinical experiences from seeing hundreds of patients.  However, the author who is a mathematician, physicist, and engineer, used a scientific approach which is based on physical phenomena observations, big data analytics, engineering modeling applications, and mathematical derivations to draw a conclusion of the range of from +8 to -7 years.  Nevertheless, these two guesstimated age ranges are actually quite obvious and also very comparable.

The life expectancy of an American male is 78.69 years (2016 data).  If the author continues his metabolic conditions improvement, chronic disease control, as well as his existing lifestyle maintenance program, he has the opportunity to extend his life for an additional eight years to reach to a real biological age of 87 (79 plus 8).

The author self-studied chronic diseases, metabolism, and food nutrition for 4-years from 2010 to 2013.  He started his medical research work by building a mathematical metabolism model in 2014.  He named his research methodology as the “GH-method: math-physical medicine (MPM approach)”.

Over the past 6.5 years of his MPM research, the author has learned that the most important thing is knowing how to apply physics principles and engineering modeling concepts on biomedical problems.  This is different from just inserting your biomedical data into some existing equations extended from those theories and models.  The reason for doing this is that the original equations associated with inventor’s theory or model include his own boundary conditions.  This may not fit into your biomedical situations perfectly.  Therefore, you must understand the scope and applicability of these physical theories and engineering models first, and then find a suitable way to apply them.  In other words, learning other people’s wisdom first and then find a way to apply them to your own problem is the most practical way.

This simple numerical calculation of expected life-span are based on applications of physics law and engineering concept, big data analytics, and sophisticated mathematical metabolic model.  It has depicted a possible way to extend our life expectancy via an effective metabolic condition improvement and lifestyle maintenance program.  This practical method has already been applied and proven effectively in the author’s own diabetes control without medications.

The author hopes that this method can also be applied in the field of geriatrics, longevity, other chronic diseases control, or even dementia and cancer preventions (Reference 4).  For example, if patients are able to collect sufficient data regarding their individual chronic disease conditions, they can then replace those input data of M1 through M4 with their own disease data and utilize similar lifestyle model of M5 through M10.  In this way, they can then guesstimate their own effective health age and life expectancy under their own disease conditions.

Life is precious and health is important.  A long and healthy life is a goal for everyone.  This article provides a logical and practical way of achieving longevity without suffering from many avoidable diseases


  1. Hsu, Gerald C., eclaireMD Foundation, USA, No. 235: “Linkage among metabolism, immune system, and various diseases using GH-Method: math-physical medicine (MPM)”
  2. J. Yang & A. I. Chahande, “Automotive applications of topology optimization”, by Structural optimization, volume 9, pages 245–249 (1995) of Springer Link
  3. Hsu, Gerald C., eclaireMD Foundation, USA, No. 152: “Applying first-order perturbation theory of quantum mechanics to predict and build a postprandial plasma glucose waveform  (GH-Method: math-physical medicine)”
  4. Hsu, Gerald C., eclaireMD Foundation, USA, No. 152: “Risk probability of having a metabolic disorder induced cancer (GH-Method: MPM)”