GH-METHODS

Math-Physical Medicine

NO. 286

Equation of relative energy associated with higher-frequency glucose components using GH-Method: math-physical medicine

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

Abstract
This paper number 286 describes the author’s application of basic concepts he learned from modern physics, quantum mechanics, theory of special relativity, and his collected glucose results to estimate the relative energy level associated with high-frequency glucose components.  During his research, he attempted to develop a simplified yet useful “equation” for this relative energy estimation.  His ultimate goal is to identify the degree of impact or damage on the human internal organs due to excessive energy caused by hyperglycemia and its other associated glucose frequency components in diabetes patients.  He has applied his developed GH-Method: math-physical medicine to conduct this medical research.

In summary, by using his own ~33,000 glucose data for the past 129 days, he has identified ~20% of relative glucose energy associated with higher-frequency glucose components (67% of total frequency numbers).  This requires spending additional effort and using Bluetooth technology to collect bigger sets of glucose data (3x more data) which allows him to identify ~20% of possible impact or damage on the internal organs from those secondary S-waves’ energy associated with higher frequency glucose components.  This finding can serve as a foundation or starting point for his future research on diabetic complications.

Introduction
This paper number 286 describes the author’s application of basic concepts he learned from modern physics, quantum mechanics, theory of special relativity, and his collected glucose results to estimate the relative energy level associated with high-frequency glucose components.  During his research, he attempted to develop a simplified yet useful “equation” for this relative energy estimation.  His ultimate goal is to identify the degree of impact or damage on the human internal organs due to excessive energy caused by hyperglycemia and its other associated glucose frequency components in diabetes patients.  He has applied his developed GH-Method: math-physical medicine to conduct this medical research.

Methods
1. Background
The author majored in mathematics, physics, engineering, and computer science in college.  He attended a few theoretical courses such as modern physics, quantum mechanics, theory of relativity, energy theory, and wave theory.  After college, he worked in various industries, including space and defense, nuclear and power, computer and information technology (IT), semiconductors and artificial intelligence (AI), where he utilized many of his learned basic concepts and academic theories on different challenging industrial applications.

In 2010, he suffered five cardiovascular episodes and many other diabetic complications, including bladder infections, kidney disorder, foot ulcer, neuropathy, diabetic retinopathy, and hyperthyroidism.  Three physicians warned him about the severity of his chronic diseases and related conditions with the possibility of an early death around 65 years old.  Facing the immediate threat of dialysis treatments, he finally woke up and decided to save his own life.  Since 2010, he has immersed himself into self-study and research on diabetes and its various complications with a special focus on glucose and metabolism.  In his opinion, based on his learned medical knowledge, glucose is the primary criminal, where blood pressure and lipids are the accomplices which damage almost all of the internal organs through the blood circulatory system.  Another broad topic of “metabolism” is far more important than the individual factors related to the foundation of overall health.  In Figure 1, moving from the inner circle towards the outer rings, this depicts the stringent lifestyle management leading into a good metabolic state, and then converting into a strong immunity to fight against three major disease categories, chronic diseases and complications (~50% of death), cancers (~29% of death), and infectious diseases (~11% of death), except for the remaining ~10% of non-diseases related death cases.  This is a logical pathway to achieve overall health conditions, including diabetes control (Reference 1).

Figure 1: From lifestyle through metabolism, immunity, to diseases and death

2. Data Collection
Since 1/1/2012, the author measured his glucose values using the finger-piercing method: once for FPG and three times for PPG each day.  On 5/5/2018, he applied a continuous glucose monitoring (CGM) sensor device (Freestyle Libre) on his upper arm and checked his glucose measurements every 15 minutes, a total of ~80 times each day.  After the first bite of his meal, he measured his postprandial plasma glucose (PPG) level every 15 minutes for a total of 3-hours or 180 minutes.  He has maintained the same measurement pattern during all of his waking hours.  However, during his sleeping hours (00:00-07:00), he measured his fasting plasma glucose (FPG) in one-hour intervals.

With his academic background and his practical working experience in high-tech industries such as the computer-aided-design (CAD), AI, and semiconductor chip design, he was intrigued with the existence of “high frequency glucose component” which is defined as those lower glucose values (i.e. lower amplitude) but occurring more frequently (i.e. higher frequency).  He wants to identify the scope of those relative energies associated with higher frequency glucose components which could still contribute to the impact or damage on the human internal organs.  Furthermore, if possible, he wants to place a numeric figure to the degree of impact or damage to his organs, which is the “contribution percentage”.  For example, there are 13 data-points per meal for the 15-minute PPG waveforms, while there are 37 data-points per meal for the 5-minute PPG waveforms.  These 24 additional data points (two thirds more data) could provide some more hidden information about the higher frequency PPG components and their influences on our internal organs.

Therefore, starting from 2/19/2020, he has conducted a new biomedical and math-physical experiment on his body.  He utilized a hardware device based on Bluetooth technology and embedded with a customized application software to automatically transmit all of his CGM collected glucose data (both 5-minute and 15-minute intervals) from the Libre sensor directly into his developed research application program known as the “eclaireMD system”.  This data transmission of his glucose values at each “5-minute” time interval would continuously go through the entire day; therefore, he is able to collect ~240 glucose data within 24 hours.

He used the past 4+ months from 2/19/2020 to 6/27/2020 (129 days), as his research period for analyzing the relative energy associated with higher-frequency glucose components.

3. Wave Theory & Frequency Domain
For medical reader’s concern, the following descriptions are directly quoted from what the author has learned from physics and mathematics in college and rewrote them to fit into the scope of this article.

Most of original medical data are presented in a time-domain” form and most of present medical research work are using some sort of statistical methods” to analyze them.  This time-domain” statistical analysis results are generally represented by the horizontal x-axis as time (in minute, hour, or day) and the vertical y-axis as glucose (in mg/dL or other suitable unit), similar to a cardiology EKG chart for the heart.  Next, he utilized a mathematical algorithm using Fourier Transform” operation to convert these time-domain data into frequency-domain data.  In the frequency domain chart, the x-axis becomes frequency, instead of time in time domain chart, and the y-axis becomes an amplitude scale associated with distinctive frequency (frequency amplitude”), instead of glucose itself in time domain chart.  In one of his previously published paper, he has proven that this frequency domains y-axis amplitude value actually is proportional to or indicates the relative” energy level associated with that particular glucose frequency on x-axis (Reference 2).  Therefore, the author calls them frequency energy amplitude” or energy amplitude”.  But, these two waveforms of time-domain and frequency-domain look vastly different.  

Based on this frequency-domain data chart, he can then segregate the total span of frequency-domain data into either three frequency bands of low, medium, and high, or two frequency bands of low and high.  The boundary number of frequency bands, two or three, is based on a better understanding of glucose waveforms biomedical characteristics, and the specific objectives of a research project.  

After revising the mathematical and statistical background of his medical research methodology for this particular project, he struggled with how he should deal with the physics part, i.e. multiple physical phenomena, of his problem.  During the process of analyzing his glucoses, his MIT friend, Dr. Toyohiko Muraki mentioned to him about Einstein’s work.  Inspired by his suggestion, he recalled courses of modern physics, quantum mechanics, and theory of relativity back from his college days.

He then tried to identify a simple expression, or an equation, to be able to quickly figure out the relative energy level associated with high-frequency components.  Here is an excerpt from some textbooks of modern physics and quantum mechanics about some historical developments:

Max Planck is considered the father of the Quantum Theory.  According to Plancks equation:

  • E=h ν

where h is Planck’s constant (6.62606957(29) x 10-34 J s), ν is the frequency, and E is energy of an electromagnetic wave.

In 1905, Albert Einstein reinterpreted Planck’s quantum hypothesis and used it to explain the photoelectric effect.  Einstein then developed the theory of special relativity, and it forms part of the basis of modern physics.  

Albert Einstein’s equation of theory of special relativity:

  • E = mc2

where E is energy, m is mass, c is speed of light, 2 means square.  This shows that energy and mass are interchangeable.  The nature and behavior of matter and energy at that level is sometimes referred to as quantum physics and quantum mechanics.  

The author was inspired by Einstein’s original concept and equation format of theory of special relativity and searched for its applicability to his problem at hand.  The biomedical glucose waves are similar to all kinds of waves such as earthquake, tsunami, light, sound, and electronics with their respective carried associated energies.  Primary and secondary glucose waves travel within our body.  If the motion and behavior of both P-type and S-type waves can be monitored and analyzed, then we can probe the interior structure of the body.  The lower-frequency with higher amplitude wave is a type of Primary “P-wave” and the higher-frequency with lower amplitude wave is a type of Secondary “S-wave”.  In his previous industrial work, he studied and investigated the structural damages to both buildings and structures resulted from earthquake waves in Alaska and tsunami waves in Japan.  Both earthquake and tsunami waves are not the direct “murderers”, but the energies carried by these waves, i.e. forces, are the true killers which create damage on the buildings and structures.  An initial impact from those waves, particularly the P-wave, causes instant destruction or collapse.  Certain structures can survive the P-wave impact but have suffered from various degree of internal structural damages, such as cracks.  As a result, the S-wave’s carried energy, even though in a smaller quantity of energy, is added on top of the P-wave‘s damage which causes the ultimate structural failure or collapse.

The structural damage from energy associated with earthquake waves or tsunami waves is remarkably similar to the human organ impact and damage from the energy associated with both of the P-wave and S-wave of the glucose waves.  Obviously, the P-wave and S-wave are combined into a bundled waveform with a total energy carried within them.  Only theoretical scientists, such as physicists and mathematicians, are interested in finding the original causes and then analyzing the problem in a segregated and progressive manner.  For example, an internal physician is only interested in diabetes caused cardiovascular risk associated with the heart, but he does not know or even care about those lower-valued glucoses effect on the heart.

Based on fundamental wave theory of physics, the energy is directly proportional to the square of the amplitude of the wave.  Therefore, the author tried to replace the “c – speed of light” in Einstein’s equation by “a – frequency energy amplitude” of wave in the frequency domain. This is his first step of defining the key components in a simplified “glucose energy equation”.  What would be the appropriate counterpart of multiplier “m – mass” in Einstein equation for his simplified glucose energy equation?  He suddenly thought about the possibility of using the total area underneath a glucose curve, i.e. using the “summation of segments of X multiplied by Y”, to estimate or represent the glucose energy.  If he uses the glucose frequency curve area to estimate or represent the corresponding relative glucose energy, this curve’s Y-axis is already proportional to the glucose energy, i.e. the square of glucose, then he can use the X-axis scale, i.e. the number of frequency components within a selected frequency band, to multiply it by the Y-axis value.  As a result, he choose the abbreviation of “n – number of frequency components” within a specified or selected frequency band as the counterpart of “m, mass” in Einstein’s equation of E=ma2” .

Here is his proposed equation of calculating the estimated relative energy level associated with certain selected frequency components.  He calls it the equation of glucose energy”:  

  • E = na2

Where “E” is relative glucose energy, “n” is the number of frequency components within a selected frequency band, and “a” is the amplitude of frequency domain’s Y-coordinates which is proportional to the square of glucose value.

The author further validated this theoretically developed simple “glucose energy equation” by using his clinical data collected from his body during the past 129 days (2/19/2020 – 6/27/2020).

Results
Figure 2 shows his 15-minute “synthesized” sensor glucose wave over the course of a day (x-scale: 24 hours).  Here “synthesized” means that the final wave is the combination of 129 days (from 2/19/2020 through 6/27/2020) averaged glucose waves. This Figure 2 also includes his synthesized 5-minute wave and the comparison chart of these two time-domain daily glucose waves (5-minutes vs. 15-minutes).

Figure 2: Time-domain daily glucose waves (15-minutes, 5-minutes, and comparison)

From this figure, it is obvious that there are more higher frequency glucose components in the 5-minute wave due to availability of three times the number of data points.  The extremely high correlation coefficient of 99% existed between 5-minutes time-domain wave and 15-minutes time-domain wave means that these two measured waveforms are very similar in shape, except for the 5-minute wave containing more glucose components, especially higher-frequency components.  

The author than enhanced his customized applications program (the eclaireMD software system) to include Fourier transform operation, frequency domain analysis, wave theory applications, and relative glucose energy calculations using his recently developed “equation of glucose energy: E=na2”.  The conclusive results of both data table and bar chart of comparison of energy distribution percentages are shown in Figure 3.  

Figure 3: Data table and distribution % of Energy, Frequency number, frequency domain Amplitude, & amplitude square

He has defined the frequency band of lower-frequency with higher amplitude (Lo f & Hi a) as 0 to 48 (n=48) and the frequency band of higher-frequency with lower amplitude (Hi f & Lo a) as 48 to 144 (n=96).  The calculated relativeglucose energies for these two frequency bands are listed as follows:

  • Lo f & Hi a: 5935 (81%)
  • Hi f & Lo a: 1411 (19%)

Furthermore, he also calculated the following distribution percentages of values of glucose amplitude square (a*a):  

  • Lo f & Hi a: (89%)
  • Hi f & Lo a: (11%)

These two sets of percentages are compatible in terms of comparing the percentage range of two relative glucose energies: i.e. 82%-89% vs. 19% -11%.  Although the comparison ratio between the higher-frequency component number (“n”) of 96 (67% or two third) and the lower-frequency component number (“n”) of 48 (33% or one third), is 2 to 1, their glucose energy (“E”) ratio is around 4 to 1, i.e. 81% vs. 19%.

The following simple calculation can further verify his descriptions of the relationship between “energy: (89% vs. 11%)” and “square of amplitude (81% vs. 19%)” from the above paragraph.

  • Lo f & Hi a (Y*X) / Hi f & Lo a (Y*X)
    = (89*33.3) / (11*66.7)
    = 4 / 1
    = 81 /19

For the past ten years of his medical research work, the author realized the most important knowledge he has learned from his school days are the original concepts, fundamental theories, effective models, and reliable methodologies.  Under many circumstances, he could not just take certain equations from textbooks and then plug his own data into those equations directly in order to get his desired results.  The reason is that an equation is an expression of a theory or a concept and it must be associated with its original related conditions, such as boundary conditions and/or initial conditions.  However, for most cases, those scenarios may not have the existing conditions matching with the problem at hand in order to directly plug-and-play.  A medical system has some similarity with an engineering system, but under most circumstances, it is still quite different.  The main reason is that the biomedical system materials are organic, which means alive and changes dynamically, while most of the engineering system materials are generally inorganic, which means static and unchanged with time. Obviously, an engineering system may sustain a dynamic external force, but its material remains inorganic and unchanged most of the time.  On the other hand, a medical system’s internal materials and external force are both dynamic, i.e. changing with time, because living cells will evolve, mutate, or die. These biological phenomena have added many degrees of difficulty and increased amplitudes of complexity on problem solving.  Therefore, in his many years of medical research experiences, he can try his best to achieve his results as accurate as possible, but he can never reach to 100% accuracy of his results.  Nevertheless, this math-physical medicine approach is still capable to get a far more accurate and better comprehension than the traditional biochemical medicine approach.  As we know, physics (a branch of applied mathematics) is based on mathematics, but biology, chemistry, and engineering (branches of applied physics) are based on physics.  As you move up the hierarchy, the easier it is to comprehend, explain, and apply the solutions of a problem at hand; however, the more sacrifices you will have in terms of the result’s accuracy or general applicability.  Therefore, the author realized that the most effective way of applying physics and engineering into his medical research are those basic building block foundations, such as concepts, theories, and modeling methods.  In many cases, he utilized those existing equations or models from textbooks in order to provide himself with a frame of thought, a hint, or a guidance in order to proceed with his own research pathway.  This article (No.286) and one of his previous papers regarding prediction of PPG waveform using perturbation theory (Reference 3) are two examples of his applications for this described research approach.

Conclusions
In summary, by using his own ~33,000 glucose data for the past 129 days, he has identified ~20% of relative glucose energy associated with higher-frequency glucose components (67% of total frequency numbers).  This requires spending additional effort and using Bluetooth technology to collect bigger sets of glucose data (3x more data) which allows him to identify ~20% of possible impact or damage on the internal organs from those secondary S-waves’ energy associated with higher frequency glucose components.  This finding can serve as a foundation or starting point for his future research on diabetic complications.

The summarized comparison ratios between (Lo f & Hi a) versus (Hi f & Lo a) are listed as follows:

  • Energy (E): 4 to 1
  • Frequency numbers (n): 1 to 2
  • Frequency amplitude (a): 3 to 1
  • Frequency amplitude square (a*a): 5 to 1

References

  1. Hsu, Gerald C. eclaireMD Foundation, USA. May 2020. No. 263: “Risk probability of having a metabolic disorder induced cancer (GH-Method: MPM).”
  2. Hsu, Gerald C. eclaireMD Foundation, USA. May 2019. No. 82: ”Using GH-Method: Math-Physical Medicine, Fourier Transform, and Frequency Segmentation Pattern Analysis to Investigate Relative Energy Associated with Glucose.”
  3. Hsu, Gerald C. eclaireMD Foundation, USA. December 2019. 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. June 2020. No.281: ”Differences between 5-minute and 15-minute measurement time intervals of the CGM sensor glucoses device using GH-Method: math-physical medicine.”
  5. Hsu, Gerald C. eclaireMD Foundation, USA. June 2020. No. 272: “Estimated relative energy level of four different Finger PPG ranges using wave theory and frequency domain analysis  (GH-Method: math-physical medicine).”
  6. Hsu, Gerald C. eclaireMD Foundation, USA. June 2020. No. 273: “Using glucose and its associated energy to study the risk probability percentage of having a stroke or cardiovascular diseases from 2018 through 2020 (GH-Method: math-physical medicine).”