## GH-METHODS

Math-Physical Medicine

### NO. 371

A summarized investigation report of GH.p-modulus values using linear elastic glucose theory of GH-Method: math-physical medicine, Part 17

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

Abstract
This article is Part 17 of the author’s linear elastic glucose behavior study. It summarizes key conclusions from the first 16 segments of his research work regarding the data range of GH.p-modulus values (References 9 through 23).

This research report includes the following:

• The author’s personal data and GH.p-modulus values;
• The data and GH.p-modulus values of three US patients and two Myanmar patients;
• The low-bound and high-bound analysis from eight hypothetical standard cases of different carbs/sugar intake amounts and post-meal walking steps;
• The data with high quite GH.p-modulus values from a special investigation case using 285 egg meals with neuroscience influences.

The following paragraphs describe his key variable definitions and mathematical operations of obtaining the GH.p-modulus:

• Baseline PPG equals to 97% of fasting plasma glucose (FPG) value, or 97% * (weight * GH.f-Modulus).
• Baseline PPG plus increased amount of PPG due to food, i.e. plus (carbs/sugar intake amount * GH.p-Modulus).
• Baseline PPG plus increased PPG due to food, and then subtracts reduction amount of PPG due to exercise, i.e. minus (post-meal walking k-steps * 5).
• The Predicted PPG equals to Baseline PPG plus the food influences, and then subtracts the exercise influences.

The linear elastic glucose equation is:

• Predicted PPG =(0.97 * GH.f-modulus * Weight) +(GH.p-modulus * Carbs&sugar) – (post-meal walking k-steps * 5)

Where,

• Incremental PPG = Predicted PPG – Baseline PPG + Exercise impact
• f-modulus = FPG / Weight
• p-modulus = Incremental PPG / Carbs intake

Therefore,

• p-modulus = (PPG – (0.97 * FPG) + (post-meal walking k-steps * 5)) / (Carbs&Sugar intake)

This study is a summarized report of the author’s previous 16 segments of research articles on linear elastic glucose theory.  He focuses on the GH.p-Modulus using four different data groups which cover patients of different nationalities, varying time periods, comparison between pre-virus vs. COVID-19 periods, finger glucoses vs. sensor glucoses, hypothetical boundary analysis (upper bound and lower bound), and a special neuroscience study of egg meals to arrive at the following observed conclusion.

In summary, the author presumes that most patients still having a reasonable normal lifestyles, their GH.p-Modulus value should be located between 1.0 and 6.0.  In this study of linear elastic glucose theory, the GH.p-modulus indeed reflects the actual general health conditions and lifestyle details of a patient.

Practical advice of GH.p-Modulus to patients

1. If you have a record for some of your glucoses, carbs/sugar intake amount, and post-meal walking steps, then you may use this equation to calculate your GH.p-Modulus:
p-Modulus = ((0.97*FPG) + (post-meal k-steps*5)) / (Carbs&sugar amount)
2. If you don’t have your data stored, then you may apply the following suggestions:  If your diabetes conditions is moderate (HbA1C ~7.0 & glucose ~150 mg/dL), then use 1.8 to 2.2 for your GH.p-Modulus; and if your diabetes conditions is more serious (HbA1C >8.0 & glucose >180 mg/dL), then use 2.5 to 3.3 for your GH.p-Modulus.
3. Normally, the GH.p-Modulus should be within 1.5 to 2.5; however, if you want to be more conservative in predicting your PPG, then you may use the GH.p-Modulus greater than 3.0 in the following equation:
Predicted PPG = (0.97 * FPG) + (GH.p-Modulus * carbs& sugar) – (post-meal walking k-steps * 5)

Introduction
This article is Part 17 of the author’s linear elastic glucose behavior study. It summarizes key conclusions from the first 16 segments of his research work regarding the data range of GH.p-modulus values (References 9 through 23).

This research report includes the following:

• The author’s personal data and GH.p-modulus values;
• The data and GH.p-modulus values of three US patients and two Myanmar patients;
• The low-bound and high-bound analysis from eight hypothetical standard cases of different carbs/sugar intake amounts and post-meal walking steps;
• The data with quite high GH.p-modulus values from a special investigation case using 285 egg meals with neuroscience influences.

Methods
1. Background
To learn more about the author’s GH-Method: math-physical medicine (MPM) methodology, readers can refer to his article to understand his developed MPM analysis method in Reference 1.

2. Stress, Strain, & Youngs modulus
Prior to his medical research work, he was an engineer in the various fields of structural engineering (aerospace, naval defense, and earthquake engineering), mechanical engineering (nuclear power plant equipments, and computer-aided-design), and electronics engineering (computers, semiconductors, and software robot).

The following excerpts come from the internet public domain, including Google and Wikipedia:

• Strain – ε:
Strain is the “deformation of a solid due to stress” – change in dimension divided by the original value of the dimension – and can be expressed as
ε = dL / L
where
ε = strain (m/m, in/in)
dL = elongation or compression (offset) of object (m, in)
L = length of object (m, in)
• Stress – σ:
Stress is force per unit area and can be expressed as
σ = F / A   </em
where
σ = stress (N/m2, lb/in2, psi)
F = applied force (N, lb)
A = stress area of object (m2, in2)

Stress includes tensile stress, compressible stress, shearing stress, etc.

• E, Young’s modulus:
It can be expressed as:
E = stress / strain
=  σ / ε
= (F / A) / (dL / L)

where

E = Young’s Modulus of Elasticity (Pa, N/m2, lb/in2, psi) was named after the 18th-century English physicist Thomas Young.

Elasticity:
Elasticity is a property of an object or material indicating how it will restore it to its original shape after distortion.  A spring is an example of an elastic object – when stretched, it exerts a restoring force which tends to bring it back to its original length.

Plasticity:
When the force is going beyond the elastic limit of material, it is into a plasticzone which means even when force is removed, the material will not return back to its original state (Figure 1).

Based on various experimental results, the following table lists some of Youngs modulus associated with different materials:

• Nylon: 7 GPa
• Concrete: 17-30 GPa
• Glass fibers: 72 GPa
• Copper: 117 GPa
• Steel: 190-215 GPa
• Diamond: 1220 GPa

Youngs modules in the above table are ranked from soft material (low E) to stiff material (higher E).”

Professor James Andrews taught the author strength of materials and linear elasticity at the University of Iowa and Professor Norman Jones taught him nonlinear and dynamic plastic behaviors of structures at Massachusetts Institute of Technology.  These two great academic mentors provided him with the foundational knowledge to understand these two important subjects in engineering.

3. Highlights of linear elastic glucose theory
Here is the step by step explanation for the predicted PPG equation using linear elastic glucose theory as described in References 9 through 24:

1. Baseline PPG equals to 97% of FPG value, or 97% * (weight * GH.f-Modulus).
2. Baseline PPG plus increased amount of PPG due to food, i.e. plus (carbs/sugar intake amount * GH.p-Modulus).
3. Baseline PPG plus increased PPG due to food, and then subtracts reduction amount of PPG due to exercise, i.e. minus (post-meal walking k-steps * 5).
4. The Predicted PPG equals to Baseline PPG plus the food influences, and then subtracts the exercise influences.

The linear elastic glucose equation is:

• Predicted PPG =(0.97 * GH.f-modulus * Weight) +(GH.p-modulus * Carbs&sugar) – (post-meal walking k-steps * 5)

Where

• Incremental PPG = Predicted PPG – Baseline PPG + Exercise impact
• f-modulus = FPG / Weight
• p-modulus = Incremental PPG / Carbs intake

Therefore,

• p-modulus = (PPG – (0.97 * FPG) + (post-meal walking k-steps * 5)) / (Carbs&Sugar intake)

By using this linear equation, a diabetes patient only needs the input data of body weight, carbs & sugar intake amount, and post-meal walking steps in order to calculate the predicted PPG value without obtaining any measured glucose data.

In early 2014, the author came up with the analogy between theory of elasticity and plasticity and the severity of his diabetes conditions when he was developing his mathematical model of metabolism using topology concept and finite element method.

On 10/14/2020, by utilizing the concept of Young’s modulus with stress and strain, which was taught in engineering schools, he initiated and engaged this linear elastic glucose behaviors research.  The following paragraphs describe his research findings at different stages:

1. He discovered that there is a “pseudo-linear” relationship existing between carbs & sugar intake amount and incremental PPG amount.  Based on this finding, he defined the first glucose coefficient of GH.p-modulus for PPG.
2. Similar to Young’s modulus relating to stiffness of engineering inorganic materials, he found that the GH.p-modulus is dependent upon the patient’s severity level of diabetes, i.e. the patient’s glucose sensitivity on carbs/sugar intake amount, which reflects this patient’s health state of liver cells and pancreatic beta cells.
3. Comparable to GH.p-modulus for PPG, in 2017, he uncovered a similar pseudo-linear relationship existing between weight and FPG with high correlation coefficient of above 90%.  Therefore, he defined the second glucose coefficient of GH.f-modulus as the FPG value divided by the weight value.  This GH.f-modulus is related to the severity of combined chronic diseases, including both obesity and diabetes.  More than 33 million Americans, about 1 in 10, have diabetes, and approximately 90% to 95% of them have type 2 diabetes (T2D), where 86% also have problems with being overweight or obese.  In other words, 7.7% to 8.2 % of the US population or 25 to 27 million Americans have issues with both obesity and diabetes.
4. He inserted these two glucose coefficients of GH.p-modulus and GH.f-modulus, into the predicted PPG equation to remove the burden of collecting measured glucoses by patients.
5. By experimenting and calculating many predicted PPG values over a variety of time length from different diabetes patients with different health conditions, he finally revealed that GH.p-modulus seems to be “near-constant” or “pseudo-linearized” over a short period of 3 to 4 months.  This short period is compatible with the known lifespan of human red blood cells, which are living organic cells.  This is quite different from the engineering inorganic materials, such as steel or concrete which can last for an exceptionally long period of time.  The same conclusion was observed using his monthly GH.p-modulus data during the COVID-19 period in 2020 when his lifestyle became routine and stabilized.
6. He used three US clinical cases during the 2020 COVID-19 period to delve into the hidden characteristics of the physical parameters and their biomedical relationships.  More importantly, through the comparison study in Part 7, he found explainable biomedical interpretations of his two defined glucose coefficients of GH.p-modulus and GH.f-modulus.
7. He conducted a PPG boundary analysis by discovering a lower bound and an upper bound of predicted PPG values for eight hypothetical standard cases and three US specific clinical cases.  The derived numerical values of these two boundaries make sense from a biomedical viewpoint and also matched the situations of the three US clinical cases.  He conducted two extreme stress tests, i.e. increasing carbs/sugar intake amount to 50 grams per meal and boosting post-meal walking steps to 5k after each meal, to examine the impacts on the lower bound and upper bound of PPG values.
8. Based on six international clinical cases, he further explored the influences from the combination of obesity and diabetes.  Using a “lifestyle medicine” approach, he offered recommendations to reduce their PPG from 130-150 mg/dL down to below 120 mg/dL via reducing carbs/sugar intake and increasing exercise level in walking.
9. Based on his neuroscience research work using both 126 solid eggs and 159 liquid eggs with a very low carbs/sugar intake amount of ~2.5 grams, producing two totally different sets of PPG data and waveforms based on neurosciences viewpoint.  He has also identified a different set of much higher values for GH.p-modulus from the very low carbs/sugar intake of egg meals. Even though this egg neuroscience research results can be served as a special boundary case, it has also further proven that the GH.p-modulus is influenced directly by the human brain and nervous system.
10. He compared the above two egg meals results, including PPG values and glucose coefficients, in particular the GH.p-modulus, against the total results of his 2,843 meals.  He discovered the vast differences of GH.p-modulus magnitudes and also learned the tight relationship between GH.p-modulus value and carbs/sugar intake amount.  By distinguishing the GH.p-modulus results from the special boundary cases of 12.7 for liquid egg meals and 20.7 for solid egg meals, his general GH.p-modulus values from his 2,843 total meals are 2.1 using finger PPG and 3.4 using sensor PPG.
11. He used his 365 egg meal data from his neurosciences research papers to further calculate detailed variations of their associated GH.p-modulus.
12. He applied the linear elastic glucose theory to formulate certain guidelines as a part of his practical “lifestyle medicine” approach for the family medicine branch.
13. He calculates three GH.p-modulus values, 1.8, 2.2, and 1.8, for three different periods, i.e. pre-virus period, COVID-19 period, and total period, respectively.  This data range of between 1.8 to 2.2 matches with his observed personal lifestyle and acquired biomedical knowledge through his medical research work during the past 9 years.
14. He calculates two GH.p-modulus values, 2.0 and 3.3, for two different measured glucoses, i.e. finger-piercing measured glucoses and CGM sensor collected glucoses, respectively.  This GH.p-Modulus difference between 2.0 and 3.3 mainly reflects the average sensor PPG value is 17% higher than the average finger PPG value.

Results
Figures 1, 2, 3 and 4 show the calculated GH.p-Modulus values based on different input data of FPG, PPG, Carbs/sugar intake amount, and post-meal walking steps for the following four different data groups with a variety of situations:

• The author’s personal data and GH.p-modulus values;
• The data and GH.p-modulus values of three US patients and two Myanmar patients;
• The low-bound and high-bound analysis from eight hypothetical standard cases of different carbs/sugar intake amounts and post-meal walking steps;
• The data with quite high GH.p-modulus values from a special investigation case using 285 egg meals with neuroscience influences.

Here again is the step by step explanation for the predicted PPG equation:

• Baseline PPG equals to 97% of FPG value, or 97% * (weight * GH.f-Modulus).
• Baseline PPG plus increased amount of PPG due to food, i.e. plus (carbs/sugar intake amount * GH.p-Modulus).
• Baseline PPG plus increased PPG due to food, and then subtracts reduction amount of PPG due to exercise, i.e. minus (post-meal walking k-steps * 5).
• The Predicted PPG equals to Baseline PPG plus the food influences, and then subtracts the exercise influences.

The linear elastic glucose equation is:

• Predicted PPG =(0.97 * GH.f-modulus * Weight) +(GH.p-modulus * Carbs&sugar) – (post-meal walking k-steps * 5)

Where

• Incremental PPG = Predicted PPG – Baseline PPG + Exercise impact
• f-modulus = FPG / Weight
• p-modulus = Incremental PPG / Carbs intake

Therefore,

• p-modulus = (PPG – (0.97 * FPG) + (post-meal walking k-steps * 5)) / (Carbs&Sugar intake)

The following is the list of the GH.p-Modulus values for the four groups in the form of (low-end of GH.p, and high-end of GH.p):

• Group 1, the author:   (1.8, 3.3)
• Group 2, clinical cases:   (1.0, 3.6)
• Group 3, standard cases: (2.0, 6.0)
• Group 4, neuroscience: (13, 21)

Figure 1 depicts the data analysis results from the author himself.  Using three different time periods, it shows the GH.p data range of 1.8 to 2.2.  However, if using two different glucose measurement devices, it depicts the GH.p data range of 2.0 for finger glucoses and 3.3 for sensor glucoses.  Group 1 has a GH.p data range between 1.8 and 3.3.

###### Figure 1: The author’s case of 3 different time periods and 2 different glucose measuring devices

Figure 2 reflects the data analysis results from three US patients and two Myanmar patients.  Group 2 with five different patients have a GH.p data range between 1.0 and 3.6.

Figure 3 illustrates the data analysis results from eight hypothetical standard cases” with different amounts of carbs/sugar intake and post-meal exercise.  Group 3 with the eight hypothetical standard cases have a GH.p data range between 2.0 and 6.0.

###### Figure 3: 8 Hypothetical standard cases to study upper-bound and lower-bound of GH.p-Modulus

Figure 4 represents the data analysis results from 285neuroscience investigation meals having the same food ingredients of one large egg with an extremely low carbs/sugar intake amount of 0.76 gram from egg alone for each meal while always maintaining ~4.3k post-meal walking steps.  These 285 experimental results show that solid egg meals (135 mg/dL at peak PPG) is 31 mg/dL higher than liquid egg meals (104 mg/dL at peak PPG).  This strange and unique physical phenomenon cannot be explained clearly or satisfactorily using the traditional knowledge of internal medicine and food nutrition.  It is a result from the biomedical neural communication model between the brain and internal organs, specifically stomach, intestine, liver, and pancreas.  The calculated values of GH.p-Modulus in Group 4 is 12.7 for liquid egg meals and 20.7 for solid egg meals.  Therefore, Group 4 of the special  neuroscience experiment indeed demonstrates a special case of high-end GH.p-Modulus values.

The GH.p-modulus value coordinates with a patient’s weight, FPG, PPG, carbs/sugar intake, and post-meal exercise that fluctuates within a reasonable numerical range.  When the author combines the results from Groups 1, 2, and 3, he obtains a data range for GH.p-Modulus values between 1.0 and 6.0.

###### Figure 4: Special case of quite high GH.p-Modulus values from 285 egg experimental meals to demonstrate the brain and neuro-scientific influences on GH.p-Modulus

Conclusions
This study is a summarized report of the author’s previous 16 segments of research articles on linear elastic glucose theory.  He focuses on the GH.p-Modulus using four different data groups which cover patients of different nationalities, varying time periods, comparison between pre-virus vs. COVID-19 periods with different lifestyles, finger glucoses vs. sensor glucoses, hypothetical boundary analysis (upper bound and lower bound), and a special neuroscience study of 285 egg meals to arrive at the following observed conclusion.

In summary, the author presumes that most patients having a reasonable normal lifestyles, their GH.p-Modulus value should be located between 1.0 and 6.0.  In this study, the GH.p-modulus indeed reflects the actual general health conditions and lifestyle details of a patient.

Practical advice of GH.p-Modulus to patients

1. If you have a record for some of your glucoses, carbs/sugar intake amount, and post-meal walking steps, then you may use this equation to calculate your GH.p-Modulus:
p-Modulus = ((0.97*FPG) + (post-meal k-steps*5)) / (Carbs&sugar amount)
2. If you don’t have your data stored, then you may apply the following suggestions:  If your diabetes conditions is moderate (HbA1C ~7.0 & glucose ~150 mg/dL), then use 1.8 to 2.2 for your GH.p-Modulus; and if your diabetes conditions is more serious (HbA1C >8.0 & glucose >180 mg/dL), then use 2.5 to 3.3 for your GH.p-Modulus.
3. Normally, the GH.p-Modulus should be within 1.5 to 2.5; however, if you want to be more conservative in predicting your PPG, then you may use the GH.p-Modulus greater than 3.0 in the following equation:
Predicted PPG = (0.97 * FPG) + (GH.p-Modulus * carbs& sugar) – (post-meal walking k-steps * 5)

References

1. Hsu, Gerald C., eclaireMD Foundation, USA, No. 310: “Biomedical research methodology based on GH-Method: math-physical medicine”
2. Hsu, Gerald C., eclaireMD Foundation, USA, No. 345: “Application of linear equations to predict sensor and finger based postprandial plasma glucoses and daily glucoses for pre-virus, virus, and total periods using GH-Method: math-physical medicine”
3. Hsu, Gerald C., eclaireMD Foundation, USA, No. 97: “A simplified yet accurate linear equation of PPG prediction model for T2D patients  (GH-Method: math-physical medicine)”
4. Hsu, Gerald C., eclaireMD Foundation, USA, No. 99: “Application of linear equation-based PPG prediction model for four T2D clinic cases  (GH-Method: math-physical medicine)”
5. Hsu, Gerald C., eclaireMD Foundation, USA, No. 339: “Self-recovery of pancreatic beta cell’s insulin secretion based on 10+ years annualized data of food, exercise, weight, and glucose using GH-Method: math-physical medicine)
6. Hsu, Gerald C., eclaireMD Foundation, USA, No. 340: “A neural communication model between brain and internal organs, specifically stomach, liver, and pancreatic beta cells based on PPG waveforms of 131 liquid egg meals and 124 solid egg meals)
7. Hsu, Gerald C., eclaireMD Foundation, USA, No. 349: “Using Math-Physics Medicine to Predict FPG”
8. Hsu, Gerald C., eclaireMD Foundation, USA, No. 264: “Community and Family Medicine via Doctors without distance:  Using a simple glucose control card to assist T2D patients in remote rural areas  (GH-Method: math-physical medicine)”
9. Hsu, Gerald C., eclaireMD Foundation, USA, No. 346: “Linear relationship between carbohydrates & sugar intake amount and incremental PPG amount via engineering strength of materials using GH-Method: math-physical medicine, Part 1”
10. Hsu, Gerald C., eclaireMD Foundation, USA, No. 349: “Investigation on GH modulus of linear elastic glucose with two diabetes patients data using GH-Method: math-physical medicine, Part 2”
11. Hsu, Gerald C., eclaireMD Foundation, USA, No. 349: “Investigation of GH modulus on the linear elastic glucose behavior based on three diabetes patients’ data using the GH-Method: math-physical medicine, Part 3”
12. Hsu, Gerald C., eclaireMD Foundation, USA, No. 356: “Coefficient of GH.f-modulus in the linear elastic fasting plasma glucose behavior study based on health data of three diabetes patients using the GH-Method: math-physical medicine, Part 4 ”
13. Hsu, Gerald C., eclaireMD Foundation, USA, No. 357: “High accuracy of predicted postprandial plasma glucose using two coefficients of GH.f-modulus and GH.p-modulus from linear elastic glucose behavior theory based on GH-Method: math-physical medicine, Part 5”
14. Hsu, Gerald C., eclaireMD Foundation, USA, No. 358: “Improvement on the prediction accuracy of postprandial plasma glucose using two biomedical coefficients of GH-modulus from linear elastic glucose theory based on GH-Method: math-physical medicine, Part 6”
15. Hsu, Gerald C., eclaireMD Foundation, USA, No. 359: “High glucose predication accuracy of postprandial plasma glucose and fasting plasma glucose during the COVID-19 period using two glucose coefficients of GH-modulus from linear elastic glucose theory based on GH-Method: math-physical medicine, Part 7”
16. Hsu, Gerald C., eclaireMD Foundation, USA, No. 360: “Investigation of two glucose coefficients of GH.f-modulus and GH.p-modulus based on data of 3 clinical cases during COVID-19 period using linear elastic glucose theory of GH-Method: math-physical medicine, Part 8”
17. Hsu, Gerald C., eclaireMD Foundation, USA, No. 361: “Postprandial plasma glucose lower and upper boundary study using two glucose coefficients of GH-modulus from linear elastic glucose theory based on GH-Method: math-physical medicine, Part 9”
18. Hsu, Gerald C., eclaireMD Foundation, USA, No. 362: “Six international clinical cases demonstrating prediction accuracies of postprandial plasma glucoses and suggested methods for improvements using linear elastic glucose theory of GH-Method: math-physical medicine, Part 10”
19. Hsu, Gerald C., eclaireMD Foundation, USA, No. 363: “A special Neuro-communication influences on GH.p-modulus of linear elastic glucose theory based on data from 159 liquid egg and 126 solid egg meals using GH-Method: math-physical medicine, Part 11”
20. Hsu, Gerald C., eclaireMD Foundation, USA, No. 364: “GH.p-modulus study of linear elastic glucose theory based on data from 159 liquid egg meals, 126 solid egg meals, and 2,843 total meals using GH-Method: math-physical medicine, Part 12”
21. Hsu, Gerald C., eclaireMD Foundation, USA, No. 365: “Detailed GH.p-modulus values at 15-minute time intervals for a synthesized sensor PPG waveform of 159 liquid egg meals, and 126 solid egg meals using linear elastic glucose theory of GH-Method: math-physical medicine, Part 13”
22. Hsu, Gerald C., eclaireMD Foundation, USA, No. 367: “A lifestyle medicine model for family medical practices based on 9-years of clinical data including food, weight, glucose, carbs/sugar, and walking using linear elastic glucose theory and GH-Method: math-physical medicine (Part 14)”
23. Hsu, Gerald C., eclaireMD Foundation, USA, No. 369: “GH.p-modulus study during 3 periods using finger-piercing glucoses and linear elastic glucose theory (Part 15) of GH-Method: math-physical medicine”
24. Hsu, Gerald C., eclaireMD Foundation, USA, No. 370: “GH.p-modulus study using both finger and sensor glucoses and linear elastic glucose theory (Part 16) of GH-Method: math-physical medicine (No. 370)