## GH-METHODS

Math-Physical Medicine

### 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

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

Abstract
This article is Part 5 of the author’s linear elastic glucose behavior study, which focuses on the predicted postprandial plasma glucose (PPG). This study is the combination and continuation of his previous four studies, Parts 1, 2, 3, and 4, on linear elastic glucose behaviors

Listed below are his two recently developed linear elastic glucose equations with two defined coefficients of GH-modulus and his third equation for the predicted PPG from combining these two equations together

(1) FPG = GH.f-modulus * Weight

Where Weight is the input component (similar to stress) and FPG is the output component (similar to strain).

(2) Incremental PPG= GH.p-modulus * Carbs&sugar

Where
Incremental PPG= Predicted PPG – (0.97 * FPG)+ (post-meal walking k-steps * 5)

When he combines the above two linear elastic equations into one, he has the following new PPG prediction equation:

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

The three equations from above were inspired by his prior knowledge in the theory of elasticity in strengths of engineering materi-als which has the following engineering equation developed in 1807 by a British scientist, Thomas Young:

• Stress = Young’s modulus * Strain

Young’s modulus and the two biomedical coefficients (GH.f-modulus and GH.p-modulus) are reciprocal to each other.

The main objective of this study is to offer numerical proof for the PPG prediction accuracy using the above-mentioned equation
(3) and based on his own health data collected from 7/1/2015 to 10/31/2020.

Listed below are the annual values of the GH.f-modulus, GH.p-modulus, PPG prediction % for the author’s case which reflect his severity levels of both obesity and diabetes, and PPG prediction accuracy %:

• Y2015: (0.71, 1.6,97%)
• Y2016: (0.68, 1.8,99%)
• Y2017: (0.69, 1.6, 100%)
• Y2018: (0.66, 1.9, 100%)
• Y2019: (0.66, 1.8,99%)
• Y2020: (0.59, 2.4, 103%)
• Average: (0.67, 1.9, 100%)

The author applied his linear elastic glucose theory of both FPG and PPG behaviors on the predicted PPG value with high accu-racy in order to help other diabetes patients.The five major inter-nal organs involved in glucose production are the brain, stomach, intestines, liver, and pancreas along with three major inter-organ systems including blood, nerves, and hormones.This study has fur-ther proved via a quantitative analysis that PPG level has a close connection with FPG, weight (food quantity), carb/sugar intake (food quality), and exercise.

This article represents the author’s special interest in using math-physical and engineering modeling methodologies to in-vestigate various biomedical problems.The methodology and approach are the results of his specific academic background and various professional experiences prior to the start of his medical research work in 2010. Therefore, he has attempted to link his newly acquired biomedical knowledge over the past decade with his previously acquired knowledge of mathematics, physics, com-puter science, and engineering for over 40 years.

The human body is the most complex system he has dealt with, which includes aerospace, navy defense, nuclear power, com-puters, and semiconductors. By applying his previous acquired knowledge to his newly found interest of medicine, he can dis-cover many hidden facts or truths inside the biomedical systems. Many basic concepts, theoretical frame of thoughts, and practical modeling techniques from his fundamental disciplines in the past can be applied to his medical research endeavor.After all, science is based on theory via creation and proof via evidence, and as long as we can discover hidden truths, it does not matter which method we use and which option we take.This is the foundation of the GH-Method: math-physics medicine.

The author has spent four decades as a practical engineer and un-derstands the importance of basic concepts, sophisticated theories, and practical equations which serve as the necessary background of all kinds of applications.As a result, he spent his time and ener-gy to investigate glucose related subjects using variety of methods he studied in the past, including this particular interesting stress-strain approach.On the other hand, he also realizes the importance and urgency on helping diabetes patients to control their glucoses. That is why, over the past few years, he has continuously simpli-fied his findings about diabetes and to derive more useful formulas and simple tools for meeting the general public’s interest on con-trolling chronic diseases and their complications to reduce their pain and probability of death.

Introduction
This article is Part 5 of the author’s linear elastic glucose behavior study, which focuses on the predicted postprandial plasma glucose (PPG). This study is the combination and continuation of his pre-vious four studies, Parts 1, 2, 3, and 4, on linear elastic glucose behaviors

Listed below are his two recently developed linear elastic glucose equations with two defined coefficients of GH-modulus and his third equation for the predicted PPG from combining these two equations together:

(1) FPG = GH.f-modulus * Weight

Where Weight is the input component (similar to stress) and FPG is the output component (similar to strain).

(2) Incremental PPG= GH.p-modulus * Carbs&sugar

Where
Incremental PPG= Predicted PPG – (0.97 * FPG)+ (post-meal walking k-steps * 5)

When he combines the above two linear elastic equations into one, he has the following new PPG prediction equation:

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

The three equations from above were inspired by his prior knowl-edge in the theory of elasticity in strengths of engineering mate-rials which has the following engineering equation developed in 1807 by a British scientist, Thomas Young:

• Stress = Young’s modulus * Strain

Young’s modulus and the two biomedical coefficients (GH.f-modu-lus and GH.p-modulus) are reciprocal to each other.

The main objective of this study is to offer numerical proof for the PPG prediction accuracy using the above-mentioned equation (3) and based on his own health data collected from 7/1/2015 to 10/31/2020.

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

2. Highlights of his Related Research
In 2015 and 2016, the author decomposed the PPG waveforms (data curves) into 19 influential components and identified carbs/sugar intake amount and post-meal walking exercise contributing to approximately 40% of PPG formation, respectively.Therefore, he could safely discount the importance of the remaining ~20% contribution by the 16 other influential components.

In 2016, he utilized optical physics, big data analytics, and artifi-cial intelligence (AI) techniques to develop a computer software to predict PPG based on the patient’s food pictures or meal photos. This sophisticated AI approach and iPhone APP software prod-uct have reached to a 98.8% prediction accuracy based on ~6,000 meal photos.

In March of 2017, he also detected that body weight contributes to over 85% to fasting plasma glucose (FPG) formation.Furthermore, in 2019, he identified that FPG could serve as a good indicator of the pancreatic beta cells’ health status; therefore, he can apply the FPG value (more precisely, 97% of FPG value) to serve as the baseline PPG value to calculate the PPG incremental amount in order to obtain the predicted PPG.

In 2018, based on his collected ~2,500 meals and associated sensor PPG waveforms, he further applied the perturbation theory from quantum mechanics, using the first bite of his meal as the initial condition to extend and build an entire PPG waveform covering a period of 180 minutes, with a 95% of PPG prediction accuracy.

In 2019, all of his developed PPG prediction models achieved high percentages of prediction accuracy, but he also realized that his prediction models are too difficult for use by the general public. The above-mentioned sophisticated methods would be difficult for healthcare professionals and diabetes patients to understand, let alone use them in their daily life for diabetes control.As a result, he supplemented his complex models with a simple linear equation of predicted PPG (see References 2, 3, 4, and 12).

Here is his simple linear formula:

• Predicted PPG= FPG * M1 + (carbs-sugar * M2) – (post-meal walking k-steps * M3)

Where M1, M2, M3 are 3 multipliers.

After lengthy research, trial and error, and data tuning, he finally identified the best multipliers for FPG and exercise as 0.97 for M1 and 5.0 for M3.In comparison with PPG, the FPG is a more stabilized biomarker since it is directly related to body weight. We know that weight reduction is a hard task.However, weight is a calmer and more stabilizing biomarker in comparison to glucose, which fluctuates from minute to minute.The influence of exercise (specifically, post-meal walking steps) on PPG (41% contribution and >80% negative correlation with PPG) is almost equal to the influence from the carbs/sugar intake amount on PPG (39% contri-bution and >80% positive correlation with PPG).In terms of inten-sity and duration, exercise is a simple and straightforward subject to study.Especially, normal-speed walking is a safe and effective form of exercise for the large portion of diabetes patients, particu-larly senior citizens.

The parameters, FPG and walking, have a lower chance of vari-ation for the author.However, for some diabetes patients, he rec-ommends them to keep the multiplier M3 as a variable if their exercise patterns are different and changing.

The relationship between food nutrition and glucose is a complex and difficult subject to fully understand and effectively manage due to many types of food and their associated carbs/sugar con-tents.For example, in the author’s developed food material and nutritional database, it contains over six million data.As a result, the author decided to implement two multipliers, M1 for FPG and M3 for exercise, as the two “constants” and keep M2 as the only “variable” in his PPG prediction equation and the linear elastic glucose research in this article.

The more simplified linear equation for predicted PPG is listed below:

• Predicted PPG= (0.97*FPG) + (Carbs&sugar * M2)- (post-meal walking k-steps * 5)

He further created two new terms:

• Term 1:
GH.p-modulus = M2
• Term 2:
The incremental PPG amount= Predicted PPG – PPG baseline (i.e. 0.97 * FPG) + exercise effect
(i.e. walking k-steps * 5)

The linear elastic PPG equation

• GH.p-modulus = (Incremental PPG)/(Carbs&sugar)

Recently, he developed his linear elastic FPG equation (Reference 11) as follows:

The linear elastic FPG equation

• GH.f-modulus = (FPG) / (Weight)

3. Stress, Strain, & Young’s Modulus
Prior to his medical research work, he was an engineer in the vari-ous 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, graphic software, and software robot).

The following excerpts come from internet public domain, includ-ing Google and Wikipedia:

• Strain – ε
Strain is the “deformation of a solid due to stress” – change in di-mension 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
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.

4. 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 (Figure 1).

###### Figure 1:Stress-Strain-Young’s modulus, Elastic Zone vs. Plastic Zone

5. Plasticity
When the force is going beyond the elastic limit of material, it is into a plastic zone 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 Young’s modulus associated with different materials:

• Nylon:2.7 GPa
• Concrete:17-30 GPa
• Glass fibers:72 GPa
• Copper:117 GPa
• Steel:190-215 GPa
• Diamond:1220 GPa

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

Professor James Andrews taught the author linear elasticity at the University of Iowa and Professor Norman Jones taught him non-linear plasticity at Massachusetts Institute of Technology.These two great academic mentors provided him the necessary founda-tion knowledge to understand these two important subjects in en-gineering.

6. Data Collection
The author is a 73-year-old male with a 25-year history of T2D. He began collecting his carbs/sugar intake amount and post-meal walking steps on 7/1/2015.From 7/1/2015 to 10/31/2020 (1,962 days), he has collected 6 data per day, i.e. 1 FPG, 3 PPG, carb/sugar amount, and post-meal walking steps.He utilized these 11,772 data of 1,962 days to conduct his prior research work on the subject of linear elastic PPG study (Reference 7).In addition, on 5/5/2018, he started to use a continuous glucose monitoring (CGM) sensor device to collect 96 glucose data each day.Within this time period, he uses the same sensor device to collect 28 FPG data per day from 00:00 to 07:00 at each 15-minute time interval. Based on his prior research, this averaged sensor FPG value is within 1% of margin of error (i.e. 99% accuracy) from his mea-sured FPG at the wake-up moment using finger-piercing and test strip method (Finger FPG).

The period of 7/1/2015 to 10/31/2020 is his “better-controlled” diabetes period, where his average daily glucoses is maintained at 116 mg/dL (<120 mg/dL).He named this as his “linear elastic zone” of diabetes health.It should also be noted that in 2010, his average glucose was 280 mg/dL and HbA1C was 10%, while tak-ing three diabetes medications. The strong chemical interventions from various diabetes medications would seriously alter glucose physical behaviors.He called the period prior to 2015 as his “non-linear plastic zone” of diabetes health.

Results
Listed below are his two recently developed linear elastic glucose equations with two defined coefficients of GH-modulus and his third equation of predicted PPG from combining these two equa-tions:

(1) FPG = GH.f-modulus * Weight

Where Weight is the input component (similar to stress) and FPG is the output component (similar to strain).

(2) Incremental PPG= GH.p-modulus * Carbs&sugar

Incremental PPG= Predicted PPG – (0.97 * FPG)+ (post-meal walking k-steps * 5)

When he combines above two linear elastic equations into one, he has the following new PPG prediction equation:

(3) Final PPG Prediction Equation
Predicted PPG= (0.97 * GH.f-modulus * Weight) +(GH.p-modu-lus * Carbs&sugar) – (post-meal walking k-steps * 5)

Where GH.f-modulus is a coefficient connecting Weight and FPG, and GH.p-modulus is a coefficient connecting Incremental PPG and Carbs&sugar amount.Incremental PPG includes base-line PPG, containing FPG and Weight, and exercise effect.These two coefficients are directly depending on the severity level of patient’s two chronic diseases, specifically obesity and diabetes. The suitable values of these two coefficients of GH-modulus can be estimated from a patient’s values of Weight and HbA1C with a reasonably high accuracy.

The input data of this final PPG prediction equation would avoid using complicated and troublesome measuring devices, either fin-ger piercing or CGM sensor.This prediction formula only needs weight, post-meal walking steps, and carbs/sugar intake amount.

However, estimation of carbs and sugar amount from food or meal is an overly complicated subject and not easy for most patients. The author utilized optical physics and artificial intelligence to de-velop a software for estimating carbs and sugar amount from the photos of food and meal, which achieved 98.8% prediction accu-racy.However, it still requires a smartphone or computer, which is difficult for some patients in underdeveloped nations and senior citizens, who are not familiar with technology.Therefore, the au-thor has continued his development effort on simplifying his pre-diction formula in order to cover a larger group of potential users while still maintaining its prediction accuracy.

Figure 2 shows the raw data and his calculation of predicted PPG with accuracy percentages.He used his annual data from 2015 to 2020, except for Y2015 from 7/1/2015 to 12/31/2015 and Y2020 from 1/1/2020 to 10/31/2020.Listed below are the annual values of the (GH.f-modulus, GH.p-modulus, and PPG prediction %) for the author’s case which reflect his severity levels of both obesity and diabetes, and PPG prediction accuracy percentage:

• Y2015: (0.71, 1.6,97%)
• Y2016: (0.68, 1.8,99%)
• Y2017: (0.69, 1.6, 100%)
• Y2018: (0.66, 1.9, 100%)
• Y2019: (0.66, 1.8,99%)
• Y2020: (0.59, 2.4, 103%)
• Average: (0.67, 1.9, 100%)
###### Figure 2:Raw data and calculated data

Figure 3 depicts the direct comparison between his predicted an-nual PPG and his finger-piercing measured annual PPG.Although there are some small deviations from year to year, those deviations are within the range of +/- 3%.Over the 6- year period, both the predicted PPG and measured PPG are at 116 mg/dL.As mentioned above, this period is his “better-controlled” elastic range, which his developed linear elastic glucose behavior theory can be applied. If a patient has remarkably, high glucose levels or hyperglycemia condition, for example above 200 mg/dL, then this predicted PPG would start to deviate from the measured PPG.The author needs more reliable collected health data from some severe diabetes pa-tients in order to continue his “nonlinear plastic glucose” research.

Figure 4 reveals the PPG prediction accuracy percentages over these 6 years.The annual PPG prediction accuracy are varying be-tween 97% and 103%, but the overall 6-year average accuracy is 100%.

###### Figure 4:Prediction accuracy % of Predicted PPG vs. Measured PPG (2015-2020)

Conclusions
The author applied his linear elastic glucose theory of both FPG and PPG behaviors on the predicted PPG value with high accu-racy in order to help other diabetes patients.The five major inter-nal organs involved in glucose production are the brain, stomach, intestines, liver, and pancreas along with three major inter-organ systems including blood, nerves, and hormones.This study has fur-ther proved via a quantitative analysis that PPG level has a close connection with FPG, weight (food quantity), carb/sugar intake (food quality), and exercise.

This article represents the author’s special interest in using math-physical and engineering modeling methodologies to in-vestigate various biomedical problems.The methodology and approach are the results of his specific academic background and various professional experiences prior to the start of his medical research work in 2010. Therefore, he has attempted to link his newly acquired biomedical knowledge over the past decade with his previously acquired knowledge of mathematics, physics, com-puter science, and engineering for over 40 years.

The human body is the most complex system he has dealt with, which includes aerospace, navy defense, nuclear power, com-puters, and semiconductors. By applying his previous acquired knowledge to his newly found interest of medicine, he can dis-cover many hidden facts or truths inside the biomedical systems. Many basic concepts, theoretical frame of thoughts, and practical modeling techniques from his fundamental disciplines in the past can be applied to his medical research endeavor.After all, science is based on theory via creation and proof via evidence, and as long as we can discover hidden truths, it does not matter which method we use and which option we take.This is the foundation of the GH-Method: math-physics medicine.

The author has spent four decades as a practical engineer and un-derstands the importance of basic concepts, sophisticated theories, and practical equations, which serve as the necessary background of all kinds of applications.As a result, he spent his time and ener-gy to investigate glucose related subjects using variety of methods he studied in the past, including this particular interesting stress-strain approach.On the other hand, he also realizes the importance and urgency on helping diabetes patients to control their glucoses. That is why, over the past few years, he has continuously simpli-fied his findings about diabetes and to derive more useful formulas and simple tools for meeting the general public’s interest on con-trolling chronic diseases and their complications to reduce their pain and probability of death.

References

1. Hsu Gerald C (2020) Biomedical research methodology based on GH-Method: math-physical medicine (No. 310). Journal of Applied Material Science & Engineering Research 4: 116-124.
2. Hsu Gerald C (2020) Application of linear equations to pre-dict sensor and finger based postprandial plasma glucoses and daily glucoses for pre-virus, virus, and total periods using GH-Method: math-physical medicine (No. 345).
3. Hsu Gerald C (2020) A simplified yet accurate linear equation of PPG prediction model for T2D patients using GH-Method: math-physical medicine (No. 97). Diabetes and Weight Man-agement 1: 9-11.
4. Hsu Gerald C (2020) Application of linear equation-based PPG prediction model for four T2D clinic cases using GH-Method: math-physical medicine (No. 99).
5. Hsu Gerald C (2020) 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-physi-cal medicine (No. 339). Internal Med Res Open J 5: 1-7.
6. Hsu Gerald C (2020) A neural communication model between brain and internal organs, specifically stomach, liver, and pan-creatic beta cells based on PPG waveforms of 131 liquid egg meals and 124 solid egg meals (No. 340).
7. Hsu Gerald C (2020) Linear relationship between carbohy-drates & sugar intake amount and incremental PPG amount via engineering strength of materials using GH-Method: math-physical medicine, Part 1 (No. 346).
8. Hsu Gerald C (2020) Investigation on GH modulus of lin-ear elastic glucose with two diabetes patients’ data using GH-Method: math-physical medicine, Part 2 (No. 349).
9. Hsu Gerald C (2020) Investigation of GH modulus on the lin-ear elastic glucose behavior based on three diabetes patients’ data using the GH-Method: math-physical medicine, Part 3 (No. 349).
10. Hsu Gerald C (2020) Using Math-Physics Medicine to Predict FPG (No. 349). Archives of Nutrition and Public Health 2.
11. Hsu Gerald C (2020)Coefficient of GH.f-modulus in the lin-ear elastic fasting plasma glucose behavior study based on health data of three diabetes patients using the GH-Method: math-physical medicine, Part 4 (No. 356).
12. Hsu Gerald C (2020) Community and Family Medicine via Doctors without distance:Using a simple glucose control card to assist T2D patients in remote rural areas via GH-Method: math-physical medicine (No. 264).

Copyright: ©2020 Gerald C. Hsu., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.