GH-METHODS

Math-Physical Medicine

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

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

Abstract
This article is a special research on the linear elasticity behavior of glucose using his defined GH-modulus (or M2) to link the input of carbs/sugar intake amount and output of incremental PPG amount.

Here is the formula he used in his previously published papers:

  • Predicted PPG= (FPG* 0.97) + (carbs/sugar grams * M2) – (post-meal waking K-steps * 5)

He has connected this biomedical equation with a basic concept of stress and strain, along with the Young’s modulus of strength of materials in structural and mechanical engineering. Using his collected 11,580 data of glucose, food, and exercise, he has demonstrated that a “pseudo-linear” relationship indeed existing between the carbs/sugar in-take amount multiplied with a “GH modulus (i.e. M2)”, which is similar to the “stress” on an engineering system; and the incremental PPG amount, which is similar to the “strain” of an engineering system. A newly defined coeffi-cient of “GH-modulus” as the value of M2 multiplier is similar to the Young’s modules of stress-strain relationship in the subject of engineering strength of materials.

This investigation has proven the existing pseudo-linear relationship between food as stress on the liver and incre-mental glucose as strain from the liver, particularly during his better controlled period of diabetes from 7/1/2015 to 10/13/2020.

This article is a special research on the linear elasticity of glucose with his defined GH-modulus (or M2) and engi-neering modeling methodologies to investigate various biomedical problems. This methodology and approach are resulted from his specific academic background and different professional experiences prior to his medical research work beginning in 2010. Therefore, he has been trying to link his newly acquired biomedical knowledge over the past decade with his previously acquired mathematics, physics, computer science, and engineering knowledge over 40 years.

The human body is the most complex system he has dealt with. However, by applying his previous acquired knowl-edge to his newly found interest of medicine, he can discover many hidden facts or truths inside the biomedical sys-tems. Many basic concepts, theoretical frame of thoughts, and practical modeling techniques from his fondamental 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 way we take. This is the foundation of the GH-Method: math-physics medicine.

Introduction
This article is a special research on the linear elasticity behavior of glucose using his defined GH-modulus (or M2) to link the input of carbs/sugar intake amount and output of incremental PPG amount.

Here is the formula he used in his previously published papers:

  • Predicted PPG= (FPG* 0.97) + (carbs/sugar grams * M2) – (post-meal waking K-steps * 5)

He has connected this biomedical equation with a basic concept of stress and strain, along with the Young’s modulus of strength of materials in structural and mechanical engineering. Using his collected 11,580 data of glucose, food, and exercise, he has demonstrated that a “pseudo-linear” relationship indeed existing between the carbs/sugar intake amount multiplied with a “GH modulus (i.e. M2)”, which is similar to the “stress” on an engi-neering system; and the incremental PPG amount, which is similar to the “strain” of an engineering system. A newly defined coeffi-cient of “GH-modulus” as the value of M2 multiplier is similar to the Young’s modules of stress-strain relationship in the subject of engineering strength of materials. 

This investigation has proven the existing pseudo-linear relation-ship between food as stress on the liver and incremental glucose as strain from the liver, particularly during his better controlled period of diabetes from 7/1/2015 to 10/13/2020.

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 the developed MPM analysis method in Reference 1.

2. Highlights of his Previous Research
In 2015, 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 approxi-mately 40% of PPG formation, respectively. Therefore, he could safely discount the importance of the remaining ~20% contribu-tion by the 16 other influential components.

In 2016, he utilized optical physics, big data analytics, and artifi-cial intelligence (AI) techniques to develop 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 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 pan-creatic beta cells’ health status; therefore, he can apply the FPG value (more precisely, 97% of FPG value) to serve as the baseline PPG value of his predicted PPG.

In 2018, based on his collected ~2,500 meals and associated sensor PPG waveforms, he applied the perturbation theory from quantum mechanics at first-bite moment of his meal to further predict the PPG waveform (i.e. PPG curve) covering the entire follow-on 180 minutes with a 95% of PPG prediction accuracy.

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

Here is the 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 stabi-lized biomarker since it is directly related to body weight. Weight reduction is a hard undertaking but is a far calmer and more sta-bilizing biomarker in comparison to glucose which fluctuate from moment to moment. The influence of exercise (specifically, post-meal walking steps) on PPG (41% contribution and >80% nega-tive correlation with PPG) is almost equal to the influence from the carbs/sugar intake amount on PPG (39% contribution and >80% positive correlation with PPG). In terms of intensity and duration, exercise is a much simpler subject to study and deal with. On the other hand, the relationship between food nutrition and glucose is an exceedingly complex and difficult subject to fully understand and effectively manage, since there are many types of food and their associated carbs/sugar contents. For example, the author’s food nutrition database has already contained over six million data. As a result, he decided to implement two multipliers, i.e. M1 for FPG and M3 for exercise, as two “constants” and keep M2 as the only “variable” in his PPG prediction equation.

This further simplified his linear equation for predicted PPG as follows:

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

He also defines the following three new terms in Equations 2, 3, and 4:

  • Term 1
    GH 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)
  • Term 3
    GH modulus (i.e. M2) = (Incremental PPG) / (Carbs&sugar)

3. Stress, Strain, & Young’s Modulus
Prior to the past decade in his self-study and medical research work, he was an engineer in the fields of structural (aerospace and naval defense), mechanical (nuclear power plants and comput-er-aided-design), and electronics (computers and semiconductors). The following excerpt comes from the public domain, e.g. Google, 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).”

In this particular study, the above-mentioned Equation 4 is remark-ably similar in “concept and format” to the stress-strain equation as shown below except GH modules and Young’s modulus are re-verse to each other. 

  • GH Modulus (i.e. M2) = (Incremental PPG)/(Carbs&sugar)
  • Young’s Modulus E= stress / strain= σ / ε

The author visualizes the carbs/sugar intake amount as the stress (the force, cause, or stimulator) on his liver and the incremental PPG amount as the strain (the response, consequence, or stimula-tion) from the liver. The GH modulus (i.e., 1/M2) is similar to the Young’s modulus (i.e., E) which describes the “pseudo-linear” re-lationship existed between the carbs/sugar (stress) and incremental PPG (strain).

Finally, conceptually, he is able to connect together the subject of liver glucose production in endocrinology with the subject of strength of materials in structural & mechanical engineering.

Results
The author has recorded his glucoses and weight data since 1/1/2012 and then began collecting carbs/sugar intake amount and post-meal walking steps on 7/1/2015. This period coincides with his “best-controlled” diabetes period, where his average daily glu-coses reduced to around or under 120 mg/dL (i.e., near a normal range) without any medications. He named this as his “linear elas-tic zone” of diabetes health. It should also be noted that in 2010, his average glucose was 280 mg/dL and HbA1C was 10%, while taking three diabetes medications (i.e., strong chemical interven-tions). Prior to 2015, he called that period as his “nonlinear plastic zone” of diabetes health.

From 7/15/2015 to 10/13/2020 (1,930 days), he has collected 6 data per day, 1 FPG, 3 PPG, carb/sugar, and post-meal walking steps. He utilized these 11,580 data and then organized them into 6 years to conduct his annual calculations.

The collected raw data and two sets of calculations are shown in Figure 2. The calculations in this figure have used two different sets of M2 values.

Figure 2: Raw data for the period of 7/1/2015 - 10/13/2020

In Case A, calculation is based on different M2 values (i.e., vari-ables) each year in order to obtain 100% of the PPG prediction ac-curacy for every year in this period. The 100% accuracy indicates that the annual predicted PPG is identical to the annual measured PPG. In Case B, calculation is based on a constant value of 1.82 for M2 (using the 6-years’ average) to obtain six different annual PPG prediction accuracies ranging from 93% to 103%. Figure 3 illustrates calculated data table of these two cases, Case A with different M2 and Cade B with constant M2.

Figure 4 and Figure 5 show the graphic results of Case A and Case B reflectively, based on the calculated data table in Figure 3.

Figure 4 depicts the results from using variable M2 values to achieve a 100% match between the predicted PPG and measured PPG of each year.

Listed below are the values for the M2 multiplier (GH-modulus) for each year:

  • Year 2015 – 1.56
  • Year 2016 – 1.76
  • Year 2017 – 1.59
  • Year 2018 – 1.87
  • Year 2019 – 1.75
  • Year 2020 – 2.41
  • Averaged – 1.82
Figure 3: Calculated PPG prediction using both Case A (vari-able M2) and Case B (constant M2) for the period of 7/1/2015 - 10/13/2020
Figure 4: Calculated PPG prediction using Case A (variable M2) to have 100% prediction accuracy for each year of the period of 7/1/2015 - 10/13/2020

In Figure 5, it reflects the results from using a constant GH-mod-ulus (M2) of 1.82 to achieve different predicted PPG values from the measured PPG values, with different prediction accuracy for each year (from 93% to 103%).

Listed below are the values of the prediction accuracy for each year:

  • Year 2015 – 103%
  • Year 2016 – 101%
  • Year 2017 – 103%
  • Year 2018 – 99%
  • Year 2019 – 101%
  • Year 2020 – 93%
  • Averaged – 100%

In fact, the prediction accuracies varying between 93% to 103% with a 6-years average accuracy of 100% are acceptable for the purpose of practical glucose control. This is equivalent to a diabe-tes patient’s situation of glucose prediction accuracy ranging from 112 mg/dL (93%) to 124 mg/dL (103%) using a normal dividing line of 120 mg/dL (100%).

Figure 5: Calculated PPG prediction using Case A (constant M2) to have different prediction accuracy for each year
(between 93% and 103%) of the period of 7/1/2015 - 10/13/2020

Figure 6 shows an x-y data diagram with a ”pseudo-linear” rela-tionship between x-values of carbs/sugar multiplied by M2, and y-values of the incremental PPG due to FPG and exercise as de-fined in the following Equation:

  • The incremental PPG amount= Predicted PPG – (FPG * 0.97) + (walking k-steps * 5)

The data ranges of x-axis and y-axis are from 20 to 32. It is ob-vious that the six-annual data “almost” form a straight line with a slope of 45% and a very small degree of deviations which is why the author calls it a “pseudo-linear” relationship. This is similar to the “elastic zone” of the Stress-Strain-Young’s modulus diagram in strength of materials of structural and mechanical engineering (Figure 1). This linear relationship makes the task of PPG predic-tion and diabetes control much easier.

Figure 6: A “pseudo-linear” relationship between x-values and y-values during the “linear elastic” zone

Discussion
The author was a severe type 2 diabetes patient since 1995. He suffered many life-threatening diabetic complications during the period of Y2000 to Y2012. After experiencing five cardiovascu-lar episodes, with an average glucose value of 280 mg/dL and HbA1C of 10%, he started to self-study and research diabetes and food nutrition in 2010. He collected his diet and exercise data since 6/1/2015. After 2015, his diabetes conditions have been un-der control via a stringent lifestyle program without taking any diabetes medications; therefore, in this study, he used his collect-ed big data of lifestyle details and glucoses to conduct his rather completed numerical analysis. From 7/1/2015 to 10/13/2020, his diabetes conditions are more or less falling into a linear “elastic” zone which suggests that his PPG would land in a reasonable range (around 120 mg/dL or below) when he consumes lesser amount of carbs/sugar along with exercising adequately.

On the other hand, during the period of 2000-2010, when his dia-betes was totally out of control, he believes that he should belong to a “nonlinear plastic” zone, or at least a “bi-linear plastic” zone, meaning his PPG would remain at a certain elevated level even if he reduced or stopped the intake of carbs/sugar. Worse than having “elevated glucoses” (hyperglycemia i.e. >180 mg/dL), he could suffer from hypoglycemia (glucose <70 mg/dL) leading to insulin shock and eventually sudden death. However, due to the lack of sufficient data collection, he cannot conduct a similar detailed and completed numerical analysis to prove his suspicion of “nonlinear plastic” zone. He can only try to use his scattered data collection from 2010 to 2014 to obtain a guesstimated observation and some partial conclusions.

As shown in Figure 7, he displayed an x-y diagram of predict-ed PPG versus measured PPG over both periods, the smaller area of linear elastic period of 2015-2020 and lager area of nonlinear plastic period of 2010-2014. The comparison between these two “strength of materials” zones are interesting, but yet he needs to find other ways to prove his suspicion on the linkage between his glucose spikes and fluctuations (i.e. nonlinearity) of glucoses in the plastic zone and carbs/sugar intake amount in order to com-pare against his controlled glucoses situations of the pseudo-linear elastic zone.

Figure 7: Discussion of variety of relationship between predicted PPG and measured PPG during 2010-2020
(“pseudo-linear elas-tic” zone and “nonlinear plastic” zone)

In his published research papers since 2019, he has proven that his pancreatic beta cells’ insulin capability of production and quality have been self-repaired at a rather slow speed of an annual rate of 2.7% (References 5 and 6). It means that at least 16% of his insu-lin production and quality problems have been repaired from the beginning of 2015 which is in the elastic zone. Perhaps even 27% of his insulin production and quality problems have been repaired since 2011 which covers both partial plastic and elastic zones. This type of “organic” cells’ regeneration capability and biomed-ical phenomena was unknown to him when he was an engineer and only dealing with various “inorganic” materials, such as metal, concrete, and silicon. As a result, since 2010, he has been fascinat-ed with working the various stimulators and complex stimulations of the biomedical system. The more research work he performs, the more unknown phenomena occur, and the more questions enter his mind, causing him to search for more problems and seek for better answers.

Conclusions
This article represents the author’s special interest in using math-physical and engineering modeling methodologies to inves-tigate various biomedical problems. This methodology and ap-proach are resulted from his specific academic background and different professional experiences prior to his medical research work beginning in 2010. Therefore, he has been trying to link his newly acquired biomedical knowledge over the past decade with his previously acquired knowledge in mathematics, physics, com-puter science, and engineering for over 40 years. 

The human body is the most complex system he has ever dealt with. However, by applying his previous acquired knowledge to his newly found interest of medicine, he can discover many hid-den facts or truths inside the biomedical systems. Many basic con-cepts, theoretical frame of thoughts, and practical modeling tech-niques from his previously acquired fundamental disciplines can be applied to his medical research endeavor. After all, science is based on theory from creation and proof via evidence, and as long as we can discover hidden truths, it does not matter which meth-od we use and what option we take. This is the foundation of the GH-Method: math-physics medicine.

Acknowledgement
Foremost, I would like to express my deep appreciation to my former professors: professor James Andrews at the University of lowa, who helped develop my foundation in basic engineering and computer science, and professor Norman Jones at the Massachu-setts Institute of Technology, who taught me how to solve tough scientific problem through the right attitude and methodology.

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).
  4. Hsu, Gerald C (2020) Application of linear equation-based PPG prediction model for four T2D clinic cases (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).

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.