## GH-METHODS

Math-Physical Medicine

### NO. 349

Investigation on GH Modulus of Linear Elastic Glucose Behavior with Two Diabetes Patients’ Data Using GH-Method: Math-Physical Medicine, Part 2

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

Abstract
This article is an extended research on the linear elasticity of glucose with the author’s defined GH-modulus or M2 cited in Reference 7 (Part 1 or his paper no. 346).  The main purpose of this study is twofold.  First, it is to study the biomedical meaning of the GH modulus which depends on a patient’s severity of type 2 diabetes (T2D) over a period of time.  Second, it is to discover when its linear elastic features would appear, under what kind of conditions, and which easier path for patients to utilize this for their daily glucose control.

Here is the simple linear formula previously defined in References 2, 3, and 4 for predicting the postprandial plasma glucose (PPG):

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

In Reference 7 (paper No. 346), the author connected the biomedical glucose prediction equation with a basic concept of stress and strain in engineering, along with the Young’s modulus of engineering strength of materials.  Using his collected 11,580 data of glucose, food, and exercise, he has demonstrated that a “pseudo-linear” relationship existing between the carbs/sugar intake amount which is similar to the “stress” part on the engineering system; and the incremental PPG amount which is similar to the “strain” part of the engineering system.  A newly defined coefficient of “GH-modulus” (the M2 multiplier for carbs/sugar intake amount) is remarkably similar to the role of Young’s modules on relating stress and strain on the subject of engineering strength of materials.

During his “better controlled” period of diabetes from 7/1/2015 to 10/13/2020, his averaged PPG is 116 mg/dL which is below 120 mg/dL and located within the normal range from diabetes concerns.  Only within this “better-controlled” glucose range, the relationship between carbs/sugar intake and incremental PPG would then be “linear” or “pseudo-linear”.  Otherwise, for severe T2D patients who has elevated PPG level above 180 mg/dL (hyperglycemia) most of the time and then suddenly decreased to below 70 mg/dL (hypoglycemia or insulin shock), the relationship between food and PPG would then follow a nonlinear plastic pattern where the defined linear relationship would not be applicable.

By 2019, approximately 6% of worldwide population (or 463 million people) have diabetes.  Although he believes that his linear elastic glucose behavior of GH modulus is only applicable for patient’s glucose levels below 180 mg/dL and above 70 mg/dL, but it is already a wide enough range for lots of diabetes patients to use.  In regard to nonlinear plastic zone, more hyperglycemic cases and associated data are required to collect and then conduct a further complex analysis.  At least, this linear elastic glucose behavior is the first stage of getting sufficient information to move further into a more complicated nonlinear plastic glucose zone.

Based on two diabetes patients data, for either fixed M2 or variable M2 values, a linear relationship between carbs/sugar intake amount and incremental PPG amount have been oobserved.  This defined GH-modulus (i.e. M2 value) is easier to be applied over a reasonable long period, for example, either 3 months or 4 months in order to match with the lab-tested HbA1C value.  Since blood and liver cells are organic material, the GH-modulus changes according to the severity of a patient’s diabetes conditions.  However, the author would like to recommend using a fixed GH-modules or M2 value within a period of 3 to 4 months due to the simplicity of calculation and practical usage.

The author has spent four decades as a practical engineer, but he does understand the importance of basic concepts, sophisticated theories, and practical equations which serve as the necessary background of all kinds of applications.  Therefore, he focused his time and energy to investigate glucose related subjects using a variety of methods he learned in the past, including this particularly interesting stress-strain approach.  In addition, he understood the importance and urgency in helping diabetes patients to control their glucoses.  That is why, over the past few years, he has continuously simplified his findings regarding diabetes and derived more useful formulas or practical tools in meeting the general public’s interest on controlling chronic diseases and their complications to reduce pain and death probability.

Introduction
This article is an extended research on the linear elasticity of glucose with the author’s defined GH-modulus or M2 cited in Reference 7 (Part 1 or his paper no. 346).  The main purpose of this study is twofold.  First, it is to study the biomedical meaning of the GH modulus which depends on a patient’s severity of type 2 diabetes (T2D) over a period of time.  Second, it is to discover when its linear elastic features would appear, under what kind of conditions, and which easier path for patients to utilize this for their daily glucose control.

Here is the simple linear formula previously defined in References 2, 3, and 4 for predicting the postprandial plasma glucose (PPG):

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

In Reference 7 (paper No. 346), the author connected the biomedical glucose prediction equation with a basic concept of stress and strain in engineering, along with the Young’s modulus of engineering strength of materials.  Using his collected 11,580 data of glucose, food, and exercise, he has demonstrated that a “pseudo-linear” relationship existing between the carbs/sugar intake amount which is similar to the “stress” part on the engineering system; and the incremental PPG amount which is similar to the “strain” part of the engineering system.  A newly defined coefficient of “GH-modulus” (the M2 multiplier for carbs/sugar intake amount) is remarkably similar to the role of Young’s modules on relating stress and strain on the subject of engineering strength of materials.

During his “better controlled” period of diabetes from 7/1/2015 to 10/13/2020, his averaged PPG is 116 mg/dL which is below 120 mg/dL and located within the normal range from diabetes concerns.  Only within this “better-controlled” glucose range, the relationship between carbs/sugar intake and incremental PPG would then be “linear” or “pseudo-linear”.  Otherwise, for severe T2D patients who has elevated PPG level above 180 mg/dL (hyperglycemia) most of the time and then suddenly decreased to below 70 mg/dL (hypoglycemia or insulin shock), the relationship between food and PPG would then follow a nonlinear plastic pattern where the defined linear relationship would not be applicable.

By 2019, approximately 6% of worldwide population (or 463 million people) have diabetes.  Although he believes that his linear elastic glucose behavior of GH modulus is only applicable for patient’s glucose levels below 180 mg/dL and above 70 mg/dL, but it is already a wide enough range for lots of diabetes patients to use.  In regard to nonlinear plastic zone, more hyperglycemic cases and associated data are required to collect and then conduct a further complex analysis.  At least, this linear elastic glucose behavior is the first stage of getting sufficient information to move further into a more complicated nonlinear plastic glucose zone.

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 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 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 artificial 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 product 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 pancreatic beta cells’ health status; therefore, he can apply the FPG value or more precisely, 97% of the 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 and then 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 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 methods would be difficult for healthcare professionals and diabetes patients to understand, let alone use them in their daily life for diabetes control.  Therefore, he tried to supplement his complex models with a simple linear equation of predicted PPG (see References 2, 3, and 4).

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, but weight is a far 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% contribution and >80% positive correlation with PPG).  In terms of intensity and duration, exercise is a much simpler and straightforward subject to study and deal with.

Therefore, for the author, these two parameters, FPG and walking, have a lower chance of variation.  However, for other diabetes patients, it is best to keep the multiplier M3 as a variable if they constantly change their exercise patterns.

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 nutritional database contains over six million data.  As a result, he 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 study in this article.

Here is his simplified 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 terms 1, 2, and 3:

• Term 1:
GH modulus = M2
• Term 2:
The incremental PPG amount = Predicted PPG – PPG baseline
(i.e. 0.97 * FPG) + exercise effect
(i.e. post-meal walking k-steps * 5)
• Term 3:
GH modulus = (Incremental PPG)/(Carbs&sugar)

3. Stress, Strain, & Youngs 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 computer-aided-design), and electronics (computers and semiconductors).

The following excerpts come from Internet, e.g. 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
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 Youngs 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

Youngs modules in 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 nonlinear plasticity at Massachusetts Institute of Technology.  These two great academic mentors provided him with the foundation knowledge of these two important subjects.

In this study, he uses the analogy of relationship among stress, strain, and Young’s modulus to illustrate a similar relationship among carbs/sugar intake amount, incremental predicted PPG, and GH modulus (i.e. M2).  They are listed below for a closer comparison.

• GH modulus (i.e. M2) = (Incremental PPG)/(Carbs&sugar)
• Youngs modulus E = stress / strain =  σ / ε

Where Incremental PPG is the incremental amount of predicted PPG (note: the predicted PPG is also replaced by the measured PPG for one of the sensitivity study of glucose behaviors in this article).

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 stimulation) from the liver.  The GH modulus (i.e. M2) is similar to the Young’s modulus (i.e. E) which describes the “pseudo-linear” relationship 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.

6. Data collection
The author (male case) 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 7/15/2015 to 10/18/2020 (1,935 days), he has collected 6 data per day, 1 FPG, 3 PPG, carb/sugar, and post-meal walking steps.  He utilized these 11,610 data of 1,935 days to conduct his prior research work on the subject of linear elastic glucose 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.

The period of 7/1/2015 to 10/18/2020 is his “best-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 taking three diabetes medications.  Please note that the strong chemical interventions from various diabetes medications would seriously alter glucose physical behaviors.  He called the period prior to 2015 as his “nonlinear plastic zone” of diabetes health.

The second set of data comes from his wife (female case) with a 22-year history of T2D.  She began to collect her glucose data via finger-piercing method (finger glucose) since 1/1/2014.  However, she does not keep a detailed record of her diet and exercise.  Both patients eat almost the same meals prepared by the author, except that she consumes more meat which partially affects her hyperlipidemia and hypertension conditions.  From the diabetes research viewpoint, he decided to use 80% of the male case’s carbs/sugar amount for her and use 50% of the male case’s post-meal walking steps for her.  On 1/1/2020, she began using the same CGM device to collect her sensor glucose data at the same rate of 96 data per day since 1/1/2020.

In order to maintain data consistency for a fair and accurate comparison, the author took both male data and female data from 1/18/2020 through 10/18/2020 and subdivided them into 9 equal-length monthly sub-periods to study their glucose fluctuation patterns and data.

Results
1. Fixed M2 Case
Figure 2 shows the collected raw data and fixed M2 values for calculating both predicted PPG and prediction accuracy percentages.  In this table, the author utilized two different fixed values of M2 for male case and female case individually to calculate both x- and y- components of his “linear elastic glucose” equation.  The comparison between the male case M2 value of 3.6 and the female case M2 of 2.6 revealed the individual severity of their respective T2D conditions.  The male case indicates a more severe diabetes patient who requires higher M2 value to increase his predicted PPG in order to match his higher measured PPG value.

###### Figure 2: Raw data and calculations for fixed M2 value (1/18/2020 - 10/18/2020).

Again, the linear elastic glucose equation using predicted PPG is listed below:

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

The “x-component of the linear elastic glucose equation is: (carbs&sugar * M2);

While the “y-component of the linear elastic glucose equation is: (Predicted PPG – (FPG * 0.97) + (post-meal walking k-steps * 5)

Due to the linearity characteristics of this equation, the relationship between the x-component and y-component is always guaranteed to be linear”. However, the different M2 values would result into different data ranges of x and y components.   Figures 3 and 4 show these different M2 values and data ranges for male case and female case, respectively.

The male case with the fixed M2 of 3.6, both x and y are within the range of 35 to 58 with an average value of 44 is shown in Figure 3.  The female case with the fixed M2 of 2.6, both x and y are within the range of 22 to 34 with an average value of 26 is observed in Figure 4.

###### Figure 4: Female case using fixed M2 value of 2.6 (1/18/2020 - 10/18/2020).

In summary, the higher M2, the higher x and y values become, and the higher predicted and measured PPG values are.  The key point from these two figures is that the M2 values are varying based on a patients body conditions.  This is similar to the different organic materials from the different Youngs modules (E) values, such as nylon’E ~3 versus steel’s E ~200.

Listed below are the values of the prediction accuracy for male and female for each month.  Please note that the prediction accuracy percentage varies with the fixed M2 input, however, their prediction accuracies are 100% for the total period of 9 months for both male case and female case which is the purpose of selecting these two fixed M2 values.

• 1/18 – 2/18: 101% & 97%
• 2/18 – 3/18: 97% & 99%
• 3/18 – 4/18: 98% & 95%
• 4/18 – 5/18: 111% & 108%
• 5/18 – 6/18: 101% & 107%
• 6/18 – 7/18: 88% & 93%
• 7/18 – 8/18: 100% & 95%
• 8/18 – 9/18: 102% & 101%
• 9/18 – 10/18: 98% & 106%
• 2020 Average: 100% & 100%

2. Variable M2 Case
Figure 5 illustrates the collected raw data to be used in his variable M2 case of calculations.  In this table, the author utilized variable value of M2 for each month in order to make the calculated x-component values to match with the calculated y-components values during each monthly sub-period; therefore, to “force” the predicted PPG value to match with the measured PPG value in each month.  As a result, a “pseudo-linear” relationship between x-component and y-component could be created and observed.  However, this approach will cause some degree of sacrifice on PPG prediction’s accuracy.

###### Figure 5: Raw data and calculations for variable M2 values (1/18/2020 - 10/18/2020).

This forced “pseudo-linear” relationship makes sense in the biomedical field since red blood cells and liver cells are organic materials which are different from those inorganic materials in the engineering systems, such as rubber, concrete, or steel.  The human organ cells are not only organic but also have different lifespans, where they can mutate, change, repair, or die. For example, the lifespan of the red blood cells is 115 to 120 days, the lifespan of liver cells is 300 to 500 days, and the lifespan of pancreatic beta cells is unknown with slightly adaptive change (this is why pancreatic beta cells self-repair process is very slow, about 2.7% per year for the author).  Not all of the body cells die at the same moment.  At any given instance, an organ would have combinations of new cells, sick cells, dying cells, and mutated cells, mixing together.  It is a very complex and extraordinarily situation; therefore, the author has chosen different M2 values for different months in order to achieve his 100% prediction accuracies for all sub-periods.  This would be a reasonable approach in proceeding with his biomedical research.

In the previous paragraph (Figures 2, 3, and 4), the fixed M2 difference between the male case of 3.6 versus the female case of 2.6 is based on the severity of their T2D between patients.  Furthermore, in this paragraph (Figures 5, 6, and 7), it has demonstrated that the variable M2 value differences of different months are resulted from the T2D conditions varying month to month for each patient.  This means that glucose is a “dynamic” function instead of being a “static” function.  The above discussions are the major differences between the linear elasticity organic glucoses and the traditional linear elasticity of strength of inorganic engineering materials.

###### Figure 7: Female case using variable M2 values (1/18/2020 - 10/18/2020).

Again, for conducting his sensitivity analysis, the linear elastic glucose equation using measured PPG is modified and listed below:

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

The “x-component of the linear elastic glucose equation is: (carbs&sugar * M2);

While the “y-component of the linear elastic glucose equation is: (Measured PPG – (FPG * 0.97) + (post-meal walking k-steps * 5)

By examining the variable M2 values, over 9 monthly sub-periods, the male case has M2 range from 2.8 to 5.2 with an average of 3.7 value, and the female case has M2 range from 1.9 to 3.6 with an average of 2.7 value (Figure 5).  Please note the minor difference between fixed M2 of 3.6 versus 2.6 and variable M2 of 3.7 versus 2.7 which are caused by rounding off in the numerical analysis.

For the male case with variable M2, both x and y components are within the range of 37 to 51 with an average value of 45 (Figure 6).  The female case with variable M2, both x and y components are within the range of 18 to 32 with an average value of 26 (Figure 7).

In summary, similar to the fixed M2 case, for most of the months, the higher variable M2, the higher x and y values become, and the higher predicted and measured PPG values are.  The key point from these two figures is that the monthly M2 values are dependent on the patients body conditions for that particular month. Figures 6 and 7 have graphically demonstrated the linear elastic glucoses data from Figure 5.

Listed below are the values of the individual M2 multiplier (i.e. GH-modulus) for each month in 2020, in the order of (male case vs. female case).

• 1/18 – 2/18: 3.5 vs. 3.0
• 2/18 – 3/18: 3.9 vs. 2.7
• 3/18 – 4/18: 3.8 vs. 3.1
• 4/18 – 5/18: 2.8 vs. 1.9
• 5/18 – 6/18: 3.5 vs. 1.9
• 6/18 – 7/18: 5.2 vs. 3.6
• 7/18 – 8/18: 3.6 vs. 3.2
• 8/18 – 9/18: 3.4 vs. 2.5
• 9/18 – 10/18: 3.8 vs. 1.9
• 2020 Average: 3.7 vs. 2.7

The purpose in selecting variable M2 values for each of the 9 monthly sub-periods is to achieve 100% match between x- component and y-component for both male case and female case.

3. Discussion of GH modulus
This “linear elastic glucose” study started from the verification and improvement for the predicted PPG through his previously defined simple formula of PPG prediction. The author has learned from his engineering background that a linear system approach would be the easiest way to study a relationship between causes and consequences.

Therefore, he started to investigate the similarity between elastic glucose system and elastic engineering system using Young’s modulus and GH-modulus as his pair of analogy models.  Nevertheless, he has never forgotten his ultimate objective is to identify an easier application model with a higher PPG prediction accuracy in order to help other diabetes patients while maintain the basic requirement of science to seek for truth with high precision.

Either using a fixed M2 value to achieve a high accuracy over a total period of 9 months or using monthly variable M2 values to achieve high accuracies for every monthly sub-period, he has observed a linear relationship existing between carbs/sugar intake amount and incremental PPG amount (including predicted or measured PPG, FPG, and exercise).  More importantly, he still maintains an extremely high PPG prediction accuracy from using both approaches.

One important viewpoint is that glucose is an organic material which consists of nonlinear and dynamic functional behaviors in its nature.  Therefore, in order to fully understand and be able to describe its behavior accurately, a research using a nonlinear plastic model is needed.  However, at present time, similar to linear elasticity engineering applications, this linear elastic glucose behavior study already covers a sufficient scope of biomedical applications, and it is useful.  As a counterpart example, many T2D patients are either in the pre-diabetes range (PPG value at 120 to 140 mg/dL) or their glucose levels fall below the hyperglycemia range (i.e., glucose at 180 mg/dL or lower). This simpler “linear glucose model” can be extremely useful for many diabetes patients worldwide already.

Depending on the approach, either the overall period’s fixed M2 or sub-period’s variable M2, it would be easier for diabetes patient to use this linear elastic glucose behavior for their glucose control.  The author prefers the fixed M2 model since traditional internal medicine utilizes the HbA1C model.  The HbA1C value is remarkably close to the average glucose over a 90-day period (conventionally) or over 120-day period (the author’s defined model based on red blood cells life span).  Besides, calculating or guess-estimating a single M2 value is much easier and acceptable by patients than using multiple M2 values for every sub-period calculations.

Conclusions
The author has spent four decades as a practical engineer, but he does understand the importance of basic concepts, sophisticated theories, and practical equations which serve as the necessary background of all kinds of applications.  Therefore, he has focused his time and energy to investigate glucose related subjects using a variety of methods he learned in the past, including this particularly interesting stress-strain approach.  In addition, he understood the importance and urgency in helping diabetes patients to control their glucoses.  That is why, over the past few years, he has continuously simplified his findings regarding diabetes and derived more useful formulas or practical tools in meeting the general public’s interest on controlling chronic diseases and their complications to reduce pain and death probability.

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. 346:  “Interpretation of relationship between carbohydrates & sugar intake amount and incremental PPG via strength of materials of Structural and Mechanical Engineering using GH-Method: math-physical medicine”