## GH-METHODS

Math-Physical Medicine

### NO. 378

A new mathematical biomarker for the general health index for medical conditions in preventing, evaluating, and controlling chronic diseases based on GH-Method: math-physical medicine

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

Abstract
The author has had chronic diseases for 30 years.  For a long time, he could not comprehend and manage the difficult medical terminologies, biomarker units, acceptance levels, numerical meanings, biomedical interpretations, along with their real applications applied to daily life. Therefore, he has been searching for a simpler and easier way to help other patients to overcome these hurdles.

The main purpose of this paper is to describe his newly developed mathematical biomarker, the General Health Index for medical conditions (GHI-MC) using some simple mathematical operations of data normalization and natural logarithm (ln).  This new biomarker can clearly reflect the general health state for patients with chronic diseases based on their routine medical examination results, which include weight, glucose, blood pressure, and lipids.  For most of patients, they do not need to know the mathematical terms, meanings, and applications of  “normalization” and “logarithm”.  They just need to look at the calculated values of GHI-MC and then understand whether they are unhealthy (positive value) or healthy (negative value).

After reading several medical papers regarding the triglyceride and glucose index (TyG) biomarker (References 2, 3, 4, 5, and 6), he was inspired to apply a similar concept of TyG to easily describing the 9-year health history of his combined medical conditions, including four chronic diseases, which are obesity, diabetes, hypertension, and hyperlipidemia.  During this self-examination and extended research process, he has created two new mathematical biomarkers, the GHI-MC1 and GHI-MC2, which are defined as follows:

• GHI-MC1 = sum(ln(Mi, i=1,4)) / 4 and
• GHI-MC2 = ln(sum(Mi, i=1,4)) – ln(4)

Where “Mi” values are “metabolism indexes” and M1 is weight, M2 is glucose, M3 is blood pressure, and M4 is lipid.  All of these Mi values are normalized with the linear equation of measured value divided by standard value”.

This article will explain the GHI-MC concept, and its calculated results using his own input data, and its real application and practice, step by step.

The author has discovered that his combined general health conditions changes into a heathy state when his GHI-MC value reflects a negative value, where the break-even point is zero.  Particularly, when the GHI-MC value reaches approximately -10%, his combined metabolic disorder conditions indicate them to be well controlled.  For example, his GHI-MC reached -14% in 2020, which depicts the “healthiest year” over his 30-year history of chronic diseases.  As we know, these four chronic conditions, obesity, diabetes, hypertension, and hyperlipidemia, are inter-related.

In his opinion, not only can this new biomarker, GHI-MC, describes the combined conditions accurately, it can easily be understood and applied to daily efforts for disease control by other patients.  Therefore, he has decided to develop a software for the mobile phone APP, which utilizes the GHI-MC concept and equations for other patients to use in their daily monitoring and controlling of their combined conditions for four chronic diseases.

Introduction
The author has had chronic diseases for 30 years.  For a long time, he could not comprehend and manage the difficult medical terminologies, biomarker units, acceptance levels, numerical meanings, biomedical interpretations, along with their real applications applied to daily life.  Therefore, he has been searching for a simpler and easier way to help other patients to overcome these hurdles.

The main purpose of this paper is to describe his newly developed mathematical biomarker, the General Health Index for medical conditions (GHI-MC) using some simple mathematical operations of data normalization and natural logarithm (ln).  This new biomarker can clearly reflect the general health state for patients with chronic diseases based on their routine medical examination results, which include weight, glucose, blood pressure, and lipids.  For most of patients, they do not need to know the mathematical terms, meanings, and applications of “normalization” and “logarithm”.  They just need to look at the calculated values of GHI-MC and then understand whether they are unhealthy (positive value) or healthy (negative value).

After reading several medical papers regarding the triglyceride and glucose index (TyG) biomarker (References 2, 3, 4, 5, and 6), he was inspired to apply a similar concept of TyG to easily describing the 9-year health history of his combined medical conditions, including four chronic diseases, which are obesity, diabetes, hypertension, and hyperlipidemia.  During this self-examination and extended research process, he has created two new mathematical biomarkers, the GHI-MC1 and GHI-MC2, which are defined as follows:

• GHI-MC1= sum(ln(Mi, i=1,4)) / 4 and
• GHI-MC2= ln(sum(Mi, i=1,4)) – ln(4)

Where “Mi” values are “metabolism indexes” and M1 is weight, M2 is glucose, M3 is blood pressure, and M4 is lipid.  All of these Mi values are normalized with the linear equation of measured value divided by standard value”.

This article will explain the GHI-MC concept, and its calculated results using his own input data, and its real application and practice, step by step.

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. The authors chronic diseases
Since 1995, he has suffered four chronic diseases, including obesity, diabetes, hypertension, and hyperlipidemia.  He has also endured five cardiovascular episodes (CVD) from 1994 to 2006, chronic kidney disease (CKD) in 2010, bladder infection, foot ulcer, diabetic retinopathy (DR), and hypothyroidism for the past decade.  By 2017, most of his metabolic disorders induced chronic diseases and their complications have been well controlled.

3. Metabolism model
Since 1/1/2012, he has spent 10 years collecting big data (~2 million data) of his health conditions and lifestyle details in order to conduct his own research on chronic diseases and their various complications.  In 2014, by using topology concept of mathematics and finite-element modeling techniques of engineering, he developed a mathematical model of metabolism, including 4 categories of disease control (health conditions as body outputs) and 6 categories of lifestyle details (body inputs).  In total, these 10 categories contain approximately 500 elements.  He has further assembled these categories into two final terms: the metabolism index (MI or Mi), which is a combined daily score to validate the body’s health situation, and general health status unit (GHSU), which is the 90-days moving average number of MI in order to show the trend of combined disease developments and lifestyle management efforts and effectiveness.

His metabolism model was designed for the majority of patients with chronic diseases, not trying to cover some “extreme cases”.  For both the MI and GHSU, he has identified an overall “break-even line” at 0.735 (73.5%) to separate his metabolism conditions between healthy (below 0.735) and unhealthy (above 0.735).  This 0.735 or 73.5% break-even line are for the combined 10 categories of 4 medical conditions and 6 lifestyle details.  However, for the category of the medical conditions, his break-even line is defined at 1.0 (100%) with the best condition at 0.5 (50%) and the worst condition at 1.5 or higher (150% or higher) in order to cover the most-likely data ranges for the majority of type 2 diabetes patients.

For the Mi values greater than 1.5, as an example, Glucose > 180, SBP > 180, triglyceride > 225, etc., they belong to a special category of “extreme high and dangerous cases”. On 5/15/2015, the author’s average daily glucose reached 227 mg/dL and its corresponding M2 value was 1.8917; however, this kind of extreme case only occurred several times in his 9-year record.  These hyperglycemic situations normally occur frequently for some type 1 diabetes patients.

4. Metabolism categories in this study
Within the medical conditions, he has defined 4 categories: weight as m1, glucose as m2, blood pressure as m3, lipid as m4.  At first, he collects his data of medical conditions, and then “normalized” them into four separate metabolism indices, m1, m2, m3, and m4.  He uses the established cutoff points as the “standards” of each category.  All of these Mi values are normalized with the linear formula of measured value divided by standard value.

• Weight: 170 lbs. (BMI 25.0) where it can be adjusted according to each patient’s height and weight
• Glucose: 120 mg/dL
• Systolic BP: 120 mmHG
• Diastolic BP: 80 mmHG
• Heart rate: 60 bpm
• Triglyceride: 150
• HDL-C: 40
• LDL-C: 130
• Total cholesterol: 200

When his measured value reaches to the standard level, he gets a normalized score of 1.0 (100%).  If his health data is higher than the standard level, then it reflects a normalized number higher than 1.0, and vice versa.  For these 4 medical conditions (m1 through m4), he has established the best condition as 0.5 and the worst condition as 1.5 or higher as discussed above.  In this article, the discussion on lifestyle details from m5 through m10 is excluded, instead he will concentrate on weight for obesity (m1), glucoses for diabetes (m2), blood pressures for hypertension (m3), and lipids for hyperlipidemia (m4).

After obtaining all four normalized metabolism indexes, he then utilizes the natural logarithm (ln) operations to develop two new biomarkers of general health index for medical conditions (GHI-MC1 and GHI-MC2).

5. Input data
For the period of ~9 years from 1/1/2012 through 12/8/2020, he has collected his input data of daily weight in the morning, daily average glucose, daily blood pressure in the morning, and periodically tested and annual average lipids.  He then normalizes these health conditions data according to the above standards into 4 sets of normalized annual metabolism indices which are data of m1, m2, m3, and m4.

6. General Health index for medical conditions (GHI-MC)
He has defined the following two  equations for GHI-MC:

• GHI-MC1
= sum(ln(Mi, i=1,4)) / 4
= (ln(m1)+ln(m2)+ln(m3)+ln(m4))/4

and

• GHI-MC2
= ln(sum(Mi, i=1,4)) – ln(4)
= ln(m1+m2+m3+m4) – ln(4)

Where “Mi” values are “metabolism indexes” and M1 is weight, M2 is glucose, M3 is blood pressure, and M4 is lipid.

He used his annual normalized data of m1, m2, m3, and m4 from 2012 through 2020 to plug into above two equations to obtain his GHI-MC1 and GHI-MC2 values for each year. He then studied the trend of his GHI-MC biomarkers and its biomedical interpretations for each year’s value.

Mathematically, the natural logarithm (e=2.7183) values of 0.5, 1, 1.5, 2, 3, 4, and 4.5 are calculated and listed:

• ln(0.5) = -0.693147
• ln(1)   = 0.0
• ln(1.5) = 0.405465
• ln(2)   = 0.693147
• ln(3)   = 1.098612
• ln(4)   = 1.386294
• ln(4.5) = 1.504077
• ln(5)    = 1.609438
• ln(6)    = 1.791759

As shown, when the variable’s value increases from 0.5 to 6.0, the value of natural logarithm (ln) of the variable also increases from a negative value to a positive value.

Results
Figure 1 shows both of his raw input data of normalized mi values and the four-line charts of normalized values of m1 weight, m2 glucose, m3 BP, and m4 lipid.  The calendar years shown in Column 1 reflects the past 9 years from 2012 to 2020.

###### Figure 1: Raw input data and line chart of m1, m2, m3, m4 with the GHI-MC calculations

Figure 2 consists of two data tables showing the step by step calculations for both GHI-MC1 and GHI-MC2.

From Figure 1 and Figure 2, it is clear that the four mi curves are declining from the upper range of 1.06-1.12 year after year, trending downward to the lower range of 0.78-1.01, with the exception of bumps of m3 BP and m4 lipid in 2018-2019.  His turning-around period occurred around 2014-2015, where mi values improved for all of these four fronts.  It should be pointed out that his higher values of m3 and m4 during 2018-2019 are caused by his stressful and hectic traveling schedules in attending ~65 international medical conferences to present ~120 papers.  For the 2020 COVID-19 quarantine period, his overall health conditions, including weight (m1), glucose (m2), BP (m3), and lipids (m4) have declined and maintained to their best status over the past 30-year history of chronic diseases.

###### Figure 2: Data table and GHI-MC1, GHI-MC2 calculations

Figure 3 reveals the author’s two GHI-MC values, GHI-MC1 and GHI-MC2, using their calculated results via two bar chart diagrams. From both Figure 2 and Figure 3, the observations mentioned above can be clearly seen.  The same conclusions can also be applied to Figure 4 involving two curves for GHI-MC1 and GHI-MC2 to demonstrate the conclusions, which are summarized below:

1. The overall trend of the GHI-MC values are declining year after year which reflects the trend of combined four Mi values.
2. The GHI-MC values are positive in 2012-2013, the “unhealthy” years.
3. The GHI-MC values are changed into negative percentages starting from 2014, the “turning-around” year.
4. The traveling impacts on GHI-MC during 2018-2019 are evident.
5. The ending year, 2020, of this study period has the lowest GHI-MC values of -14%, which is the best condition or the “healthiest” year. The overall medical conditions revealed by GHI-MC value of -14% in 2020 is even better than his second best year of -12% / -13% in 2017.
6. The GHI-MC1 values and GHI-MC2 values are almost identical to each other, with an extremely high 99.5% matchability.
###### Figure 4: Line chart of comparison between GHI-MC1 and GHI-MC2 with a high 99.5% matchability

Conclusions
The author has discovered that his combined general health conditions changes into a heathy state when his GHI-MC value reflects a negative value, where the break-even point is zero.  Particularly, when the GHI-MC value reaches approximately -10%, his combined metabolic disorder conditions indicate them to be well controlled.  For example, his GHI-MC reached -14% in 2020, which depicts the “healthiest year” over his 30-year history of chronic diseases.  As we know, these four chronic conditions, obesity, diabetes, hypertension, and hyperlipidemia, are inter-related.

In his opinion, not only can this new biomarker, GHI-MC, describes the combined conditions accurately, it can easily be understood and applied to daily efforts for disease control by other patients.  Therefore, he has decided to develop a software for the mobile phone APP, which utilizes the GHI-MC concept and equations for other patients to use in their daily monitoring and controlling of their combined conditions for four chronic diseases.

References

1. Hsu, Gerald C., eclaireMD Foundation, USA, No. 310: “Biomedical research methodology based on GH-Method: math-physical medicine”
2. Endocrinology and Metabolism Triglyceride Glucose Index Is Superior to the Homeostasis Model Assessment of Insulin Resistance for Predicting Nonalcoholic Fatty Liver Disease in Korean Adults. Endocrinol Metab (Seoul) 2019 Jun;34(2):179-186. doi: 10.3803/EnM.2019.34.2.179.
3. PubMed, NIH, national center for biotechnology information Lipids Health Dis. 2017 Jan 19;16(1):15. doi: 10.1186/s12944-017-0409-6. “The triglyceride and glucose index (TyG) is an effective biomarker to identify nonalcoholic fatty liver disease”, Shujun Zhang  1 , Tingting Du  1 , Jianhua Zhang  1 , Huiming Lu  2 , Xuan Lin  3 , Junhui Xie  1 , Yan Yang  1 , Xuefeng Yu  4
4. RESEARCH, The triglyceride-glucose index (TyG) and Nonalcoholic fatty liver in the Japanese population: a retrospective cross-sectional study, Enqian Liu, Yaping Weng, Aiming Zhou, Chunlai Zeng, DOI: 21203/rs.3.rs-21504/v1
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