GH-METHODS

Math-Physical Medicine

NO. 389

Applying the concept of glycemic variability and primary characters of glucose wave theory to study the pancreatic beta cells’ self-recovery using GH-Method: math-physical medicine

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

Abstract
The concept and practice of glycemic variability (GV) have existed since the clinical usage of continuous glucose monitoring (CGM) devices to monitor severe diabetes patients and insulin treatments in hospitals.  Many medical papers have been published on GV; however, there is no universally accepted formula or equation for general applications.

Defining GV remains a challenge primarily due to the difficulty of data collection with its associated data cleaning, processing, comprehension and interpretation of the results by physicians and patients along with no consensus regarding the optimal approach for its clinical management. For example, the GV derivation involves the usage of standard deviation (SD) from statistics.  Although SD is widely used, it has limitations because the assumption of measured glucose data are normally distributed, which is typically not the case.  Besides, many research articles use glucose data collected within a few days from hospitalized patients rather than glucose data over a few years from outpatients.  The reason is that until recently after 2016-2017, the self-monitored blood glucose (SMBG) devices became available to diabetes patients to collect their own glucose data at home, instead of in the hospitals or clinic centers.  However, the tasks of glucose data transfer from CGM device to a computer and then the necessary follow-on tasks of data processing, data management, and data analysis still remain a challenge.  Due to the lack of professional training and academic knowledge in this domain, most patients and clinical physicians have encountered difficulties with these tasks.  Data without careful cleaning and proper preparation belong to the category of “garbage inputs” which would result in “garbage outputs”.

Based on the above-mentioned theoretical and technical points, the author decided to conduct this study on applying the basic concept of glycemic variability (i.e. glucose fluctuation between peak and valley) in combination with the primary characters of wave theory (mainly frequencies and amplitudes) to investigate the self-recovery of his pancreatic beta cells.  In addition to the pancreatic health state, GV could provide useful clues on diabetic complications, especially both macro- and micro-blood vessels related diseases, such as stroke, cardiovascular diseases (CVD), and mortality reduction in intensive care units resulting from hypoglycemia.

In summary, GV can be applied on clinical cases of greater mortality in intensive care, increased rate of diabetes complications, and postprandial beta-cell dysfunction (insulin health).  

Although GV can be used as an indicator of insulin resistance, diabetes complications, and hypoglycemia risk for ICU patients, in this article, the author focuses on his continuous medical research work on the “self-recovery” of pancreatic beta cells.  He uses “self-recovery” because he has kept his carbs/sugar intake amount less than 15 grams and his post-meal walking exercise more than 4,000 steps during the past 5 years.  Since 12/8/2015, he has ceased taking any diabetes medication, which is the strongest influential factor for glucose fluctuations.  Therefore, his body is totally free of any external chemical intervention that may alter the organ’s biochemical process and reactions.  Under this strictly controlled lifestyle and environment, his damaged pancreatic beta cells must go through the self-repairing process in order to show any meaningful improvement signs of diabetes conditions.  This is his chosen approach of “fixing his diabetes conditions from their root causes via a stringent lifestyle management”.

In this article, he utilized three different but still inter-related approaches.  The first approach is to evaluate the glucose fluctuation difference for both PPG and daily glucose, which is defined as the “maximum glucose minus the minimum glucose”.  The second approach is to calculate the specific “percentages of both hypoglycemia and hyperglycemia”.  The third approach is to assess the beta cells conditions via the traditional “HbA1C” value changes (HbA1C is the mean value of glucoses, not the short-term or long-term glucose fluctuations).  All of these three approaches have demonstrated that his Period B performance in 2020 is better than his Period A performance from 2018-2019, which resulted from the self-recovery of his pancreatic beta cells.

Introduction
The concept and practice of glycemic variability (GV) have existed since the clinical usage of continuous glucose monitoring (CGM) devices to monitor severe diabetes patients and insulin treatments in hospitals.  Many medical papers have been published on GV; however, there is no universally accepted formula or equation for general applications.

Defining GV remains a challenge primarily due to the difficulty of data collection with its associated data cleaning, processing, comprehension and interpretation of the results by physicians and patients along with no consensus regarding the optimal approach for its clinical management. For example, the GV derivation involves the usage of standard deviation (SD) from statistics.  Although SD is widely used, it has limitations because the assumption of measured glucose data are normally distributed, which is typically not the case.  Besides, many research articles use glucose data collected within a few days from hospitalized patients rather than glucose data over a few years from outpatients.  The reason is that until recently after 2016-2017, the self-monitored blood glucose (SMBG) devices became available to diabetes patients to collect their own glucose data at home, instead of in the hospitals or clinic centers.  However, the tasks of glucose data transfer from CGM device to a computer and then the necessary follow-on tasks of data processing, data management, and data analysis still remain a challenge.  Due to the lack of professional training and academic knowledge in this domain, most patients and clinical physicians have encountered difficulties with these tasks.  Data without careful cleaning and proper preparation belong to the category of “garbage inputs” which would result in “garbage outputs”.

Based on the above-mentioned theoretical and technical points, the author decided to conduct this study on applying the basic concept of glycemic variability (i.e. glucose fluctuation between peak and valley) in combination with the primary characters of wave theory (mainly frequencies and amplitudes) to investigate the self-recovery of his pancreatic beta cells.  In addition to the pancreatic health state, GV could provide useful clues on diabetic complications, especially both macro- and micro-blood vessels related diseases, such as stroke, cardiovascular diseases (CVD), and mortality reduction in intensive care units resulting from hypoglycemia.

In summary, GV can be applied on clinical cases of greater mortality in intensive care, increased rate of diabetes complications, and postprandial beta-cell dysfunction (insulin health).  

Methods
1. MPM Background:
To learn more about the author’s GH-Method: math-physical medicine (MPM) methodology, readers can refer to his articles to understand his developed MPM methodology in References 1 and 2.

2. Other GV research work:
There are many available articles regarding glycemic variability (GV), however, the author decides to include the following combined excerpt from two particular published articles (References 3, 4, and 5).  These two references have cited a total of 114 published papers.  In this way, readers do not have to search for key information from a long list of their cited reference articles.  References 3 focuses on comparison of many published GV articles.  Reference 4 focuses on algorithm, method and firmware design of a web-based APP software for calculating GV values.

Here is the combined excerpt:

Several pathophysiological mechanisms were reported, unifying the two primary mechanisms: excessive protein glycation end products and activation of oxidative stress, which causes vascular complications.  Intermittent high blood glucose exposure, rather than constant exposure to high blood glucose, has been shown to have deleterious effects in experimental studies.  In in-vitro experimental settings and in animal studies, glycemic fluctuations display a more deleterious effect on the parameters of CV risk, such as endothelial dysfunction.  There is a significant association between GV and the increased incidence of hypoglycemia. Hypoglycemic events may trigger inflammation by inducing the release of inflammatory cytokines.  Hypoglycemia also induces increased platelet and neutrophil activation. The sympathoadrenal response during hypoglycemia increases adrenaline secretion and may induce arrhythmias and increase the cardiac workload. Underlying endothelial dysfunction leading to decreased vasodilation may contribute to CV risk.  Published studies have demonstrated that GV, particularly when associated with severe hypoglycemia, could be harmful not only to people with diabetes but also to non-diabetic patients in critical care settings.  Overall, the pathophysiological evidence appears to be highly suggestive of GV being an important key determinant of vascular damage.  Growing evidence indicates that significant GV, particularly when accompanied by hypoglycemia, can have a harmful effect not only on the onset and progression of diabetes complications but also in clinical conditions other than diabetes treated in intensive care units (ICUs).  In addition to HbA1c, GV may have a predictive value for the development of T1DM complications.  In insulin-treated T2DM, the relevance of GV varies according to the heterogeneity of the disease, the presence of residual insulin secretion and insulin resistance.  HbA1c is a poor predictor of hypoglycemic episodes because it only considers 8% of the likelihood of severe hypoglycemia; on the contrary, GV can account for an estimated 40% to 50% of future hypoglycemic episodes.  HbA1c is a poor predictor of hypoglycemic risk, whereas GV is a strong predictor of hypoglycemic episodes. GV was an independent predictor of chronic diabetic complications, in addition to HbA1c. We should note that PPG and GV are not identical, even if they are closely related.  The attention dedicated to GV is derived from the above evidence concerning its effects on oxidative stress and, from the latter, on chronic diabetes complications.  Control of GV has been the focus of a number of interventional studies aimed at reducing this fluctuation. Diet and weight reduction are the first therapeutic instrument that can be used for reducing GV.  

Despite the various formulas offered, simple and standard clinical tools for defining GV have yet to evolve and different indexes of GV should be used, depending on the metabolic profile of the studied population.  Moreover, the absence of a uniformly accepted standard of how to estimate postprandial hyperglycemia and GV adds another challenge to this debate.

The majority of these studies have used time-averaged glucose values measured as glycosylated hemoglobin (HbA1c), an indicator of the degree of glycemic control, which is why HbA1c has become the reference parameter for therapies aimed at reducing the risk of complications from diabetes.  Chronic hyperglycemia is almost universally assessed by HbA1c which has been shown to correlate closely with mean glucose levels over time, as determined by continuous glucose monitoring (CGM). However, the relative contribution of postprandial glycemic excursions and fasting to overall hyperglycemia has been the subject of considerable debate. Monnier et al. suggested that the relative contributions of fasting and postprandial glucose differ according to the level of overall glycemic control.  Fasting glucose concentrations present the most important contribution to hemoglobin glycosylation, whereas at lower levels of HbA1c, the relative contribution of postprandial hyperglycemia becomes predominant. Collectively, GV is likely to be incompletely expressed by HbA1c, particularly in patients with good metabolic control.  

GV is a physiological phenomenon that assumes an even more important dimension in the presence of diabetes because it not only contributes to increasing the mean blood glucose values but it also favors the development of chronic diabetes complications. It appears that GV is poised to become a future target parameter for optimum glycemic control over and above standard glycemic parameters, such as blood glucose and HbA1c.  Avoiding both hyperglycemia and hypoglycemia by careful use of SMBG and the availability of new agents to correct hyperglycemia without inducing hypoglycemia is expected to reduce the burden of premature mortality and disabling CV events associated with diabetes mellitus.  However, defining GV remains a challenge primarily due to the difficulty of measuring it and the lack of consensus regarding the most optimal approach for patient management.

The risk of developing diabetes-related complications is related not only to long-term glycemic variability, but may also be related to short-term glucose variability from peaks to nadirs. Oscillating glucose concentration may exert more deleterious effects than sustained chronic hyperglycemia on endothelial function and oxidative stress, two key players in the development and progression of cardiovascular diseases in diabetes.  Percentages of hyperglycemia (levels between 126 and 180 mg/dl) and hypoglycemia (levels below 70.2 mg/dl) episodes should be used in the GV related research.  Mean amplitude of glycemic excursions (MAGE), together with mean and SD, is the most popular parameter for assessing glycemic variability and is calculated based on the arithmetic mean of differences between consecutive peaks and nadirs of differences greater than one SD of mean glycemia. It is designed to assess major glucose swings and exclude minor ones.  

The features discouraging use of glycemic variability as a parameter in clinical practice and trials are the difficulty of interpreting numerous parameters describing this phenomenon and a limited number of computational opportunities allowing rapid calculation of glycemic variability parameters in CGM data.

The UK Prospective Diabetes Study (UKPDS) showed that after an initial improvement, glycemic control continues to deteriorate despite the use of oral agents to enhance insulin secretion and to reduce insulin resistance.  This deterioration can be attributed to the progressive decline of β-cell function.  Even in subjects with well-controlled type 2 diabetes, 70% of the variability of A1C can be explained by abnormalities in postprandial glucose.  Chronic sustained hyperglycemia has been shown to exert deleterious effects on the β-cells and the vascular endothelium.  Monnier et al. and Brownlee and Hirsch have recently emphasized that another component of dysglycemia, i.e., glycemic variability, is even more important than chronic sustained hyperglycemia in generating oxidative stress and contributing to the development of secondary diabetes complications.  In vivo studies have convincingly demonstrated that hyperglycemic spikes induce increased production of free radicals and various mediators of inflammation, leading to dysfunction of both the vascular endothelium (3) and the pancreatic β-cell.

3. Data and analysis by the author:
The author has collected 96 glucose data per day (every 15 minutes) using CGM since 5/5/2018 and 288 glucose data per day (every 5 minutes) since 2/17/2020.  During the past 971 days (5/5/2018 – 12/31/2020), he has collected 93,216 glucose data (15-minutes model).  He decides to use this 15-minute model due to its sufficient long period of data collection.  In order to study his pancreatic beta cells, he divided the data collected by the 15-minute model into two time periods based on his distinguished lifestyles, Period A of the years 2018-2019 (from 5/5/2018 to 12/31/2019) with heavy traveling schedules and busy lifestyle, and Period B of the year 2020 (from 1/1/2020 – 12/31/2020) with a calm, peaceful, non-traveling quarantined lifestyle.  His research work was conducted by using three different but related key components.  The first component is the glucose fluctuation amount, which is the glucose difference between maximum glucose and minimum glucose.  The second component is the occurrence frequency of hypoglycemia (less than 70 mg/dL) and hyperglycemia (both greater than 140 mg/dL and greater than 180 mg/dL), which is expressed in terms of occurrence percentage of total glucose data amount.  The third component is routinely utilized by clinical physicians and diabetes patients using the changes of HbA1C values.  The HbA1C is related to the average glucose value (the mean value) which still can provide an overall picture of diabetes conditions.

4. Candlesticks (K-Line) Model:
A Japanese merchant, who traded in the rice market in Osaka, Japan, started the candlestick charting around 1850.  An American fellow, Steve Nison, brought the candlestick model concept and method to the Western world in 1991.  These techniques are largely used in today’s stock market to predict the stock price trend.

The author was the CEO of a public-traded company.  Therefore, he is quite familiar with the Candlestick model (aka the “K-line” model).  On 4/17/2018, he had an idea to study glucose behavior by using the candlestick chart and subsequently developed a customized software to analyze his big data of glucose.  The analogies between fluctuations of stock price and glucose value are described as follows:

  1. Stock prices are closely related to the psychology of the buyers and sellers, which is similar to the glucoses related to a patient body’s biochemical interactions and lifestyle behaviors.
  2. Stock price wave of a public traded company is dependent upon its product line, internal management, marketing efforts, and public events and customer perception.  This is remarkably similar to the PPG wave of a diabetes patient being dependent on his/her complex food & diet (buying stock), exercise pattern and amount (selling stock), weather temperature (buying and selling stock), and pancreatic beta cell insulin function (similar to SEC regulations). From a trained mathematician’s eyes, these biomedical wave and financial wave are just two different but similar mathematical representations.  Wave theory can be applied on both of their behaviors.
  3. When there are more buyers than sellers, the stick price goes up, which is similar to the glucose value rising when carbs/sugar intake increases which infuses the energy generation (more buyers) or lack of exercise which reduces the energy consumption (less sellers).
  4. When there are more sellers than buyers, price goes down, which is similar to the glucose value decreasing when carbs/sugar intake decreases (less buyers) or exercise increases (more sellers).

During his period of using the CGM sensor to collect his glucoses data, his standard PPG wave covers a period of 180 minutes, or 3 hours from the first bite of his meal.  Each PPG waveform contains the following five key characteristic data:

  1. “Open” value as his PPG at first-bite, 0 minute
  2. “Close” value as PPG at 180 minutes
  3. “Minimum” value as the lowest PPG
  4. “Maximum” value as the highest PPG
  5. “Average” glucose (HbA1C) as the average value of 13 recorded PPG data per meal over 3 hours.

Results
Figure 1 shows six Candlestick or K-line charts for three meals in Period A (5/18-12/19) and Period B (1/20-12/20).  Although each candlestick chart contains five glucose values, the main focus should be on the maximum glucose and minimum glucose in order to calculate and study the glucose fluctuations, i.e., the GV concept.

Figure 1: K-line charts for 3 meals (breakfast, Lunch, Dinner)

Figure 2 depicts the PPG differences between maximum value and minimum value in both daily curves and 90-days moving average curves.  Period B’s “max-min” data are higher than Period A, and Period A’s 90-day solving average cure is fluctuating more forcefully than Period B which is trending downward until the end of 2020.  

Figure 2: PPG (max-min) for 3 meals

Figure 3 is a conclusive bar chart that represents both line charts of Figure 1 and Figure 2.  Period A’s fluctuated PPG difference (i.e., max PPG – min PPG) is 49 mg/dL, while Period B is 38 mg/dL.  This physical phenomenon of 11 mg/dL lesser-amount of PPG fluctuations (i.e. difference) comes from three possible sources: diet, exercise, and insulin secretion.  

Figure 3: PPG (max-min) bars for 3 meals and daily PPG

Figure 4 reflects the daily PPG (including three meals) curves and candlestick charts for Period A and Period B.  The most important data from this figure is shown in the format of carbs/sugar intake amount in grams, post-meal walking steps, Finger-piercing PPG amount, and CGM collected PPG amount:

  • Period A: 14.5 / 4270 / 116 / 136
  • Period B: 13.8 / 4463 / 108 / 121
  • (A – B):  0.7 /  -193 /     8 /   15

Even though the carbs/sugar intake amount and post-meal walking steps are almost equal between Period A and Period B, the combined impact on their PPG is within 2 mg/dL difference based on the author’s previous research of the Predicted PPG.  However, the finger PPG difference is 8 mg/dL and the CGM sensor PPG difference is 15 mg/dL.  This means that the “insulin produced or released by the pancreatic beta cells” is the only key factor remaining which controls the final PPG difference results.  

Figure 4: PPG for 2 periods (same amount of carbs/sugar & walking)

Furthermore, Figure 5 indicates the daily glucose difference of max minus min are 101 mg/dL for Period A and 87 mg/dL with a difference of 14 mg/dL.  We have learned that there is a 15 mg/dL difference from the CGM sensor PPG’s max-min value.  As a result, there is a mere “-1 mg/dL” difference from the fasting plasma glucose (FPG), glucoses between meals, and pre-bedtime glucose.  

Figure 5: HbA1C comparison

Figure 6 reveals the percentages of both hypoglycemia case (<70 mg/dL) and hyperglycemia cases (both>140 mg/dL and >180 mg/dL) for these two periods.  The data table, in the lower portion of Figure 6, signifies these percentages while the bar chart, in the upper portion, provides a clear graphic view of these percentage differences.  The hypoglycemic situations with almost 0% indicate a low risk of having an insulin shock for the author.  On the other hand, for the hyperglycemic situations of both >140 mg/dL and >180 mg/dL, Period B have consistent lower percentages than Period A.  Again, this Figure shows the observed improvement on his pancreatic beta cells health state.  

Figure 6: daily glucose (max-min) comparison

Finally, Figure 7 demonstrates the HbA1C comparison between two periods.  The HbA1C differences between these two periods are:

  • Lab-tested HbA1C: 0.5%
  • Finger HbA1C: 0.4%
  • Sensor HbA1C: 0.7%

Although HbA1C only reflects the average value or mean value of glucose during a time period of 3 to 4 months, it still can function as a useful tool to judge the overall glucose conditions, including the self-recovery of pancreatic beta cells. 

Figure 7: Comparison of percentages of Hypoglycemia (<70) and Hyperlipidemia (>140 & >180)

Conclusions
Although GV can be used as an indicator of insulin resistance, diabetes complications, and hypoglycemia risk for ICU patients, in this article, the author focuses on his continuous medical research work on the “self-recovery” of pancreatic beta cells.  He uses “self-recovery” because he has kept his carbs/sugar intake amount less than 15 grams and his post-meal walking exercise more than 4,000 steps during the past 5 years.  Since 12/8/2015, he has ceased taking any diabetes medication, which is the strongest influential factor for glucose fluctuations.  Therefore, his body is totally free of any external chemical intervention that may alter the organ’s biochemical process and reactions.  Under this strictly controlled lifestyle and environment, his damaged pancreatic beta cells must go through the self-repairing process in order to show any meaningful improvement signs of diabetes conditions.  This is his chosen approach of “fixing his diabetes conditions from their root causes via a stringent lifestyle management”.

In this article, he utilized three different but still inter-related approaches.  The first approach is to evaluate the glucose fluctuation difference for both PPG and daily glucose, which is defined as the “maximum glucose minus the minimum glucose”.  The second approach is to calculate the specific “percentages of both hypoglycemia and hyperglycemia”.  The third approach is to assess the beta cells conditions via the traditional “HbA1C” value changes (HbA1C is the mean value of glucoses, not the short-term or long-term glucose fluctuations).  All of these three approaches have demonstrated that his Period B performance in 2020 is better than his Period A performance from 2018-2019, which resulted from the self-recovery of his pancreatic beta cells.

References

  1. Hsu, Gerald C., eclaireMD Foundation, USA, “Biomedical research using GH-Method: math-physical medicine, version 3 (No. 386)”
  2. Hsu, Gerald C., eclaireMD Foundation, USA, “From biochemical medicine to math-physical medicine in controlling type 2 diabetes and its complications (No. 387)”
  3. Sunghwan Suh and Jae Hyeon Kim, “Glycemic Variability: How Do We Measure It and Why Is It Important?”; Diabetes & Metabolism Journal, https://www.ncbi.nlm.nih.gov › pmc; http://www.e-dmj.com
  4. Dorota Czerwoniuk, M.Sc., Wojciech Fendler, M.D., Lukasz Walenciak, M.Sc., and Wojciech Mlynarski, M.D., Ph.D.; Department of Pediatrics, Oncology, Hematology, and Diabetology, Medical University of Lodz, Lodz, Poland, Journal of Diabetes Sci Technol. 2011 Mar; 5(2): 447–451, Published online 2011 Mar 1; doi:1177/193229681100500236, PMCID: PMC3125941, PMID: 21527118
  5. Klaus-Dieter Kohnert, MD, PHD1, Petra Augstein, MD, PHD1, Eckhard Zander, MD2, Peter Heinke, MSC1, Karolina Peterson, MD1, Ernst-Joachim Freyse, MD, PHD1, Roman Hovorka, PHD3 and Eckhard Salzsieder, PHD1; Author Affiliations:1Institute of Diabetes “Gerhardt Katsch,” Karlsburg, Germany; 2Clinics for Diabetes and Metabolic Diseases, Karlsburg, Germany; 3Institute of Metabolic Science, University of Cambridge, Cambridge, U.K.; “Glycemic Variability Correlates Strongly With Postprandialβ-Cell Dysfunction in a Segment of Type 2 Diabetic Patients Using Oral Hypoglycemic Agents”
  6. Hsu, Gerald C., eclaireMD Foundation, USA, “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 (No. 339)”
  7. Hsu, Gerald C., eclaireMD Foundation, USA, “Self-recovery of pancreatic beta cell’s insulin secretion based on annualized fasting plasma glucose, baseline postprandial plasma glucose, and baseline daily glucose data using GH-Method: math-physical medicine (No. 297)”
  8. Hsu, Gerald C., eclaireMD Foundation, USA, “Relationship between metabolism and risk of cardiovascular disease and stroke, risk of chronic kidney disease, and probability of pancreatic beta cells self-recovery using GH-Method: Math-Physical Medicine, No. 259”
  9. Hsu, Gerald C., eclaireMD Foundation, USA, “Guesstimate probable partial self-recovery of pancreatic beta cells using calculations of annualized glucose data using GH-Method: math-physical medicine (No. 139)”
  10. Hsu, Gerald C., eclaireMD Foundation, USA, “Probable partial self-recovery of pancreatic beta cells using calculations of annualized fasting plasma glucose (GH-Method: math-physical medicine) No. 138”
  11. Hsu, Gerald C., eclaireMD Foundation, USA, “Probable partial recovery of pancreatic beta cells insulin regeneration using annualized fasting plasma glucose (GH-Method: math-physical medicine) No. 133”
  12. Hsu, Gerald C., eclaireMD Foundation, USA, “Changes in relative health state of pancreas beta cells over eleven years using GH-Method: math-physical medicine (No. 112)”