Math-Physical Medicine

NO. 271

Estimated relative energy level of eight different meal groups using wave theory and frequency domain analysis (GH-Method: math-physical medicine)

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

In this paper, the author describes his research results on the relative energy level of eight different meal groups using wave theory and frequency domain analysis.

1. Database
Since 6/1/2015, the author has collected all of his meal-related data, including carbs/sugar amount, post-meal waking steps, finger PPG at two-hours after the first bite of food, country and location of each meal, and key contents of each meal.  In addition, from 5/5/2018 until 6/6/2020, he has collected 58,370 glucoses via a continuous glucose monitor (CGM) sensor device at ~76.5 data per day.

In this particular analysis, he has utilized all of the data from 2,351 meals including 62 snacks/fruits within 763 days from 5/5/2018 through 6/6/2020.  Since he has collected 13 glucoses for each meal (every 15-minute time interval), these 13 data points build up a “waveform” which contains sufficient characters of a wave, such as frequency, amplitude, and period (wavelength).  He can then apply the wave theory techniques to decompose, analyze, or convert each PPG waveform for further investigation or discovery of many hidden information regarding diabetes disease and overall health conditions.

In his food and meal database, the four major country categories are the USA, Japan, Taiwan, and other nations (such as European, Australia, New Zealand, Middle East,

and Asia).  His five major meal locations are home cooking, chain restaurant, individual restaurant (including American, Asian, and others), Supermarket ready-made, and Airline offered meals.

For this particular research project, he selected eight meal groups, which consist of Japan meals, Total meals, USA meals, Home Cooking meals, Airline meals, individual Restaurant meals, Supermarket meals, and Asian restaurant meals.  The Asian restaurant is a sub-group of the individual restaurant group.  These eight meal groups were chosen to cover the entire spectrum from the lowest to the highest values of both glucoses and energies.  He has already published a few medical papers regarding this subject, from different angles; however, none has ever discussed the specific subject of relative energy from glucose using frequency domain analysis.  An example of these papers can be found in Reference 1.

His customized software program can extract his needed data for a specific research purpose by searching for certain keywords.  The presentation of analysis results can be displayed in the form of time-series, spatial, frequency domain, or author-defined specific empirical formula or academic equation.

2. Wave Theory & Frequency Domain
The following descriptions are directly quoted from what the author has learned from physics and mathematics in his college days.

This time-domain” analysis results are represented by the horizontal x-axis as time (in day) and the vertical y-axis as glucose (in mg/dL), similar to an EKG chart for the heart.  Next, he utilized a mathematical algorithm using Fourier Transform” operation to convert these time-domain data into frequency-domain data.  In the frequency domain chart, the x-axis becomes frequency, instead of time, and the y-axis becomes an amplitude scale associated with distinctive frequency, instead of the glucose itself.  In one of his published paper (Reference 2), he has proved that this frequency domains y-axis amplitude value actually indicates the relative” energy associated with that particular glucose frequency on x-axis.  How many data points on x-axis of frequency curve depends on how many data points on x-axis of time-domain wave.  These two waveforms from time-domain and frequency-domain look very different.  

Based on this frequency-domain data chart, he can then segregate the total span of frequency-domain data into either three frequency sub-ranges of low, medium, and high, or two frequency sub-ranges of low and high.

In the glucose related frequency domain diagram, we can see that its waveform (or curve) pattern is usually a symmetric salad bowl shape with the high edge on each rim.  Let us focus on the left half portion of the chart.  The far left side indicates the lower-frequency range, those much higher glucose energy values associated with lower frequencies of glucose components (less of glucose happening times), while the center portion specifies the higher-frequency range, those much lower glucose energy values associated with higher frequencies of glucose components (more of glucose happening times).

The boundary number of frequency sub-ranges, two or three, is based on a deeper understanding of biomedical waveforms of glucose, and specific objectives of the research project.

3. Energy Theory
After converting the time-series glucose curve into the frequency-domain energy curve, it will be easier to distinguish the difference between primary glucoses (i.e. elevated glucose values associated with higher energy and provide the organs a higher degree of impact or damage) versus secondary glucoses (i.e. moderate glucose values associated with lower energy and provide the organs a lesser degree of impact or damage).  In other words, the degree of impact or damage on the human internal organs are actually due to the energy associated with different glucose values, not the glucose directly.  This situation is similar to a tsunami wave or earthquake wave hitting a building.  It is the energy associated with the wave which damages the building.

Therefore, we must integrate the energy theory from mechanical engineering with the wave theory from geophysics and communication engineering together.  Through this, we can identify and calculate the level of relative energy resulting from glucose components within a frequency sub-range.  Finally, we can utilize the level of relative energy from glucoses to provide a proper and reasonable biomedical interpretation of the degree of impact or damage on the human organs.  The author will conduct more research work and then write more papers regarding how to interpret high energy’s impact on his major organs.

In order to accomplish his research objectives, he had to modify and enhance his software programs in order to be able to calculate the relative energy level of any user-defined frequency range.  This research project has been on-going for more than two years since early 2018.

Figure 1 through Figure 8 display eight distinctive meal groups.  They include many key data, such as number of meals, carbs/sugar amount, post-meal walking steps, average finger PPG, five prominent values of sensor PPG waveform (opening, closing, maximum, minimum, averaged), and time-series waveform.  Readers can delve deeper into each of these eight figures to find out more detailed information regarding each meal group.

Figure 1: Japan 161 meals group
Figure 2: Total 2351 meals group
Figure 3: USA 1310 meals group
Figure 4: Home cook 1318 meals group
Figure 5: Airline 82 meals group
Figure 6: Individual Restaurant 547 meals group
Figure 7: Supermarket 16 meals group
Figure 8: Individual Asian Restaurant 229 meals group

Figure 9 is a data table of his summarized glucoses and energies for theses eight meal groups.  

Figure 9: Summarized data table

Although his objectives are to discover relative energy level from PPG of these eight meal groups, he must start with a better understanding of the behaviors of PPG waveform data.  Figure 10 shows both average glucose bars of Sensor PPG and Finger PPG, while Figure 11 illustrates the total relative energy level of these meal groups.  Figure 12 depicts energy % of low-frequency range versus high-frequency range.  It should be noted that the following three defined values were used as the “cutoff” lines to separate different performance levels:  Finger PPG at 120 mg/dL, Sensor PPG at 140 mg/dL, and Energy at 70.

Several prominent findings are described as follows:  

  1. Average sensor PPG of 134 md/dL is 17% higher than average finger PPG of 115 mg/dL.  
  2. In the glucose analysis, 3 meal groups (Airline, Individual restaurant, and Asian restaurant) are exceeding both 120 mg/dL for Finger PPG and 140 mg/dL for Sensor PPG. 
  3. In the energy analysis, the same 3 meal groups (Airline, individual restaurant, and Asian restaurant) are also exceeding 70 of associated relative energy level.
  4. One meal group (Supermarket ready-made meal) belongs to the grey area” since it only exceeds the energy cutoff line of 70, but its glucoses are within the boundaries of 120 for finger PPG and 140 for sensor PPG.  
  5. In summary, the Total, USA, and Home Cook are the three best performing meal groups (i.e. eating home-cooked meal and staying inside the USA).  Airline, Individual restaurant, and Asian restaurant are the three worst performing meal groups (i.e. not eating in airplane or airport facility or dinning out at individual restaurants, especially eating at Asian restaurants).  However, for the author himself, the Japan meal group produces the least amount of relative energy at a level of 43. This was due to the fact that he usually cooked his meals at his home in Japan and he only ate sashimi (i.e. raw fish) when he dined out.  

It is worthwhile to list below the key information of relative energy levels from both Figure 11 and Figure 12.

Each meal group contains three data: total energy level, % of low-frequency range, and % of high-frequency range.  

  • Japan meals:  43, 79%, 21%
  • Total meals:  55, 90%, 10%
  • USA meals:  56, 91%, 9%
  • Home Cook meals:  65, 89%, 11%
  • Airline meals:  70, 76%, 24%
  • Individual Restaurant meals:  74, 73%, 27%
  • Supermarket meals: 83, 67%, 33%
  • Asian Restaurant meals:  103, 69%, 31%

In Figure 12, The four worst performing meal groups (i.e. airline, individual restaurant, supermarket ready-made, and Asian restaurant) have lower energy % on the low-frequency range, and higher energy % on the high-frequency range.  This significant observation is due to their overall higher average Sensor PPG, resulting in their higher maximum PPG and lasting for a longer period of time in their PPG waveform, as shown in Figures 5, 6, 7, 8, and 13.

Lessons the author has learned from the observations of this PPG energy study are:

  • Avoiding too much carbs/sugar which would push his maximum glucose value too high. Remember that 33% of those high glucoses would create 79% of total associated energy.  The author got this conclusion from applying rather sophisticated physical theories and several complicated mathematical & programming operations.  But, incidentally, the square of 1.33 is 1.77.  The author learned from his college freshman’s physics in 1964 that “Energy of a wave is proportional to the square of wave amplitude.” 
  • Walking more steps after meal, particularly after eating higher amount of carbs/sugar food. This exercise would bring down high glucose values quickly and reducing their relative energies. 

Watching out for the entire PPG waveform’s shape and size (i.e. area underneath the PPG wave) instead of looking at a few glucose points at certain discrete time instants.  Again, watching out for total energy level instead of discrete glucose values.

Figure 10 : Averaged PPG (both sensor and finger) of 8 different meal groups
Figure 11: Relative energy level of 8 different meal groups
Figure 12: Relative energy distribution % between low-frequency (higher energy) vs. high-frequency (lower energy)
Figure 13: Relationship between energy level and low-frequency % (with higher energy)

This study of relative energy resulting from PPG waveforms of eight different meal groups offers a deeper understanding and a better view on the impact and damage on human organs due to elevated glucoses.  This article is only a part of his series of research projects.  Through the application of wave theory and frequency domain analysis from his developed GH-Method: math-physical medicine, he could better understand certain key behaviors and characteristic performance of “glucose” which are able to provide a more in-depth knowledge of diabetic complications prevention.


  1. Hsu, Gerald C., eclaireMD Foundation, USA. December 2019. No. 146: “Geographical segmentation analysis of Sensor PPG data by nations and eating places  (GH Method: math-physical medicine)”
  2. Hsu, Gerald C., eclaireMD Foundation, USA. October 2019. No. 120: “The study on the damage to internal organs and the pancreatic beta cells health state due to excessive energy associated with high PPG components and distinctive waveforms using GH-Method: math-physical medicine.”
  3. Hsu, Gerald C., eclaireMD Foundation, USA. April 2020. No. 246: “Segmentation analysis of sensor glucoses and their associated energy (GH-Method: math-physical medicine).”
  4. Hsu, Gerald C., eclaireMD Foundation, USA. June 2020. No. 267: “Investigation on the impact of different glucose ranges and the damage on human internal organs using frequency domain analyses (GH-Method: math-physical medicine).”