GH-METHODS

Math-Physical Medicine

NO. 245

Predicting Finger PPG by using Sensor PPG waveform and data via regression analysis with two different methods, matching time, and matching glucose (GH-Method: math-physical medicine)

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

Introduction
This paper describes the research results of predicted finger-piercing postprandial plasma glucose (PPG) value using a Sensor PPG waveform and its data collected from the continuous glucose monitoring (CGM) device.  The author utilized a regression analysis based on two distinctive methods, Method A on matched timing and Method B on matched PPG.  In other words, he tries to identify one particular sensor PPG value on the sensor’s 3-hour waveform, which is “nearly-equal” to the measured finger PPG value.

Methods
Since 1/1/2012, the author has measured his glucose values using finger-piercing method: once for FPG and three times for PPG each day.  On 5/5/2018, he applied a CGM device on his upper arm and checked his glucose measurements ~80 times each day.  After the first bite of his meal, he measures his interstitial glucose level every 15 minutes for a total of 3-hours or 180 minutes.

He has maintained these dual glucose testing for 706 days (5/5/2018 – 4/11/2020) for the purpose of in-depth glucose research and a special comparison of these two different PPG measurement results.  During the period of 2014-2017, he has already developed some conversion formulas, calculation equations, and outcome refinements for some important diabetes variables, such as PPG relationship with diet, exercise, weather temperature, glucose prediction, HbA1C prediction, and much more.  The author has also discovered that both finger and sensor measurements have some inherent issues related to device reliability and data accuracy.  In addition, there are no strong correlation (R = 29% to 46%) between his finger PPG curve and his sensor PPG curve (see Figure 1). Therefore, it is vital for him to continue with these two parallel glucose measurements for a longer period in order to conduct a big data analytics to have a better understanding of device reliability, data accuracy, and data integrity.  He tries extremely hard not to introduce more uncertainty or inaccuracy on top of his existed pool of data, equations, and conclusions.

Figure 1: Correlation Coefficient R between Finger PPG and Sensor PPG (daily data with R of 46% and 90-days moving average with R of 29%)

On 5/4/2020, he will have collected glucose data on two parallel tracks for two complete years (730 days).  If he can find out that one specific PPG value at a specific time instant on the sensor waveform is “near-equal” go Finger measured PPG value, he can then stop his time-consuming finger piercing task and solely rely on this mathematically derived Finger PPG prediction value from his sensor collected glucose data.  Meanwhile, all of his existing ready-developed equations and formulas for prediction of HbA1C and other important variables will still be useful.

All meals must be distinguished among breakfast, lunch, and dinner.

In addition, he has conducted two sets of numerical calculations regarding these “near-equal” PPG data, both Finger and Sensor.  For the first set, the quarterly analysis, he divided this entire 706 days into 8-quarters (three-months each, with the exception of the last one only having 66 days) for comparison of each quarter’s findings.  For the second set, the cumulative analysis, he added the present quarter results on top of the summary results of all of his previous quarters for deriving out the final cumulative conclusions.

Within these quarterly and cumulative analyses, he has further utilized the following two different models:

  • Model A (timing based):
    Using regression analysis to search for the matching time instants and then calculate their associated PPG values.
  • Model B (glucose based):
    Using regression analysis to search for the near-equal glucoses and then calculate their associated time instants.

Other than using the regression analysis concept and method, the majority of his tasks are actually quite simple and straightforward mathematics and statistics work plus some software modifications for big data analytics.  His primary concerns are still his data accuracy and data integrity because he cannot allow to create an inaccurate Finger PPG prediction value from a collected Sensor PPG waveform.

Final step, his computer algorithm of “auto-detection and auto-correction” and its associated software programs must start from the initial value of the first two-years data which end on 5/4/2020.  Starting from 5/5/2020, he will automatically update his calculation on his iPhone’s data server on a monthly basis.  These computer operations will run automatically and continuously in order to keep the high accuracy of this “predicted Finger PPG” which are inverted from his collected Sensor PPG results.  This is a never-ending task of data accumulation, processing, verification, and correction.

Results
First, he has calculated the average PPG (mg/dL) for three meals on a daily basis and continuously during this entire period of 706 days.  These results are shown in Figure 2:

  • Finger PPG
    breakfast 116 mg/dL
    lunch 116 mg/dL
    dinner 112Gg mg/dL
    daily 114 mg/dL
Figure 2: Measured Finger PPG (5/5/18 - 4/8/20)

Second, based on Model A, he calculates the matching time instant (minutes) in which these two methods have “near-equal” PPG values for three meals each day throughout the entire period of 706 days.  These results are reflected in Figure 3:

  • Match timing
    breakfast 91 minutes
    lunch 106 minutes
    dinner 101 minutes
    daily 99 minutes

From his previous research work, the sensor collected PPG peaks occur approximately 60 minutes (between 45 min to 75 min) after the first bite of food.  Based on his recent neuroscienctific research on food and neuroscience, he has also identified that liquid meals reach to their peaks around 30-45 minutes, while solid meals reach to their peaks around 60-75 minutes.  The conventional medical advice of taking finger-piercing glucose samples about 2-hours after the first bite of food, would result in missing the peak glucose.

Figure 4 illustrates the synthesized PPG curves (i.e. waveforms) for three meals and daily average PPG curve with a yellow ring on the diagram indicating the matching time instant (via Model A) of his finger PPG data.  Listed below are average sensor PPG values (Figure 4):

  • Sensor PPG
    breakfast 136 mg/dL
    lunch 139 mg/dL
    dinner 129 mg/dL
    daily 135 mg/dL
Figure 3: Example of Matching time instants of Sensor PPG with Finger PPG
Figure 4: Matched PPG values and time instants (yellow rings)

By comparing his PPG results of finger vs. sensor, it is evident that the average sensor PPG values are 18.4% higher than the average finger PPG values.  In Figure 5, the exceeding % amount of PPG values are listed below:

  • Sensor PPG > Finger PPG
    breakfast 17%
    lunch 20%
    dinner 15%
    daily 18%

The sensor/finger glucose difference % is defined as follows:

  • Difference %=(Sensor PPG – Finger PPG)/(Sensor PPG)

Figures 6, 7, and 8 show comparison between Model A and Model B regarding PPG, matching time, and sensor/finger difference % for quarterly case.  

Figure 5: Comparison between Sensor and Finger PPG, daily average measurements (Sensor is 18% higher than Finger)
Figure 6: Calculation Table Comparison between Model A and Model B (Quarterly)
Figure 7: Two PPG & Matching Time Comparison between
Model A and Model B (Quarterly)
Figure 8: Sensor/Finger Ratio % Comparison between
Model A and Model B (Quarterly)

Figures 9, 10, and 11 show comparison between Model A and Model B regarding PPG, matching time, and sensor/finger difference % for cumulative case.  

For a better understanding of his first conclusion, let us focus on the latest quarter (ending on 4/11/2020) of the cumulative case.  For Model A, the matched sensor PPG value is 121 mg/dL which is higher than finger PPG 114.4 mg/dL at the matching time of 99 minutes.  For Model B, the matched sensor PPG value is 127 mg/dL which is also higher than finger PPG 114.4 mg/dL at the matching time of 132 minutes.  

His second conclusion is the sensor/finger difference %.  For Model A, the sensor/finger difference % is stabilized around 5.2%; and for Model B, the sensor/finger difference % is stabilized around 10.2%.

Figure 9: Calculation Table Comparison between
Model A and Model B (Cumulative)
Figure 10: Two PPG & Matching Time Comparison between
Model A & Model B (Cumulative)
Figure 11: Sensor/Finger Ratio % Comparison Table between Model A & Model B (Cumulative)

These two conclusive findings are especially important (see Figures 12 & 13).  For Model A, the author can use his future sensor PPG waveform’s glucose at 99 minutes (between 90 minutes and 105 minutes after first bite of food) and then multiply it by 0.948 to get a predicted Finger PPG at 144.4 mg/dL (100% accuracy).  For Model B, the author can use his future sensor PPG waveform’s glucose at 132 minutes (between 120 minutes and 135 minutes after first bite of food) and then multiply it by 0.898 to get a predicted Finger PPG at 144.5 mg/dL (99.9% accuracy).  

Both Model A and Model B have yielded the same predicted Finger PPG value at 114 mg/dL with a >99.9% accuracy.  

Figure 12: Accuracy % between measured PPG and Predicted PPG
(from Sensor PPG and difference % adjustments ) for both Quarterly and Cumulative
Figure 13: Almost identical values of (114.4 mg/dL & 114.5 mg/dL) Predicted Finger PPG via Sensor PPG waveform and applying two different adjustment factors for Model A (5.2%) and Model B (10.2%)

Conclusion
After obtaining these two conclusive results, particularly the findings of the two matched timing instants at 99 and 135 minutes, the matched Finger PPG of 114.4 mg/dL will then be further modified by multiplying two different adjustment factors of 0.948 and 0.898 to achieve a predicted Finger PPG with an accuracy of >99.9%.

The author can then proceed with his software enhancement work of replacing finger PPG measurement data entry by using the computer calculated input results from the measured sensor PPG waveform data directly.  This approach will not only save the author lots of data-entry time, but also maintain the continuous usage and data accuracy’s confidence level of applying his existed equations and formulas to further predict other important biomedical variables, such as the predicted HbA1C value.

References

  1. Hsu, Gerald C. (2018). Using Math-Physical Medicine to Control T2D via Metabolism Monitoring and Glucose Predictions. Journal of Endocrinology and Diabetes, 1(1), 1-6.
  2. Hsu, Gerald C. (2018). Using Signal Processing Techniques to Predict PPG for T2D. International Journal of Diabetes & Metabolic Disorders, 3(2),1-3.
  3. Hsu, Gerald C. (2018). Using Math-Physical Medicine and Artificial Intelligence Technology to Manage Lifestyle and Control Metabolic Conditions of T2D. International Journal of Diabetes & Its Complications, 2(3),1-7.
  4. Hsu, Gerald C. (2018, June). Using Math-Physical Medicine to Analyze Metabolism and Improve Health Conditions. Video presented at the meeting of the 3rd International Conference on Endocrinology and Metabolic Syndrome 2018, Amsterdam, Netherlands.
  5. Hsu, Gerald C. (2018). Using Math-Physical Medicine to Study the Risk Probability of having a Heart Attack or Stroke Based on Three Approaches, Medical Conditions, Lifestyle Management Details, and Metabolic Index. EC Cardiology, 5(12), 1-9.