Method Of
Non-Invasive Of Blood Sugar By Arterial Pulse.

This paper proposes a method for non-invasive blood sugar determination by arterial pulse. A technique has been developed to collect volumetric pulse wave signal and thermal metabolic signal at the radial artery of the subject's wrist. This method will allow everyone to monitor blood glucose levels according to a personalized effective range of blood glucose levels based on a scientific approach.

Author Zlata Tikhonenko.


Glucose is the main source of energy for the cells, it is the fuel for normal functioning of all organs and systems of the human body. Blood glucose content is quite variable, however in healthy individuals it is maintained in a fairly narrow range and rarely falls below 2.5 mmol/l and rises above 8 mmol/l (even immediately after a meal). A specific hormonal mechanism maintains blood glucose levels. Glucose enters the body with food. Food is broken down in the gastrointestinal tract, after which the glucose is absorbed into the blood. Insulin is needed to get the glucose into the cell. This hormone is produced in special cells of the pancreas and increases the permeability of cell membranes to glucose. If the cells of the pancreas do not produce enough insulin, or if the cells of the body stop receiving insulin, the glucose remains in the blood. The cells of organs and tissues are then deprived of energy and "starved".

 If glucose enters the body in excessive amounts, it is transformed into energy reserves. Glucose is converted into glycogen, the body's mobile carbohydrate reserve, which is found in the liver and muscles. The liver of adults contains enough glucose in the form of glycogen to maintain normal blood glucose levels for 24 hours after the last meal. In pre-school children, glycogen lasts for 12 hours or less. If glycogen reserves are already high enough, then glucose starts to be converted into fat.

 In the absence of carbohydrates in food (starvation or no carbohydrate diet), glucose is formed in the body from fats, proteins and the breakdown of glycogen. An increase in blood glucose levels is caused by several hormones: glucagon produced by pancreatic cells; adrenal hormones; pituitary growth hormones; and thyroid hormones.

Fluctuations in blood glucose concentrations other than normal values are sensed by receptors in the hypothalamus (the area of the brain that regulates the body's internal environment). Due to the influence of the hypothalamus on the autonomic nervous system, there is an urgent increase or decrease in the production of insulin, glucagon and other hormones.

Adult blood glucose levels are between 4.1 and 6.1 mmol/l. An imbalance between glucose and insulin causes blood sugar levels to rise or fall. If sugar levels rise, the body will respond by producing more insulin and excreting glucose in the urine. When blood glucose levels fall, the glycogen stored in the liver is converted back into sugar. This is how a healthy body stabilizes the vital rate of glucose.

 A huge problem with diabetes mellitus is the labile, difficult to control course and the development of many complications, including blindness, kidney failure, heart attacks, stroke and amputation, etc. It is known that a "healthy lifestyle" can prevent the development of diabetes mellitus and its complications, and is also an integral part of the treatment strategy. However, the reality is that people with diabetes do not have the exact tools to easily control it. Millions of people around the world face questions that most cannot get answers to. It's about how easy it is to understand the specifics of controlling blood glucose levels, the principles of diet, physical activity and the prevention of complications.

The glucose test is prescribed for the preventive purpose of early detection of possible diabetes mellitus, which does not show itself in the early stages of development. In recent years, portable glucose meters have become widespread for measurements at home. It is sufficient to put a drop of blood on a disposable indicator plate installed in the glucometer and after a few seconds the concentration of glucose in the blood (glycaemia) is known.

Each glucometer has a measurement error range of 20% (according to ISO 15197), so blood glucose measurement results may vary slightly from instrument to instrument and laboratory to laboratory at the same time. It should also be kept in mind that in 5% of cases the measurement error may exceed 20%. In addition, many modern glucose meters show plasma glucose levels that are 11-15% higher than laboratory data for capillary blood (the instrument will show more when analyzing from a single drop of blood).

There are many methods for obtaining blood sugar data, but all of them are invasive (puncturing a blood vessel of the finger and taking a blood sample for the test strip) and minimally invasive (placing a sensor with a minimal skin puncture) for taking subcutaneous fluid for analysis. Non-invasive methods, without a puncture, do not exist, at least not known to the authors.

However, the authors have developed a method for non-invasive blood sugar determination by the arterial pulse. It is based on the pulse diagnosis of Chinese traditional medicine.

According to ancient Oriental medicine, any illness, physical or mental, that has a physiological effect is reflected directly in the pulse and usually even before the manifestation of symptoms in the human body. As a consequence, pulse diagnosis is the cornerstone of Chinese medicine. An experienced doctor, when assessing the pulse, can determine not only the presence of excess or deficiency of energy, but also the location, severity, type, duration and even cause of the disease.

The place where carpal tunnel pulses are palpated is the pulse concentration point, which is divided into three segments or three positions.

  In pulse diagnosis, examinations are carried out by finger palpation, pressing the superficial pulse harder with the finger, then, even harder, until it registers in depth. By pressing on the pulse in the hand, the doctor determines the strength of the resistance under the finger. He then relieves the pressure until a shallow pulse is felt, and then examines the pulse under the finger.

There are already developed pulse wave detection devices with three-probe and single-probe sensors. Wearable hand-held pulse wave detection devices with a single probe sensor (a product of Shanghai Asia & Pacific Computer Information System Co., Ltd., Shanghai, China) are also in use.

 The authors of this paper have developed a handheld pulse wave collection device of their own design, with both an integrated and a remote Pulse Sensor Module. Studies were conducted on a large number of diabetic and healthy individuals to refine the algorithm for calculating glucose and creating a database.

Equipment used.

OMRON M3 automatic blood pressure monitor (HEM-7200-E, OMRON HEALTHCARE Co., Ltd. Kyoto, Japan) was used to measure blood pressure and pulse rate. 

Accu-Chek Performa Blood Glucose Monitoring System (Roche Diabetes Co., Mannheim, Germany) was used for invasive blood sugar measurement.

A mercury thermometer was used to measure a person's body temperature.

The data obtained from the bracelet and the medical devices were recorded in a table.

Conducting the studies.

The studies were conducted with two normotensive groups. The first group consisted of people without diabetes with a normal resting blood pressure of 120/80.

The second group consisted of people with diabetes mellitus and heart disease.

Exclusion criteria were pregnant women and people with any physical, sensory or cognitive impairment. 

In this study, age was divided in each normotensive group into young age (18-34 years), middle age (35-64 years) and old age (≥65 years). Because the arterial pulse rate differs in the young, middle-aged and elderly groups (Fei, 2003).

Before the studies, the personal parameters of the study subject were entered into the table: Gender, Age, Height, Weight, Demographic information, smoking status and medication status.

Gender is an extraneous variable which can affect arterial heart rate.

When height and weight were entered, the software automatically calculated Body Mass Index (BMI). This is a measure which is widely used in clinical practice to detect weight problems. Weight was calculated as weight-for-height in kilograms per square meter (kg/m2) and categorized into three groups, underweight, normal weight and overweight, according to local or national standards (Choo, 2002). 

Body mass index is calculated using the formula: 


where m - is weight in kilograms and h - is height in meters, and is measured in kg/m².

For example, a person's mass = 77 kg, height = 170 cm. Therefore, the body mass index in this case is: BMI = 77:(1.70 × 1.70) ≈ 26.64 kg/m².

The ratio of actual weight in relation to ideal body weight is the determining factor for the retention pressure.

Age, sex and weight are all factors that influence the pulse rate. Fluctuations in ambient temperature also have an effect on the pulse rate.

Known variables.

The blood sugar level (fasting rate), determined in the morning after a night's sleep, is between 59 and 99 mg per 100 ml of blood (the lower limit of normal is 3.3 mmol/l, and the upper limit is 5.5 mmol/l).

Normal blood viscosity is 5 mPa*s. But in pathology the viscosity coefficient is observed in the range of 1.7 - 23 mPa*s, being a significant diagnostic indicator. Blood viscosity is highly dependent on the diameter of the vessel. In arterioles and capillaries, it reaches 800 mPa*s.

In 1 minute, each ventricle of the heart pumps about 5 liters of blood. This is also the volume velocity of blood (W = 5 L/min).

di - the average diameter of the vessels (Large and medium arteries) is 2.5 mm. small arteries - 0.5 mm.

vi - linear velocity of blood flow: Large and medium arteries - 0.4 m/s, small arteries - 0.2 m/s. (Average velocity of blood particles in a vessel (aorta - ~20-50 cm/s, radial artery - 10-15 cm/s, capillary - 0.3-1.0 mm/s).

Cardiac output SVy - CO (CO - cardiac output) = SV·HR, HR - heart rate, SV - stroke volume. The CO of the left ventricle and right ventricle are equal. In stationary resting state, the CO of an adult of 60-70 kg is approximately 5 liters of blood per minute.

The resting heart rate is between 44 and 70 beats.

The T parameter is the cardiac cycle, at a heart rate of 75 beats per minute the cardiac cycle lasts 0.8 s: the atria contract for 0.1 s, the ventricles for 0.3 s, and the total pause lasts 0.4 s. Atrial diastole lasts 0.7 s and ventricular diastole lasts 0.5 s. The atria act as a reservoir, in which blood is collected while the ventricles contract and release blood into the main vessels.

  Pressure difference and resistance to blood flow are factors affecting the volume of blood flow (Q) in the overall vascular system and in individual regional networks: it is directly proportional to the difference in blood pressure in the initial (P1) and final (P2) sections of the vascular network and inversely proportional to the resistance (R) to blood flow:


Increases in pressure or decreases in resistance to blood flow at the systemic, regional, microcirculatory levels increase the blood flow volume respectively in the circulatory system, organ or microregion, while reduction of pressure or increases in resistance decrease the blood flow volume.

Pulse wave velocity is determined by elastic properties of arterial wall and varies with age from 400 cm/s in children up to 1000 cm/s in people over 65 years old.

In normal healthy individuals the pulse wave velocity in elastic vessels varies between 500-700 cm/s, in muscular vessels - between 500-800 cm/s.

Elastic resistance and, consequently, pulse wave propagation velocity depend primarily on individual characteristics, morphological structure of arteries and age of the subjects.

Many authors note that the pulse wave propagation velocity increases with age, somewhat more so in elastic type vessels than in muscular type. Such direction of age-related changes probably depends on decreasing tensile strength of muscular type vessel walls that can be compensated to some extent by the change of functional state of its muscular elements. Thus, according to Ludwig N.N. Savitsky gives the following norms of pulse wave velocity as a function of age (Table 1). When comparing average values of EV and MV, obtained by V.P. 

Nikitin (1959) and K.A. Morozov (1960), with Ludwig (1936) data, it should be noted, that they rather closely coincide. 

Particularly the speed of pulse wave propagation through elastic vessels increases with the development of atherosclerosis, which is evident by a number of anatomically traced cases.

Table 1. 

Age-related rates of pulse wave velocity in elastic (EV) and muscular (MV) vessels:

Age, years

EV, m/s

Age, years

MV, m/s













71 and older




51 and older


E.B. Babsky and V.L. Karpman propose formulas for determining individual due values of pulse wave velocity according to or with regard to age:

EV = 0.1-A2 + 4A + 380;

MV = 8-A + 425.

 In these equations there is one variable A, age, and the coefficients are empirical constants.

Table 1 shows the individual due values calculated using these formulas for ages 16 to 75 years. The pulse wave velocity in elastic vessels also depends on the level of mean dynamic pressure. 

When mean pressure rises, the pulse wave velocity increases and represents an increase in vessel "tension" due to passive stretching of the vessel from inside by high arterial pressure. When studying the elastic state of large vessels, it is constantly necessary to determine not only the pulse wave propagation velocity but also the average pressure level.

When analyzing the pulse wave parameters, it was found that the pulse waveform differs significantly in patients with different blood viscosity and hematocrit.

Blood viscosity as well as hematocrit has a significant influence on the amplitude and shape of the pulse wave posterior front oscillations. The relationship between blood viscosity and pulse waveform during diastole, i.e. in the recessional section of the pulse wave.

In addition, the blood pressure calibration model is that,

SBP=SBP ± 0.33 * age

DBP=DBP ± 0.14 * age

where SBP and DBP are the measured high and low PPG blood pressure values from the current measurement, age is the person's age and SBP and DBP are the calibrated high and low blood pressure values from the current calculation.

The Personal Mark information also contains the systolic and diastolic pressures from the clinical measurement, and the systolic and diastolic pressures from the clinical measurement are used as the initial PPG blood pressure measurement value.


At the beginning of data collection, subjects were asked to sit in a resting chair for 20 minutes before data collection, as changes in hemodynamics stabilize after 20 minutes in the new position.

Accofrisk smart watch. 

A wrist strap with a photo-sensor for pulse signal collection, placed on the wrist pulse, was worn on the subject's arm (Figure 1). Data was collected from both the right and left arms. The wrist with the wristband should be aligned with the heart

Calm down during the measurement, do not talk, do not make any excessive movements, keep your emotions stable and do not allow anyone to interfere with the measurement.

On an empty stomach 7.30-9.00

On an empty stomach before lunch

On an empty stomach before dinner

30 min after breakfast

30 min after lunch

30 min after dinner

60 min after breakfast

60 min after lunch

60 min after dinner

2 hours after breakfast

2 hours after lunch

2 hours after dinner

3 hours after breakfast

3 hours after lunch

3 hours after dinner

More than 3 hours after breakfast

More than 3 hours after dinner

On an empty stomach two hours before bedtime

Once the wristband was switched on, it was paired with the PC via Bluetooth and the parameters of heart rate, heart rate and body temperature were taken. The data obtained was placed in the software on the PC.

After receiving data from the bracelet for 1.0 - 2.0 minutes, we proceeded to measuring blood sugar with an invasive glucometer, blood pressure with a tonometer and body temperature with a mercury thermometer. The data were entered into a program table with the data obtained from the bracelet.

Data from the bracelet, numerical values were filtered, the most effective values were selected and stored in the database. Displayed in the same coordinate system, these numerical points form a fluctuating change in the coordinate system as a whole (as shown in Figure 3).

Figure 3. Data segmentation diagram based on a single heartbeat.

These values are then taken as the baseline blood glucose values. The resulting values are then used as reference values.

A separate calculation of baseline variables was performed according to the baseline values of the heart rate measures. Baseline variables include: blood vessel radius ry, blood flow velocity Vr2y, blood viscosity coefficient Jy, pulse limit points R1y, cardiac output SVy, blood flow rate, peripheral vascular resistance, amplitudes of each heartbeat, pulse limit values, segment averages, differential threshold values, heartbeat intervals and intervals, segment and level contact values, and corresponding time-sequence values. These data are used to verify subsequent blood glucose calculations and to select effective blood glucose values. The aim is to avoid the inaccuracies that would arise in the case of calculations based on single heartbeat data.

The reference variable associated with the blood glucose reference is retained as the baseline blood glucose value. At the same time, based on the reference blood glucose level and the baseline numerical values of the heart rate (Ps, Pd and Pm), the calculation of k, where 

k = (Ps-Pm)/(Ps-Pd).

All data obtained is stored in a database. Then, in new calculations of actual blood glucose levels, the k-indicator is used to perform validation of the results. In subsequent calculations, each individual k-indicator is calculated according to each cardiac pulse, so the k-indicator may vary continuously.

For example, the reference blood glucose level is 5, the corresponding calculated k value is 0.3. In the case of a new data collection, the above calculated value will be 0.5; in the case of another data collection, the above calculated value k will be 0.4.

For example, the reference blood glucose level is 5, the corresponding calculated k value is 0.3. In the case of a new data collection, the above calculated value will be 0.5; in the case of another data collection, the above calculated value k will be 0.4.

The process of calculating the different actual values of the variables is as follows.

- Calculation of blood flow data, accumulation of numerical values of pulse rates, calculation of rate of change of numerical values, obtaining blood flow rates using inverse proportionality to the rate of change of numerical values;

 - Calculation of cardiac output, cardiac output is calculated using the formula: 

SV n = (0.2 8 3 / (k * k)) (P s - P d) * T,


k = (P s - P m) / (P s - P d),

parameter T - cardiac cycle, Ps - maximal value of single pulse waveform, Pd - minimal value of single pulse waveform, Pm - average value of single pulse waveform. 

Figure 4. Wave diagram of a single heart pulse.

- Calculation of the segment contact values, is done by dividing the pulse curve resulting from a single change by the number of segments A, then extracting the time and location data of all segments contact values, where A is a natural number greater than 0. Figure 3.

In the example we are considering, the pulse curve is divided into 8 segments: A1, A2, A3, B1, B2, B3, C1, C2 and C3. The corresponding points of contact of the segments are also 8. By subdividing the measured pulse curve, it is possible to detail the pulse curve, obtaining specific data on the changes in the value of each segment.

 - To calculate the level contact values, we divide the above-described segments by b number of levels, and extract the values of all level contact points, where b is a natural number greater than 0. In our example, the variable b = 7. Based on each of the 8 segments described above, 7 levels are extracted, with even more detail on the values of each segment and also with specific data on the changes of the values of each level. 

- Calculation of blood viscosity coefficient: 


where I and R default to 1 and r is the radius of the blood vessel.

   - The calculation of the blood vessel radius is based on the assumption that the blood vessel radius is constant over a certain range. The ratio of the maximum pulse value to the minimum pulse value is calculated. Both values are derived from continuous pulse data over a period of time. Continuous heart rate data is heart rate data that is continuously collected over a period of time. For example, 100 heartbeats have been collected over a period of 90 seconds. For each beat, the ratio of the maximum value to the minimum value can be calculated.

- Blood flow velocity is calculated by varying the angle ratio after linearly normalizing the multiple velocity numeric values over a period of time.

- Calculation of the peripheral blood vessel resistance index: peripheral resistance is the ratio of the descending isthmus value (position R2 in Figure 4) to the extreme point on the pulse data graph.

- Calculation of the amplitude of each heartbeat, selecting the maximum value of the pulse rate over a period of time.

- Calculation of the mean value: the variable Pm divides a given set of data into two equal parts.

- Calculation of differential thresholds: selection of maximum and minimum values for each heartbeat.

- Calculation of heartbeat intervals: to establish a relationship between the thresholds of the two heartbeats.

- Calculation of heartbeat intervals: calculation of the shortest intervals between each two heartbeats.

- Calculation of corresponding time-sequence values: saving the time-sequences of the blood glucose reference values and comparing them with the newly collected heart rate data.

Once the actual values of the above variables have been calculated, the actual blood glucose level is calculated according to the data obtained.

Figure 5. Diagram of cardiac output from a single cardiac pulse.

The formula for calculating the actual blood glucose level is as follows:


where is the actual blood glucose value, b is the reference blood glucose level, SVy is the baseline cardiac stroke volume variable, R2y is the limit values, R1y is the mean values, Sy is the baseline area ratio variable (as shown in Figure 5, Jy is the baseline blood viscosity ratio variable, Vr2y is the baseline blood flow rate variable,

R1n - limit values, R2n - mean values, SVn - actual value of cardiac stroke volume variable, Sn - actual value of area ratio variable, Jn - actual value of blood viscosity coefficient variable, Vr2n - actual value of blood flow rate variable.


 The solution generates a data model, calculates the user's blood glucose levels and associated variables according to heart rate data. These variables are then used to test the effectiveness of a particular value of blood glucose, find multiple effective values of blood glucose levels, and determine the personalized intervals of blood glucose levels of users, so that users can scientifically manage their blood glucose levels accurately and efficiently according to the personalized intervals.

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