# Treatment of Diabetes Mellitus by Acupuncture: Dynamics of Blood Glucose Level and Its Mathematical Modelling

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}), healthy lifestyle and positive family history of T2DM in a first-degree relative (father). The elevated BGLs were first noticed during a routine doctor’s examination 7 months prior to the first acupuncture session. The BGL at the time of diagnosis was 9.3 mmol/L, indicative of T2DM. Extensive diabetes self-management education and a trial of individualized medical nutrition therapy were each pursued for three months, resulting in significant lowering of BGLs to an average of 7.2 mmol/L, without achieving prediabetes or normal BGL values. After she was reluctant to begin the suggested therapy with metformin, the preferred initial glucose-lowering medication, a trial period of two weeks of acupuncture was initiated with very good results, which encouraged her to continue in our study without pharmacological therapy.

^{2}) and was diagnosed with T2DM several years ago, with an initial blood glucose value of 9 mmol/L. Since then, she has been taking metformin 1000 mg/day, exercising on a regular basis and strictly adhering to nutrition advice provided by medical counselor. Blood glucose levels have since become stable, averaging around 6 mmol/L with moderate variability.

^{2}) and changed neither his nutritional nor his life habits. His family history for T2DM is negative.

^{2}), does not perform physical exercise and is following neither the instructions for a healthy diet nor for healthy life habits. He was diagnosed with diabetes several years ago, with initially very high BGL values (larger than 30 mmol/L) and has since been taking metformin with vildagliptin 1000 mg/day. The BGL stabilized at an average of about 9 mmol/L after starting with drug therapy, with periodic larger fluctuations. His family history for T2DM is also negative.

## 3. Results

#### 3.1. Measurement and Analysis of the Glucose Level

- (i)
- Lowering effect. The glucose level significantly lowers after each single acupuncture treatment (green arrows); the reduction is especially strong after 2 treatments that are closer together in time (2 days separation). A delay in the response of the body of about 2–3 days is evident.
- (ii)
- Rising effect. The glucose level rises back to the initial high value during the 5 day acupuncture-free period for the first 9 acupuncture treatments (red arrows).
- (iii)
- Overall lowering effect. An overall lowering effect, i.e., BGL normalization, was observed after the 10th treatment, so the glucose level dropped below 6.2 mmol/L after the 12 treatments (violet dashed-line arrow).

#### 3.2. Modelling of the Glucose Levels

_{l}(t), and the total number of applied acupuncture treatments is denoted by N

_{A}. G

_{l}(t) has a constant value equal to the elevated BGL named G

_{high}, before the first treatment (i = 0), where i is the number of the already applied acupuncture treatments. For details, please see the Equations (A1) and (A2) given in Appendix A.

_{l}(t) assumes the existence of three main effects, as was observed in the experiment presented in the previous section. Thus, it actually consists of three sub-functions (named F1–F3), each of which describe one of the observed effects. Their main features are shown in Figure 4 and include:

_{high}towards the normal level G

_{norm}. The function is illustrated in Figure 4a by the green line. The time of the acupuncture is denoted by t

_{AP}, and the time when the effect of the acupuncture starts to be measurable is t

_{a}. Thus, a delay in the body’s response to the acupuncture exists as was observed in the experiment, and that time is denoted by t

_{delay}.

_{high}after a single acupuncture treatment—rising effect. This function, named by F2 (t) is plotted by the red line in Figure 4a, and its details are given in Appendix A, Equations (A7)–(A10). The same delay time of the response (t

_{delay}) is assumed as that for the F1.

_{down}and C

_{up}, respectively, which determine the slope of lowering and rising. Simulations of the functions F1 and F2 using different values of the parameters C

_{down}and C

_{up}are shown in Figure 4b–d. Clearly, the increase of the parameters C

_{down}and C

_{up}causes the slower lowering and rising effects, respectively. These actually describe the level of the body response to the treatment. We additionally assume that the constants C

_{down}and C

_{up}in functions F1 and F2 depend linearly on the number of the already applied treatments. This effect is described by the two constants a

_{1}and a

_{2}(Appendix A, Equations (A6) and (A10)). Thus, their values associated with BGL lowering and rising may change during the multiple acupuncture treatments.

_{high}after the acupuncture treatment. The overall lowering effect that is observed experimentally cannot be described using those functions alone. Therefore, a third function F3 is needed to obtain the complete description, as it is described in the following text.

_{high}over time towards a normal level G

_{norm}—overall lowering effect. This function describes the lowering of the maximal elevated sugar level after several acupuncture treatments. It was observed experimentally after the 10 and 4 acupuncture treatments in Figure 1a,b and Figure 2a,b, respectively. This actually represents the long-term effect of the acupuncture treatment. It is named F3 (t) and is shown in Figure 4f. This function is needed in addition to F1, because F2 always raises the glucose level back to the G

_{high}value after the treatment is stopped. F3 is described by parameters C

_{slow}and a

_{3}, defining the strength of the lowering effect. Formula and all details of F3 are given in the Appendix A Equations (A11)–(A13). In the simulation shown in Figure 4f, this function has no effect until the eighth acupuncture treatment (indicated by violet vertical dashed line). After that, the function slowly lowers the G

_{high}value to some equilibrium level G

_{eq}at which it again stays constant. In an ideal case, G

_{eq}is equal to the G

_{norm}; however, this may be different depending on the specific case. This function has similar properties to fracture healing vs. time after the fracture [31]. The healing shows a nearly constant value several days after the fracture, then starts rising toward the completely healed bone, and then again has a constant value. The final function G

_{l}(t) used for the simulations and for the fitting of the experimental data consists of all three of the functions F1–F3. The formula for this final function for the simulation of BGL, obtained after N

_{A}treatments is given in Appendix A, Equations (A14) and (A15).

#### 3.3. Simulations and the Predictions of the Glucose Levels

_{high}= 7.2 mmol/L. Figure 4a shows the simulated glucose levels as a function of time for three separations (periods) between the treatments, T1 = 7 days, T2 = 3 days and T3 = 1 day, and for one two-period separation (T4a = 2 days, T4b = 5 days). The last case means that the acupuncture was performed on the 2nd and 7th day each week.

_{high}value, while the other two periods (T2 and T3) are shorter than that time. Therefore, the glucose level rises back to the initial value between two acupuncture treatments for the T1, while it stays lower for the T2 and T3. The fourth simulation in Figure 5a is calculated for two different separations between the treatments, as was the case in the experiment (shown in Figure 1), so it shows mixed behavior as will be explained.

_{delay}= 3 days. The other parameters describing body response (C

_{down}= 0.7, C

_{slow}= 14.0), and their dependence on the number of already applied treatments (a

_{1}= a

_{2}= 0), and strength of the lowering effect (a

_{3}= 1) are taken to be the same for all four simulations. The function F3 is assumed to lower G

_{high}after the eighth (i

_{D}= 8) acupuncture treatment for all cases. This is clearly visible in the simulations from Figure 5a. The glucose level rises completely to its initial G

_{high}value for the period T1. For the other two cases the next acupuncture occurs before the glucose levels raise back to the initial value, so the maximal glucose levels are smaller than the initial G

_{high}value. The function F3 lowers their values as well after the eighth treatment, but its effect is not so obvious as for the T1.

_{high}before the characteristic 8th treatment (indicated by the vertical black dashed line in Figure 5b), and lowers after it. Minimal and average values lower slowly before the 8th treatment and more rapidly after it, due to the effect of F3. For the other two equal periods (T2 and T1) the lowering effect is visible from the beginning of the treatment and increases with the decrease of the period between the treatments. This is expected because the time between the treatments is shorter than the time needed for the glucose level to rise to the G

_{high}value, so each new treatment starts lowering from the smaller BGL maximal value. Therefore, the average value of the BGL is smaller for the shorter periods. The effect of F3 is not so obvious as for the case of T1, but the function F3 is still needed to fully describe the BGL normalization.

#### 3.4. Analysis of the Measured Glucose Using the Proposed Model

_{l}(t), given in Appendix A, Equation (A15). The results of the fitting for Patient 1 and Patient 2 are shown in Figure 6a and 6b, respectively. The experimental data are shown by the green line and symbols while the fit is shown by the light-blue full line. First, we note that the acupuncture periods (the time between the treatments) for Patients 1 and 2 are slightly different for the first several treatments. Patient 1 has two close treatments (2 day separation) followed by a 5 day acupuncture-free period. The separations for Patient 2 are longer (6 and 8 days). This strongly affects the shape of the BGL curves, as well as the fitted curves. In the first case the curve shows deep double-peaks (similar to the simulation for T4 in Figure 4), while the oscillations for Patient 2 are more regular due to the similar and longer times between the treatments (similar to T1 in Figure 5).

_{high}, C

_{up}, C

_{down}and t

_{delay}. The value of the G

_{high}(shown by the blue line and symbols) is constant until the 10th and 14th treatments in the first and second sets of the measurements, respectively, as was experimentally observed for both patients. It then lowers toward the normal BGL. The constant C

_{down}(black line and symbols) has smaller values than the C

_{up}(red line and symbols), also for both patients, showing that the glucose level drops faster towards the normal level after each single treatment than it rises back to the high value. Another important feature of these two constants is that C

_{down}increases with the number of treatments, while C

_{up}decreases, also for both patients. This shows that the glucose level lowering effect becomes faster with each new treatment, while its rising back to the high value becomes slower. Finally, we have determined that the time of the body response to the acupuncture is between 2 and 3 days for the first set of the acupuncture treatments. This shows similar values at the beginning of the second set of treatments, but drops toward a value of 1 after 8th treatment of the second set.

_{up}. However, this constant shows the same type of behavior as just described, with Patient 1 having significantly lower values (about two-times lower). Its influence on the BGL lowering and rising is shown in Figure 7e, where the effects of a single treatment of acupuncture on BGL are compared for Patients 1 and 2. Patient 1 shows significantly faster rising of the BGL after the acupuncture before and after the break, (i.e., the smaller values of the constants) than Patient 2. This effect may be attributed to the metformin, which is taken only by Patient 2, as will be discussed later.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Functions for Description of BGL Time Evolution during the Multiple Acupuncture Treatment

_{l}(t). The total number of applied acupuncture treatments is denoted by N

_{A}. G

_{l}has a constant value equal to the elevated BGL named G

_{high}, before the first treatment (i = 0), where i is the number of the acupuncture treatment, as given in Equation (A1).

_{a}

^{(i)}) when the ith acupuncture treatment starts to produce an effect on G

_{l}(t) is given by:

_{AP}

^{(i)}is the day of the ith treatment, and t

_{delay}

^{(i)}is the time of the effect of the ith treatment delay.

- BGL lowering effect:

_{down}

^{(i)}is the parameter that describes the function drop for the ith acupuncture treatment. This linearly depends on the number of the already applied treatments as given by Equation (A6), where a

_{1}is the parameter describing its dependence on the number of the applied treatments. The parameter defining the normal BGL is named G

_{norm}. The multiplication is indicated by × sign to avoid confusion with functions.

- 2.
- BGL rising effect:

_{2}.

- 3.
- Overall BGL lowering effect:

^{D}is the day of the acupuncture treatment (i

_{D}th) after which the overall BGL starts to reduce (i

_{D}≤ N

_{A}), and C

_{slow}defines the slope of the overall BGL drop (slower or faster drop), and a

_{3}is the constant that describes the value of the final BGL decrease towards a normal BGL.

_{A}acupuncture treatments we apply the following procedure for each acupuncture treatment (i = 1 … N

_{A}):

## References

- DeFronzo, R.A. Lilly lecture 1987. The triumvirate: Beta-cell, muscle, liver. A collusion responsible for NIDDM. Diabetes
**1988**, 37, 667–687. [Google Scholar] [CrossRef] [PubMed] - World Health Organization [Homepage on the Internet]. Updated 9 December 2020. The Top 10 Causes of Death. Available online: https://www.who.int/news-room/fact-sheets/detail/the-top-10-causes-of-death (accessed on 20 June 2023).
- Sun, H.; Saeedi, P.; Karuranga, S.; Pinkepank, M.; Ogurtsova, K.; Duncan, B.B.; Stein, C.; Basit, A.; Chan, J.C.; Mbanya, J.C.; et al. IDF Diabetes Atlas: Global, regional and country-level diabetes prevalence estimates for 2021 and projections for 2045. Diabetes Res. Clin. Pract.
**2022**, 183, 109119. [Google Scholar] [CrossRef] [PubMed] - Riddle, M.C.; Herman, W.H. The cost of diabetes care—An elephant in the room. Diabetes Care
**2018**, 41, 929–932. [Google Scholar] [CrossRef] [PubMed] - Guo, Y.; Xing, M.; Sun, W.; Yuan, X.; Dai, H.; Ding, H. Plasma Nesfatin-1 Level in Obese Patients after Acupuncture: A Randomised Controlled Trial. Acupunct. Med.
**2014**, 32, 313–317. [Google Scholar] [CrossRef] [PubMed] - Belivani, M.; Lundeberg, T.; Cummings, M.; Dimitroula, C.; Belivani, N.; Vasilakos, D.; Hatzitolios, A. Immediate Effect of Three Different Electroacupuncture Protocols on Fasting Blood Glucose in Obese Patients: A Pilot Study. Acupunct. Med.
**2015**, 33, 110–114. [Google Scholar] [CrossRef] - Yin, J.; Kuang, J.; Chandalia, M.; Tuvdendorj, D.; Tumurbaatar, B.; Abate, N.; Chen, J.D.Z. Hypoglycemic effects and mechanisms of electroacupuncture on insulin resistance. Am. J. Physiol. Regul. Integr. Comp. Physiol.
**2014**, 307, R332–R339. [Google Scholar] [CrossRef] - Tomina, A.; Ishizaki, N.; Naruse, Y.; Kitakoji, H.; Yamamura, Y. Repeated application of low-frequency electroacupuncture improves high-fructose diet-induced insulin resistance in rats. Acupunct. Med.
**2011**, 29, 276–283. [Google Scholar] [CrossRef] - Yu, Z.; Xia, Y.; Ju, C.; Mao, Z.; Gu, Y.; Xu, B. Electroacupuncture regulates glucose-inhibited neurons in treatment of simple obesity. Neural Regen. Res.
**2013**, 8, 809–816. [Google Scholar] - Tzeng, C.Y.; Lee, Y.C.; Ho, T.Y.; Chen, Y.I.; Hsu, T.H.; Lin, J.G.; Lee, K.R.; Chang, S.L. Intracellular signalling pathways associated with the glucose-lowering effect of ST36 electroacupuncture in streptozotocin-induced diabetic rats. Acupunct. Med.
**2015**, 33, 395–399. [Google Scholar] [CrossRef] - Lee, Y.C.; Li, T.M.; Tzeng, C.Y.; Cheng, Y.W.; Chen, Y.I.; Ho, W.J.; Lin, J.G.; Chang, S.L. Electroacupuncture-induced cholinergic nerve activation enhances the hypoglycemic effect of exogenous insulin in a rat model of streptozotocin-induced diabetes. Exp. Diabetes Res.
**2011**, 2011, 947138. [Google Scholar] [CrossRef] - Lin, R.T.; Tzeng, C.Y.; Lee, Y.C.; Ho, W.J.; Cheng, J.T.; Lin, J.G.; Chang, S.L. Acute effect of electroacupuncture at the Zusanli acupoints on decreasing insulin resistance as shown by lowering plasma free fatty acid levels in steroid-background male rats. BMC Complement. Altern. Med.
**2009**, 9, 26. [Google Scholar] [CrossRef] - Liao, H.Y.; Sun, M.F.; Lin, J.G.; Chang, S.L.; Lee, Y.C. Electroacupuncture plus metformin lowers glucose levels and facilitates insulin sensitivity by activating MAPK in steroid-induced insulin-resistant rats. Acupunct. Med.
**2015**, 33, 388–394. [Google Scholar] [CrossRef] [PubMed] - Benrick, A.; Maliqueo, M.; Johansson, J.; Sun, M.; Wu, X.; Mannerås-Holm, L.; Stener-Victorin, E. Enhanced insulin sensitivity and acute regulation of metabolic genes and signaling pathways after a single electrical or manual acupuncture session in female insulin-resistant rats. Acta Diabetol.
**2014**, 51, 963–972. [Google Scholar] [CrossRef] [PubMed] - Peplow, P.V. Electroacupuncture treatment of insulin resistance in diabetes mellitus. Acupunct. Med.
**2015**, 33, 347–349. [Google Scholar] [CrossRef] [PubMed] - Liang, F.; Koya, D. Acupuncture: Is it effective for treatment of insulin resistance? Diabetes Obes. Metab.
**2010**, 12, 555–569. [Google Scholar] [CrossRef] [PubMed] - Xu, J.; Chen, L.; Tang, L.; Chang, L.; Liu, S.; Tan, J.; Chen, Y.; Ren, Y.; Liang, F.; Cui, J. Electroacupuncture inhibits weight gain in diet-induced obese rats by activating hypothalamic LKB1-AMPK signaling. BMC Complement. Altern. Med.
**2015**, 15, 147. [Google Scholar] [CrossRef] [PubMed] - Liang, F.; Chen, R.; Nakagawa, A.; Nishizawa, M.; Tsuda, S.; Wang, H.; Koya, D. Low-frequency electroacupuncture improves insulin sensitivity in obese diabetic mice through activation of SIRT1/PGC-1α in skeletal muscle. Evid. Based Complement. Altern. Med.
**2011**, 2011, 735297. [Google Scholar] [CrossRef] - Firouzjaei, A.; Li, G.C.; Wang, N.; Liu, W.X.; Zhu, B.M. Comparative evaluation of the therapeutic effect of metformin monotherapy with metformin and acupuncture combined therapy on weight loss and insulin sensitivity in diabetic patients. Nutr. Diabetes
**2016**, 6, e209. [Google Scholar] [CrossRef] - Ma, F.Q.; Sun, C.J.; Wei, J.J.; Wang, Y.D.; Shen, J.C.; Chang, J.J. Electro-acupuncture regulates glucose metabolism in chronic stress model rats. Sci. Rep.
**2020**, 10, 11281. [Google Scholar] [CrossRef] - Martinez, B.; Peplow, P.V. Treatment of insulin resistance by acupuncture: A review of human and animal studies. Acupunct. Med.
**2016**, 34, 310–319. [Google Scholar] [CrossRef] - Choate, C.J. Modern Medicine and Traditional Chinese Medicine: Diabetes Mellitus, Part two. J. Chin. Med.
**1999**, 59, 1. [Google Scholar] - Zhang, H.; Han, G.; Litscher, G. Traditional Acupuncture Meets Modern Nanotechnology: Opportunities and Perspectives. Evid. Based Complement. Altern. Med.
**2019**, 2019, 2146167. [Google Scholar] [CrossRef] [PubMed] - World Health Organization. Acupuncture: Review and Analysis of Reports on Controlled Clinical Trials; World Health Organization: Geneva, Switzerland, 2002. [Google Scholar]
- López-Palau, N.E.; Olais-Govea, J.M. Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus. Sci. Rep.
**2020**, 10, 12697. [Google Scholar] [CrossRef] [PubMed] - Vasquez-Muñoz, M.; Arce-Alvarez, A.; von Igel, M.; Veliz, C.; Ruiz-Esquide, G.; Ramirez-Campillo, R.; Alvarez, C.; Ramirez-Velez, R.; Crespo, F.A.; Izquierdo, M.; et al. Oscillatory pattern of glycemic control in patients with diabetes mellitus. Sci. Rep.
**2021**, 11, 5789. [Google Scholar] [CrossRef] [PubMed] - Cedersund, G.; Strålfors, P. Putting the pieces together in diabetes research: Towards a hierarchical model of whole-body glucose homeostasis. Eur. J. Pharm. Sci.
**2009**, 36, 91–104. [Google Scholar] [CrossRef] - Seo, W.; Park, S.W.; Kim, N.; Jin, S.M.; Park, S.M. A personalized blood glucose level prediction model with a fine-tuning strategy: A proof-of-concept study. Comput. Methods Programs Biomed.
**2021**, 211, 106424. [Google Scholar] [CrossRef] - Chou, C.-Y.; Hsu, D.-Y.; Chou, C.-H. Predicting the Onset of Diabetes with Machine Learning Methods. J. Pers. Med.
**2023**, 13, 406. [Google Scholar] [CrossRef] - World Health Organization [Homepage on the Internet]. Updated 10 July 2023. Mean Fasting Blood Glucose. Available online: https://www.who.int/data/gho/indicator-metadata-registry/imr-details/2380 (accessed on 20 June 2023).
- Cosman, F.; Lindsay, R. Chapter 85—Parathyroid Hormone Treatment for Osteoporosis, In Osteoporosis, 4th ed.; Marcus, R., Feldman, D., Dempster, D.W., Luckey, M., Cauley, J.A., Eds.; Academic Press: Cambridge, MA, USA, 2013; pp. 1949–1961. ISBN 9780124158535. [Google Scholar]
- Chen, Y.; Wu, S.; Tian, Y. Cholecystectomy as a risk factor of metabolic syndrome: From epidemiologic clues to biochemical mechanisms. Lab. Investig.
**2018**, 98, 7–14. [Google Scholar] [CrossRef] - Oestreich, A.K.; Moley, K.H. Developmental and Transmittable Origins of Obesity-Associated Health Disorders. Trends Genet.
**2017**, 33, 399–407. [Google Scholar] [CrossRef] - Rivera, E.J.; Goldin, A.; Fulmer, N.; Tavares, R.; Wands, J.R.; de la Monte, S.M. Insulin and insulin-like growth factor expression and function deteriorate with progression of Alzheimer’s disease: Link to brain reductions in acetylcholine. J. Alzheimer’s Dis.
**2005**, 8, 247–268. [Google Scholar] [CrossRef] - Gudala, K.; Bansal, D.; Schifano, F.; Bhansali, A. Diabetes mellitus and risk of dementia: A meta-analysis of prospective observational studies. J. Diabetes Investig.
**2013**, 4, 640–650. [Google Scholar] [CrossRef] [PubMed] - Hu, Z.; Jiao, R.; Wang, P.; Zhu, Y.; Zhao, J.; De Jager, P.; Bennett, D.A.; Jin, L.; Xiong, M. Shared Causal Paths underlying Alzheimer’s dementia and Type 2 Diabetes. Sci. Rep.
**2020**, 10, 4107. [Google Scholar] [CrossRef] [PubMed] - Moloney, A.M.; Griffin, R.J.; Timmons, S.; O’Connor, R.; Ravid, R.; O’Neill, C. Defects in IGF-1 receptor, insulin receptor and IRS-1/2 in Alzheimer’s disease indicate possible resistance to IGF-1 and insulin signalling. Neurobiol. Aging
**2010**, 31, 224–243. [Google Scholar] [CrossRef] [PubMed] - Steen, E.; Terry, B.M.; Rivera, E.J.; Cannon, J.L.; Neely, T.R.; Tavares, R.; Xu, X.J.; Wands, J.R.; de La Monte, S.M. Impaired insulin and insulin-like growth factor expression and signaling mechanisms in Alzheimer’s disease-is this type 3 diabetes? J. Alzheimer’s Dis.
**2005**, 7, 63–80. [Google Scholar] [CrossRef] - Hoyer, S.; Nitsch, R. Cerebral excess release of neurotransmitter amino acids subsequent to reduced cerebral glucose metabolism in early-onset dementia of Alzheimer type. J. Neural Transm.
**1989**, 75, 227–232. [Google Scholar] [CrossRef] - Talbot, K.; Wang, H.Y.; Kazi, H.; Han, L.Y.; Bakshi, K.P.; Stucky, A.; Fuino, R.L.; Kawaguchi, K.R.; Samoyedny, A.J.; Wilson, R.S.; et al. Demonstrated brain insulin resistance in Alzheimer’s disease patients is associated with IGF-1 resistance, IRS-1 dysregulation, and cognitive decline. J. Clin. Investig.
**2012**, 122, 1316–1338. [Google Scholar] [CrossRef] - Correia, S.C.; Santos, R.X.; Carvalho, C.; Cardoso, S.; Candeias, E.; Santos, M.S.; Oliveira, C.R.; Moreira, P.I. Insulin signaling, glucose metabolism and mitochondria: Major players in Alzheimer’s disease and diabetes interrelation. Brain Res.
**2012**, 1441, 64–78. [Google Scholar] [CrossRef] - Nguyen, T.T.; Ta, Q.T.H.; Nguyen, T.K.O.; Nguyen, T.T.D.; Giau, V.V. Type 3 Diabetes and Its Role Implications in Alzheimer’s Disease. Int. J. Mol. Sci.
**2020**, 21, 3165. [Google Scholar] [CrossRef] - Baker, L.D.; Cross, D.J.; Minoshima, S.; Belongia, D.; Watson, G.S.; Craft, S. Insulin resistance and Alzheimer-like reductions in regional cerebral glucose metabolism for cognitively normal adults with prediabetes or early type 2 diabetes. Arch. Neurol.
**2011**, 68, 51–57. [Google Scholar] [CrossRef] - Samuraki, M.; Matsunari, I.; Chen, W.P.; Yajima, K.; Yanase, D.; Fujikawa, A.; Takeda, N.; Nishimura, S.; Matsuda, H.; Yamada, M. Partial volume effect-corrected FDG PET and grey matter volume loss in patients with mild Alzheimer’s disease. Eur. J. Nucl. Med. Mol. Imaging
**2007**, 34, 1658–1669. [Google Scholar] [CrossRef] - Dukart, J.; Kherif, F.; Mueller, K.; Adaszewski, S.; Schroeter, M.L.; Frackowiak, R.S.; Draganski, B.; Alzheimer’s Disease Neuroimaging Initiative. Generative FDG-PET and MRI model of aging and disease progression in Alzheimer’s disease. PLoS Comput. Biol.
**2013**, 9, e1002987. [Google Scholar] [CrossRef] [PubMed] - Barrett, C.E.; Koyama, A.K.; Alvarez, P.; Chow, W.; Lundeen, E.A.; Perrine, C.G.; Pavkov, M.E.; Rolka, D.B.; Wiltz, J.L.; Bull-Otterson, L.; et al. Risk for Newly Diagnosed Diabetes >30 Days After SARS-CoV-2 Infection Among Persons Aged <18 Years—United States, 1 March 2020-28 June 2021. MMWR Morb. Mortal. Wkly. Rep.
**2022**, 71, 59–65. [Google Scholar] [PubMed] - Al-Aly, Z.; Xie, Y.; Bowe, B. High-dimensional characterization of post-acute sequelae of COVID-19. Nature
**2021**, 594, 259–264. [Google Scholar] [CrossRef] [PubMed] - Ayoubkhani, D.; Khunti, K.; Nafilyan, V.; Maddox, T.; Humberstone, B.; Diamond, I.; Banerjee, A. Post-COVID syndrome in individuals admitted to hospital with COVID-19: Retrospective cohort study. BMJ
**2021**, 372, 693. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**,

**b**) Blood glucose levels during acupuncture as function of time for Patient 1. The days in which the acupuncture was received are indicated by vertical pink dashed lines, while the pink numbers above them indicate the number of the already applied treatments. Blue arrows and numbers indicate the minima of the glucose level that appear after each acupuncture treatment and the number of the applied treatments. The lowering and rising effects are denoted by green and red arrows. The overall lowering effect is indicated by dashed violet arrows. The small, red horizontal arrow indicates the break in the acupuncture due to COVID-19. Normal, prediabetes and diabetes BGL are indicated by green-yellow and red patterns (color areas). (

**c**) BGL for Patient 1 controlled 1 year after the acupuncture treatment. (

**d**) BGL during metformin-based treatment of Control 1 with a similar disease history. The average BGL value is indicated by horizontal blue line.

**Figure 2.**(

**a**,

**b**) Blood glucose levels during acupuncture as a function of time for Patient 2. The days in which the acupuncture was received are indicated by vertical pink dashed lines, while the pink numbers above them indicate the number of the treatment. Blue arrows and numbers indicate the minima of the glucose levels that appear after each acupuncture treatment, and the number of the treatment. The lowering and rising effects are denoted by green and red lines. The overall lowering effect is indicated by dashed violet arrows. Small red horizontal arrows indicate the break in the acupuncture treatment. Normal, prediabetes and diabetes BGL are indicated by green-yellow and red patterns (color areas). (

**c**) BGL of Patient 2 controlled 1 year after the acupuncture treatment. (

**d**) BGL during metformin-based treatment of Control 2, with a similar disease history.

**Figure 3.**Analysis of the measured BGL, including maximal, average and minimal values of BGL during the acupuncture or drug treatment. (

**a**–

**d**) Patient 1 and Control 1, i.e., analysis of the measurements from Figure 1. (

**e**–

**h**) Analysis of the BGL values for Patient 2 and Control 2, i.e., the measurements from Figure 2. The measurements taken for the analysis are indicated by light gray lines. Maximal value is indicated by red, average by green, and minimal value by the blue line and symbols. The averaging and determination of the maximal and minimal glucose levels are performed over a time interval that included two acupuncture treatments or seven days of taking the drug-therapy. The time of acupuncture treatment is indicated by vertical dashed pink lines. Normal, prediabetes and diabetes BGL are indicated by green-yellow and red patterns (color areas).

**Figure 4.**Properties of the functions used for modelling of BGL during acupuncture. (

**a**) Function F1 shown by the green line describes the lowering of the BGL by acupuncture towards a normal value G

_{norm}, while F2 (red line) represents its rising back to the elevated value G

_{high}. The resulting function shown by the blue line is the sum of F1 and F2. The time of the acupuncture (t

_{AP}) is denoted by the vertical pink dashed line, while the time when its effect starts to be visible (t

_{0}) is denoted by the vertical blue dashed line. This means that there is a delay in the body’s response named t

_{delay}. (

**b**–

**d**) Simulations of F1 and F2, and their sum using three different function parameters C

_{down}for F1 and C

_{up}for F2 corresponding to faster and slower body responses. (

**e**) Simulation of the BGL for the multiple acupuncture treatment using functions F1 and F2 only. This describes only the oscillatory nature of the measured curves caused by acupuncture. The time of the acupuncture is shown by the pink dashed line. (

**f**) The effect of the addition of function F3, corresponding to the overall lowering, to F1 and F2 on the BGL. This lowers the value of G

_{high}towards G

_{norm}during the treatment which then stabilizes at the value G

_{eq}, which may be different from G

_{norm}. The effect is illustrated by violet arrows, while its beginning is denoted by vertical violet dashed line.

**Figure 5.**(

**a**) Simulations of the glucose level vs. time for four different frequencies of the acupuncture (T1 = 7days, T2 = 3 days, T3 = 1 day, T4 = 2 and 5 days, C

_{up}= 3.3, C

_{down}= 0.7, C

_{slow}= 14.0, t

_{delay}= 3 days, i

_{D}= 8, a

_{1}= a

_{2}= 0, a

_{3}= 1). Green and red arrows demonstrate the lowering and rising effects, while the violet dashed arrows show the overall lowering effect. (

**b**) Maximal, average and minimal values of the BGL simulations shown in (

**a**) as function of the days of the acupuncture treatment. The determination of the maximal and minimal glucose levels is performed over two acupuncture treatments (14 days for T1, 6 days for T2, 2 days for T3 and 7 days for T4). The horizontal dashed lines show the boundaries between normal, prediabetes and diabetes BGL values.

**Figure 6.**(

**a**,

**b**) Measured and simulated BGL for Patient 1 and Patient 2, respectively. Experimental data (green line with symbol) and simulations obtained using the best-fit parameters (full light blue line). Pink numbers and vertical dashed lines indicate the order number of the applied treatment, while the blue numbers and arrows indicate the corresponding number of the BGL minima. Different times between the two treatments are applied for Patient 1 and Patient 2 (indicated for the first three treatments), resulting in different shapes of the BGL curves. The lowering, rising and overall lowering effects (indicated by green, red and violet arrows respectively) are clearly visible in both the experimental and modelled curves.

**Figure 7.**(

**a**,

**b**) Maximal, minimal and average (main) values of the experimental BGL values and their simulations for Patient 1 and Patient 2. The values are determined for the time period of 2 acupuncture treatments. (

**c**,

**d**) The parameters obtained by fitting of the BGL curves of Patient 1 and Patient 2 to the model. (

**e**) Body response to single acupuncture treatment calculated using the fitting parameters for Patient 1 and Patient 2. The initial values (i = 0) for the values of C

_{up}and C

_{down}are taken for the simulation.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Šimat, M.; Janković Makek, M.; Mičetić, M.
Treatment of Diabetes Mellitus by Acupuncture: Dynamics of Blood Glucose Level and Its Mathematical Modelling. *Sci* **2023**, *5*, 38.
https://doi.org/10.3390/sci5040038

**AMA Style**

Šimat M, Janković Makek M, Mičetić M.
Treatment of Diabetes Mellitus by Acupuncture: Dynamics of Blood Glucose Level and Its Mathematical Modelling. *Sci*. 2023; 5(4):38.
https://doi.org/10.3390/sci5040038

**Chicago/Turabian Style**

Šimat, Marija, Mateja Janković Makek, and Maja Mičetić.
2023. "Treatment of Diabetes Mellitus by Acupuncture: Dynamics of Blood Glucose Level and Its Mathematical Modelling" *Sci* 5, no. 4: 38.
https://doi.org/10.3390/sci5040038