Physical exercise is known to reduce the chronic inflammatory status that leads to Type 2 Diabetes. Its beneficial effects seem to be exerted trough a primary production of the cytokine Interleukin-6 (IL-6) which triggers a cascade of anti-inflammatory cytokines. Consequently, IL-6 has a central role in the description of the metabolic effects of exercise. The aim of this study was to develop a model of IL-6 dynamics during exercise. A model constituted by two non-linear differential equations is proposed. Since IL-6 production seems to be dependent not only on exercise duration but also on exercise intensity, input to the model is represented by heart rate, which is known to correlate well with exercise intensity. Model implementation in a Matlab-based parametric identification procedure allowed optimization of adjustable characteristic coefficients of IL-6 dynamics during exercise. From the reported results, it can be concluded that this model is a suitable tool to reproduce IL-6 time course during the execution of a physical exercise. This model was the first step of a project aimed at describing the complete immune system response to exercise and at giving a comprehensive sight of the effects that exercise has on the metabolic system

Cappozzo, A.

Mazzà, C.

Morettini, M.

Sacchetti, M.

White Rose Research Online

This is a repository copy of A mathematical model of interleukin-6 dynamics during exercise.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/93624/Version: Accepted VersionProceedings Paper:Morettini, M., Sacchetti, M., Cappozzo, A. et al. (1 more author) (2015) A mathematical model of interleukin-6 dynamics during exercise. In: 6th European Conference of the International Federation for Medical and Biological Engineering. Springer International Publishing , pp. 431-434. ISBN 9783319111278 https://doi.org/10.1007/978-3-319-11128-5_108The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-11128-5_108eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.  1 MORETTINI_MBEC2014.docx A mathematical model of Interleukin-6 dynamics during exercise M. Morettini1, M. Sacchetti2, A. Cappozzo1,2 and C. Mazzà3,4 1 Interuniversity Centre of Bioengineering of the Human Neuromusculoskeletal System, University of Rome “Foro Italico”, Rome, Italy 2Department of Movement, Human and Health Sciences, University of Rome “Foro Italico”, Rome, Italy 3Department of Mechanical Engineering, The University of Sheffield, Sheffield, UK 4INSIGNEO Institute for in silico Medicine, The University of Sheffield, Sheffield, UK Abstract— Physical exercise is known to reduce the inflam-matory status that leads to Type 2 Diabetes. Its beneficial effects seem to be exerted trough a primary production of Interleukin-6 (IL-6) which triggers a cascade of anti-inflammatory cytokines. Consequently, IL-6 has a central role in the description of the metabolic effects of exercise. The aim of this study was to develop a model of IL-6 dynamics during exercise. A model constituted by two non-linear differential equations is proposed. Input to the model is represented by heart rate, which is known to correlate well with exercise in-tensity. Model implementation in a Matlab-based parametric identification procedure allowed optimization of adjustable characteristic coefficients of IL-6 dynamics during exercise. From the reported results, it can be concluded that this model is a suitable tool to reproduce IL-6 time course during the execution of a physical exercise. This model was the first step of a project aimed at describing the complete immune system response to exercise and at giving a comprehensive sight of the effects that exercise has on the metabolic system. Keywords— Inflammation, physical activity, cytokines, met-abolic syndrome. I. INTRODUCTION  Type 2 Diabetes (T2D) is one of the most common dis-eases all over the world and is characterized by a deficit in insulin action and secretion. This deficit seems to entail a state of low-grade inflammation giving T2D the aspect of a chronic inflammatory disease [1]. The inflammatory milieu originates in the adipose tissue, considering that, in this pathological situation, adipocytes are inflamed and release pro-inflammatory cytokines [2]. Exercise has the ability to contrast and delay the evolution of the disease. In fact, con-traction of skeletal muscles during exercise is able to induce a series of modifications of the inflammatory pathway [3], which eventually induces a reduction of insulin resistance [4]. Interleukin-6 (IL-6) was identified as the first cytokine increasing in the circulation during exercise and stimulating the secretion of a cascade of anti-inflammatory cytokines [5, 6]. Plasma IL-6 was shown to augment up to 100-fold depending on exercise intensity and duration. The exercise-induced increase of plasma IL-6 is not linear over time; repeated measurements during exercise showed an acceler-ating increase of the IL-6 in plasma in an almost exponen-tial manner [7]. Furthermore, the peak IL-6 level is reached at the end of the exercise or shortly thereafter, followed by a rapid decrease towards pre-exercise levels [7]. Although exercise is one of the major factors acting on T2D mecha-nisms, there are only few mathematical models describing its effects on the metabolic system [8–10], and none of these describing them at immunological level. Thus, the aim of the present study was to fill this gap and formulate and validate a mathematical model of IL-6 dynamics during exercise. II.  METHODS A. Model equations Since IL-6 dynamics depends on the intensity of the ex-ercise performed and considering that heart rate (HR) corre-lates well with exercise intensity, the HR signal was used as input to the model. The model is constituted by the follow-ing two non-linear differential equations: 鳥彫挑滞岫痛岻鳥痛 噺 倦怠結汝岫禰岻培 伐 倦態荊詣は岫建岻 髪 眺銚内薙展蝶    (1)  鳥超岫痛岻鳥痛 噺 伐 怠脹那馴 岷岫茎迎岫建岻 伐 茎迎長岻 伐 桁岫建岻峅  (2) In eq. (1), IL6(t) represents IL-6 concentration in the plasma compartment. In eq. (2), taken from Dalla Man et al. [10], Y is a delayed version of the suprabasal HR(t) signal. The first nonlinear term on the right hand side of eq. (1) accounts for IL-6 increase from its basal value in response to muscle contraction during exercise and it is conceived as non-linearly dependent on a delayed version of the supraba-sal HR signal. The second term of the same equation repre-sents IL-6 removal from the circulation after exercise. Fi-nally, the third term accounts for IL-6 production during non-perturbed conditions, and is mainly representing adi-pose tissue contribution [11]. V is the volume of distribu-tion. The initial conditions are: IL6(0) = IL6b and Y(0) = 0. From measurements of the basal levels of plasma IL-6, and 2 MORETTINI_MBEC2014.docx the k1, k2 and V parameters, the value of RaIL6 was calculat-ed imposing steady-state conditions.  B. Clinical data and model parameter estimation The model output was tested against the values of mean IL-6 plasma concentration taken from an experimental study that investigated the dynamics of several cytokines in ten male athletes before, during and after 2.5 hours of treadmill running at 75% of maximal oxygen consumption (VO2max) [12]. Plasma IL-6 and HR were measured at each time point. The model consists of five independent parameters (Ta-ble 1). V and THR were assigned numerical values as ob-tained from reported observations [10, 13], value for k was manually adjusted while k1, and k2 were assumed as “free” and their optimal value was estimated by setting up a weighed least squares (WLS) fitting procedure implemented in Matlab. Errors in IL-6 measurements were assumed to be normal-ly distributed random variables with zero mean and a con-stant percent coefficient of variation (CV%) equal to 6.9% [7]. Precision of parameter estimates was expressed as CV(pi)%= SDpi/pi•100, where pi is the i-th component of the model parameters vector and SDpi is the related stand-ard deviation computed as the square root of diagonal terms of the inverse of the Fisher information matrix. Table 1 Values of model parameters Parameter Value (CV%) Units k1(*) 0.0056 (4) pg·ml-1·min-1 k 20 beats per min k2(*) 0.0045 (4) min-1 V 8250 ml THR 1 min RaIL6 7.385 pg·min-1 (*) Parameters were estimated by fitting to clinical data as described in the Methods. Fixed values of THR was taken from Dalla Man et al. [10] whereas V was taken from [13] Value for k was manually adjusted. III.  RESULTS Estimates (with CV% in round brackets) of the free mod-el parameters are given in Table 1 (asterisk marked parame-ters). In Fig. 1, the model predicted profile (solid line) of IL-6 plasma concentration in response to exercise was com-pared to experimental data from Ostrowsky et al. [7].  Fig. 1. The profile of mean values of plasma IL-6 measured in 10 healthy human males during 2.5 hour running (black diamonds) are com-pared with the corresponding IL-6 profile estimated by the proposed model (solid line). IV.  DISCUSSION  Beneficial effects of exercise on insulin resistance lead-ing to T2D seem to be initiated by IL-6 secretion due to skeletal muscle contraction. Subsequently, IL-6 is able to stimulate the secretion of anti-inflammatory cytokines.  This study proposed and validated a mathematical model of IL-6 during exercise. IL-6 increase in the circulation during exercise is hypothesised to be non-linearly depend-ent from exercise intensity. In particular, an exponential dependence from HR, taken as a marker of exercise intensi-ty, was hypothesized. Even if IL-6 dynamics is mainly regu-lated by skeletal muscle contraction, in non-perturbed con-ditions, IL-6 is released by adipose tissue. Experimental data showed that IL-6 is released from the adipocytes and is thereby able to act as a endocrine mediator [11]. The pro-posed model accounts for both contributions.  V. CONCLUSIONS  The good approximation of experimental data shows that the proposed model is a suitable tool to reproduce IL-6 time course during exercise. This model constitutes the first step in describing the complete immune system response during exercise and paves the way to the mathematical description of the physiological effects of exercise on the metabolic system [14].  05101520253035400 100 200 300 400 500IL-6 plasma concentration (pg/ml) Time (min)  3 MORETTINI_MBEC2014.docx ACKNOWLEDGMENT This study was funded by the European Commission un-der the 7th Framework Programme (MISSION-T2D project, contract No.600803).  CONFLICT OF INTEREST The authors declare that they have no conflict of interest.  REFERENCES  1. Kolb H, Mandrup-Poulsen T (2005) An immune origin of type 2 diabetes? Diabetologia 48:1038–1050 2. Kershaw EE, Flier JS (2004) Adipose tissue as an endocri e organ. J Clin Endocrinol Metab 89:2548–2556 DOI 10.1210/jc.2004-0395 3. Petersen A, Pedersen B (2005) The anti-inflammatory effect of exercise. J Appl Physiol 1154–1162. DOI: 10.1152/japplphysiol.00164.2004 4. Hotamisligil GS, Shargill NS, Spiegelman BM (1993) Adipose expression of tumor necrosis factor-g: Direct role in obesity-linked insulin resistance. Science 259:87–91 5. Pedersen BK, Febbraio M (2005) Muscle-derived interleukin-6--a possible link between skeletal muscle, adipose tissue, liver and brain. Brain Behav Immun 19:371–376 DOI 10.1016/j.bbi.2005.04.008 6. Febbraio MA, Hiscock N, Sacchetti M, et al. (2004) Interleukin-6 is a novel factor mediating glucose homeostasis during skeletal muscle contraction. 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Eur J Appl Physiol 83:512–515 DOI 10.1007/s004210000312 13. Xu Z, Bouman-Thio E, Comisar C, et al. (2011) Pharmacokinetics, pharmacodynamics and safety of a human anti-IL-6 monoclonal antibody (sirukumab) in healthy subjects in a first-n-human study. Br J Clin Pharmacol 72:270–281 DOI 10.1111/j.1365-2125.2011.03964.x 14. Castiglione F, Tieri P, De Graaf A, et al. (2013) The onset of type 2 diabetes: proposal for a multi-scale model. JMIR Res Protoc 2:e44. doi: 10.2196/resprot.2854  Corresponding author: Author: Micaela Morettini Institute: University of Rome “Foro Italico”  Street: Piazza Lauro de Bosis, 6 City: Rome Country: Italy Email: micaela.morettini@uniroma4.it      

A mathematical model of interleukin-6 dynamics during exercise

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