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      Model of fluid and solute shifts during hemodialysis with active transport of sodium and potassium

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          Abstract

          Background

          Mathematical models are useful tools to predict fluid shifts between body compartments in patients undergoing hemodialysis (HD). The ability of a model to accurately describe the transport of water between cells and interstitium ( J v, ISIC ), and the consequent changes in intracellular volume (ICV), is important for a complete assessment of fluid distribution and plasma refilling. In this study, we propose a model describing transport of fluid in the three main body compartments (intracellular, interstitial and vascular), complemented by transport mechanisms for proteins and small solutes.

          Methods

          The model was applied to data from 23 patients who underwent standard HD. The substances described in the baseline model were: water, proteins, Na, K, and urea. Small solutes were described with two-compartment kinetics between intracellular and extracellular compartments. Solute transport across the cell membrane took place via passive diffusion and, for Na and K, through the ATPase pump, characterized by the maximum transport rate, Jp MAX . From the data we estimated Jp MAX and two other parameters linked to transcapillary transport of fluid and protein: the capillary filtration coefficient Lp and its large pores fraction α LP . In an Expanded model one more generic solute was included to evaluate the impact of the number of substances appearing in the equation describing J v, ISIC .

          Results

          In the baseline model, median values (interquartile range) of estimated parameters were: Lp: 11.63 (7.9, 14.2) mL/min/mmHg, α LP : 0.056 (0.050, 0.058), and Jp MAX : 5.52 (3.75, 7.54) mmol/min. These values were significantly different from those obtained by the Expanded model: Lp: 8.14 (6.29, 10.01) mL/min/mmHg, α LP : 0.046 (0.038, 0.052), and Jp MAX : 16.7 (11.9, 25.2) mmol/min. The relative RMSE (root mean squared error)averaged between all simulated quantities compared to data was 3.9 (3.1, 5.6) %.

          Conclusions

          The model was able to accurately reproduce most of the changes observed in HD by tuning only three parameters. While the drop in ICV was overestimated by the model, the difference between simulations and data was less than the measurement error. The biggest change in the estimated parameters in the Expanded model was a marked increase of Jp MAX indicating that this parameter is highly sensitive to the number of species modeled, and that the value of Jp MAX should be interpreted only in relation to this factor.

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          Most cited references46

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          Chronic Fluid Overload and Mortality in ESRD.

          Sustained fluid overload (FO) is considered a major cause of hypertension, heart failure, and mortality in patients with ESRD on maintenance hemodialysis. However, there has not been a cohort study investigating the relationship between chronic exposure to FO and mortality in this population. We studied the relationship of baseline and cumulative FO exposure over 1 year with mortality in 39,566 patients with incident ESRD in a large dialysis network in 26 countries using whole-body bioimpedance spectroscopy to assess fluid status. Analyses were applied across three discrete systolic BP (syst-BP) categories ( 160 mmHg), with nonoverhydrated patients with syst-BP=130-160 mmHg as the reference category; >200,000 FO measurements were performed over follow-up. Baseline FO value predicted excess risk of mortality across syst-BP categories ( 160 mmHg: HR, 1.30; 95% CI, 1.19 to 1.42; all P 160 mmHg: HR, 1.62; 95% CI, 1.39 to 1.90). In conclusion, chronic exposure to FO in ESRD is a strong risk factor for death across discrete BP categories. Whether treatment policies that account for fluid status monitoring are preferable to policies that account solely for predialysis BP measurements remains to be tested in a clinical trial.
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            Interstitial-lymphatic mechanisms in the control of extracellular fluid volume

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              Modelling the lymphatic system: challenges and opportunities

              The lymphatic system is a vital part of the circulatory and immune systems, and plays an important role in homeostasis by controlling extracellular fluid volume and in combating infection. Nevertheless, there is a notable disparity in terms of research effort expended in relation to the treatment of lymphatic diseases in contrast to the cardiovascular system. While similarities to the cardiovascular system exist, there are considerable differences in their anatomy and physiology. This review outlines some of the challenges and opportunities for those engaged in modelling biological systems. The study of the lymphatic system is still in its infancy, the vast majority of the models presented in the literature to date having been developed since 2003. The number of distinct models and their variants are few in number, and only one effort has been made thus far to study the entire lymphatic network; elements of the lymphatic system such as the nodes, which act as pumps and reservoirs, have not been addressed by mathematical models. Clearly, more work will be necessary in combination with experimental verification in order to progress and update the knowledge on the function of the lymphatic system. As our knowledge and understanding of its function increase, new and more effective treatments of lymphatic diseases are bound to emerge.
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                Author and article information

                Contributors
                Role: Formal analysisRole: SoftwareRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: SupervisionRole: Writing – review & editing
                Role: InvestigationRole: Resources
                Role: InvestigationRole: Resources
                Role: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                28 December 2018
                2018
                : 13
                : 12
                : e0209553
                Affiliations
                [1 ] Nalecz Institute of Biocybernetics and Biomedical Engineering Polish Academy of Sciences, Warsaw, Poland
                [2 ] Department of Rehabilitation and Physiotherapy, Medical University of Lublin, Lublin, Poland
                [3 ] Department of Nephrology, Medical University of Lublin, Lublin, Poland
                [4 ] Renal Medicine and Baxter Novum, Karolinska Institutet, Stockholm, Sweden
                Delft University of Technology, NETHERLANDS
                Author notes

                Competing Interests: We have the following interests. Baxter Novum is the result of a grant from Baxter Healthcare Corporation to the Karolinska Institutet. Bengt Lindholm is employed by Baxter Healthcare Corporation. There are no patents, products in development or marketed products to declare. This does not alter our adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors.

                Author information
                http://orcid.org/0000-0001-8224-783X
                Article
                PONE-D-18-05839
                10.1371/journal.pone.0209553
                6310262
                30592754
                6e4572a0-31bc-499c-b295-2b29925f76ec
                © 2018 Pietribiasi et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 22 February 2018
                : 7 December 2018
                Page count
                Figures: 9, Tables: 6, Pages: 22
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100004281, Narodowe Centrum Nauki;
                Award ID: UMO-2014/15/N/ST7/05316
                Award Recipient :
                This work was supported by grant no. UMO-2014/15/N/ST7/05316 issued by the National Science Center (Poland, http://www.ncn.gov.pl/). M.P. is the beneficiary of the grant. The data were originally collected for the study "Evaluation of disturbances of calcium-phosphate management in patients on dialysis" supported by the National Science Centre, grant no N N518 289840. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Baxter Novum provided support in the form of salaries for author BL, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific role of this author is articulated in the ‘author contributions’ section.
                Categories
                Research Article
                Biology and Life Sciences
                Plant Science
                Plant Physiology
                Solute Transport
                Biology and Life Sciences
                Cell Biology
                Cellular Structures and Organelles
                Cell Membranes
                Physical Sciences
                Physics
                Classical Mechanics
                Continuum Mechanics
                Fluid Mechanics
                Fluid Dynamics
                Fluid Flow
                Medicine and Health Sciences
                Nephrology
                Medical Dialysis
                Physical Sciences
                Chemistry
                Chemical Compounds
                Organic Compounds
                Urea
                Physical Sciences
                Chemistry
                Organic Chemistry
                Organic Compounds
                Urea
                Biology and Life Sciences
                Anatomy
                Body Fluids
                Blood
                Plasma Volume
                Medicine and Health Sciences
                Anatomy
                Body Fluids
                Blood
                Plasma Volume
                Biology and Life Sciences
                Physiology
                Body Fluids
                Blood
                Plasma Volume
                Medicine and Health Sciences
                Physiology
                Body Fluids
                Blood
                Plasma Volume
                Biology and Life Sciences
                Cell Biology
                Cellular Structures and Organelles
                Cell Membranes
                Intracellular Membranes
                Biology and Life Sciences
                Anatomy
                Body Fluids
                Interstitial Fluid
                Medicine and Health Sciences
                Anatomy
                Body Fluids
                Interstitial Fluid
                Biology and Life Sciences
                Physiology
                Body Fluids
                Interstitial Fluid
                Medicine and Health Sciences
                Physiology
                Body Fluids
                Interstitial Fluid
                Custom metadata
                The data used are publicly available on the RepOD database, at the following URL: http://dx.doi.org/10.18150/repod.0627189.

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