Dialysis therapies: Investigation of transport and regulatory processes using mathematical modelling

Biocybernetics and Biomedical Engineering - Tập 42 - Trang 60-78 - 2022
Leszek Pstras1, Joanna Stachowska-Pietka1, Malgorzata Debowska1, Mauro Pietribiasi1, Jan Poleszczuk1, Jacek Waniewski1
1Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland

Tài liệu tham khảo

Fresenius Annual Report 2019. Bad Homburg: Fresenius Medical Care AG & Co. KGaA; 2020. Jager, 2019, A single number for advocacy and communication-worldwide more than 850 million individuals have kidney diseases, Nephrol Dial Transplant, 34, 1803, 10.1093/ndt/gfz174 Fresenius Annual Report 2018. Care and Live: Fresenius Medical Care AG & Co. KGaA; 2019. Pecoits-Filho, 2020, Capturing and monitoring global differences in untreated and treated end-stage kidney disease, kidney replacement therapy modality, and outcomes, Kidney Int Suppl (2011), 10, e3, 10.1016/j.kisu.2019.11.001 Locatelli, 2018, Haemodialysis or haemodiafiltration: that is the question, Nephrol Dial Transplant, 33, 1896, 10.1093/ndt/gfy035 Ronco, 2018, Expanded haemodialysis: from operational mechanism to clinical results, Nephrol Dial Transplant, 33, iii41, 10.1093/ndt/gfy202 Locatelli, 2015, Optimizing haemodialysate composition, Clin Kidney J, 8, 580, 10.1093/ckj/sfv057 Mahmood U, Cho Y, Johnson DW. Peritoneal dialysis solutions. In: Ekart R, editor. Some special problems in peritoneal dialysis: IntechOpen; 2016. Daugirdas, 2015 Pstras, 2019 Amerling, 2012, Continuous flow peritoneal dialysis: update 2012, Contrib Nephrol, 178, 205, 10.1159/000337854 van Esch, 2016, The natural time course of membrane alterations during peritoneal dialysis is partly altered by peritonitis, Perit Dial Int, 36, 448, 10.3747/pdi.2014.00215 Waniewski, 2017, Changes of peritoneal transport parameters with time on dialysis: assessment with sequential peritoneal equilibration test, Int J Artif Organs, 40, 595, 10.5301/ijao.5000622 Stachowska-Pietka, 2019, Alterations of peritoneal transport characteristics in dialysis patients with ultrafiltration failure: tissue and capillary components, Nephrol Dial Transplant, 34, 864, 10.1093/ndt/gfy313 Kim, 2018 Coli, 2000, Evaluation of intradialytic solute and fluid kinetics. Setting Up a predictive mathematical model, Blood Purif, 18, 37, 10.1159/000014406 Schneditz, 2009, A diffusion-adjusted regional blood flow model to predict solute kinetics during haemodialysis, Nephrol Dial Transplant, 24, 2218, 10.1093/ndt/gfp023 Debowska, 2005, Dialysis adequacy indices for peritoneal dialysis and hemodialysis, Adv Perit Dial, 21, 94 Debowska, 2007, Bimodal dialysis: theoretical and computational investigations of adequacy indices for combined use of peritoneal dialysis and hemodialysis, ASAIO J, 53, 566, 10.1097/MAT.0b013e31810c06d2 Eloot, 2006, Optimisation of solute transport in dialysers using a three-dimensional finite volume model, Comput Methods Biomech Biomed Engin, 9, 363, 10.1080/10255840601002728 Donato, 2017, Optimization of dialyzer design to maximize solute removal with a two-dimensional transport model, J Membr Sci, 541, 519, 10.1016/j.memsci.2017.07.018 Rippe, 2004, Fluid and electrolyte transport across the peritoneal membrane during CAPD according to the three-pore model, Perit Dial Int, 24, 10, 10.1177/089686080402400102 Dedrick, 1982, Is the peritoneum a membrane?, ASAIO J, 5, 1 Daugirdas, 2009, Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients, Am J Kidney Dis, 54, 798, 10.1053/j.ajkd.2009.06.033 Debowska, 2007, An integrative description of dialysis adequacy indices for different treatment modalities and schedules of dialysis, Artif Organs, 31, 61, 10.1111/j.1525-1594.2007.00341.x Ursino, 2000, Prediction of solute kinetics, acid-base status, and blood volume changes during profiled hemodialysis, Ann Biomed Eng, 28, 204, 10.1114/1.245 de los Reyes, 2016, A physiologically based model of vascular refilling during ultrafiltration in hemodialysis, J Theor Biol, 390, 146, 10.1016/j.jtbi.2015.11.012 Ursino, 1997, Modeling arterial hypotension during hemodialysis, Artif Organs, 21, 873, 10.1111/j.1525-1594.1997.tb00247.x Cavalcanti, 1999, Numerical simulation of the hemodynamic response to hemodialysis-induced hypovolemia, Artif Organs, 23, 1063, 10.1046/j.1525-1594.1999.06295.x Coli, 1998, A simple mathematical model applied to selection of the sodium profile during profiled haemodialysis, Nephrol Dial Transplant, 13, 404, 10.1093/oxfordjournals.ndt.a027838 Ursino, 2017, Mathematical Model of Potassium Profiling in Chronic Dialysis, Contrib Nephrol, 190, 134, 10.1159/000468960 Gotch, 1989, An analysis of thermal regulation in hemodialysis with one and three compartment models, ASAIO Trans, 35, 622, 10.1097/00002216-198907000-00148 Droog, 2012, Mathematical modeling of thermal and circulatory effects during hemodialysis, Artif Organs, 36, 797, 10.1111/j.1525-1594.2012.01464.x Ene-Iordache, 2017, Blood flow in idealized vascular access for hemodialysis: a review of computational studies, Cardiovasc Eng Technol, 8, 295, 10.1007/s13239-017-0318-x Grechy, 2017, The effect of arterial curvature on blood flow in arterio-venous fistulae: realistic geometries and pulsatile flow, Cardiovasc Eng Technol, 8, 313, 10.1007/s13239-017-0321-2 Casagrande, 2009, Determination of cardiovascular mechanics evolution in the presence of the arteriovenous fistula, ASAIO J, 55, 484, 10.1097/MAT.0b013e3181ab55fb Manini, 2014, Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients, Comput Methods Biomech Biomed Engin, 17, 1358, 10.1080/10255842.2012.745857 Cavalcanti, 2002, Role of short-term regulatory mechanisms on pressure response to hemodialysis-induced hypovolemia, Kidney Int, 61, 228, 10.1046/j.1523-1755.2002.00095.x Ursino, 1997, Mathematical investigation of some physiological factors involved in hemodialysis hypotension, Artif Organs, 21, 891, 10.1111/j.1525-1594.1997.tb00248.x Schneditz, 2013, A regional blood flow model for glucose and insulin kinetics during hemodialysis, ASAIO J, 59, 627, 10.1097/MAT.0000436714.72752.13 Galach, 2009, Kinetic analysis of peritoneal fluid and solute transport with combination of glucose and icodextrin as osmotic agents, Perit Dial Int, 29, 72, 10.1177/089686080902900111 Riggs, 2012, Multiscale physiology-based modeling of mineral bone disorder in patients with impaired kidney function, J Clin Pharmacol, 52, 45S, 10.1177/0091270011412967 Spalding, 2002, Phosphate kinetics during hemodialysis: Evidence for biphasic regulation, Kidney Int, 61, 655, 10.1046/j.1523-1755.2002.00146.x Ciandrini, 2009, Model-based analysis of potassium removal during hemodialysis, Artif Organs, 33, 835, 10.1111/j.1525-1594.2009.00806.x Pietribiasi, 2018, Model of fluid and solute shifts during hemodialysis with active transport of sodium and potassium, PLoS ONE, 13, 10.1371/journal.pone.0209553 Sargent, 2018, Acid-base homeostasis during hemodialysis: New insights into the mystery of bicarbonate disappearance during treatment, Semin Dial, 31, 468, 10.1111/sdi.12714 Leypoldt, 2020, Acid-base kinetics during hemodialysis using bicarbonate and lactate as dialysate buffer bases based on the H(+) mobilization model, Int J Artif Organs, 43, 645, 10.1177/0391398820906524 Eloot, 2012, What can the dialysis physician learn from kinetic modelling beyond Kt/V(urea)?, Nephrol Dial Transplant, 27, 4021, 10.1093/ndt/gfs367 Debowska, 2010, Adequacy indices for dialysis in acute renal failure: kinetic modeling, Artif Organs, 34, 412, 10.1111/j.1525-1594.2009.00873.x Waniewski, 2006, Theoretical and numerical analysis of different adequacy indices for hemodialysis and peritoneal dialysis, Blood Purif, 24, 355, 10.1159/000093199 Agar, 2011, Kinetic model of phosphorus mobilization during and after short and conventional hemodialysis, Clin J Am Soc Nephrol, 6, 2854, 10.2215/CJN.03860411 Daugirdas, 2018, A two-pool kinetic model predicts phosphate concentrations during and shortly following a conventional (three times weekly) hemodialysis session, Nephrol Dial Transplant, 33, 76 Leypoldt, 2003, Kinetics and dosing predictions for daily haemofiltration, Nephrol Dial Transplant, 18, 769, 10.1093/ndt/gfg019 Pietribiasi, 2020, Comparison of two single-solute models of potassium kinetics during hemodialysis, Biocybern Biomed Eng, 40, 938, 10.1016/j.bbe.2020.04.001 Vanholder, 2003, An overview of uremic toxicity, Hemodial Int, 7, 156, 10.1046/j.1492-7535.2003.00034.x Dumler, 2004, Best method for estimating urea volume of distribution: comparison of single pool variable volume kinetic modeling measurements with bioimpedance and anthropometric methods, ASAIO J, 50, 237, 10.1097/01.MAT.0000123689.48886.71 Moissl, 2006, Body fluid volume determination via body composition spectroscopy in health and disease, Physiol Meas, 27, 921, 10.1088/0967-3334/27/9/012 Sargent, 1980, Mathematic modeling of dialysis therapy, Kidney Int Suppl, 10, S2 Sargent, 1996, Principles and biophysics of dialysis, 34 Leypoldt, 1999 Ziolko, 2000, Accuracy of hemodialysis modeling, Kidney Int, 57, 1152, 10.1046/j.1523-1755.2000.00942.x Severi, 2000, Electrolyte and pH dependence of heart rate during hemodialysis: a computer model analysis, Artif Organs, 24, 245, 10.1046/j.1525-1594.2000.06480.x Maheshwari, 2017, A novel mathematical model of protein-bound uremic toxin kinetics during hemodialysis, Sci Rep, 7, 10371, 10.1038/s41598-017-10981-z Schneditz, 1993, A regional blood circulation alternative to in-series two compartment urea kinetic modeling, ASAIO J, 39, M573 Schneditz, 1994, Formal analytical solution to a regional blood flow and diffusion based urea kinetic model, ASAIO J, 40, M667, 10.1097/00002480-199407000-00082 Korohoda, 2013, Analytical solution of multicompartment solute kinetics for hemodialysis, Comput Math Methods Med, 2013, 10.1155/2013/654726 Grandi, 1995, Analytic solution of the Variable-Volume Double-Pool urea kinetics model applied to parameter estimation in hemodialysis, Comput Biol Med, 25, 505, 10.1016/0010-4825(95)00040-0 Casagrande, 2016, Patient-specific modeling of multicompartmental fluid and mass exchange during dialysis, Int J Artif Organs, 39, 220, 10.5301/ijao.5000504 Bianchi, 2019, A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model, Stat Methods Med Res, 28, 2069, 10.1177/0962280217745572 Daugirdas, 2016, Solute solver 'what if' module for modeling urea kinetics, Nephrol Dial Transplant, 31, 1934, 10.1093/ndt/gfw311 Flythe, 2017, Turning the tide: improving fluid management in dialysis through technology, J Am Soc Nephrol, 28, 2260, 10.1681/ASN.2017050491 Hecking, 2018, Greater fluid overload and lower interdialytic weight gain are independently associated with mortality in a large international hemodialysis population, Nephrol Dial Transplant, 33, 1832, 10.1093/ndt/gfy083 Flythe, 2020, Blood pressure and volume management in dialysis: conclusions from a Kidney Disease: Improving Global Outcomes (KDIGO) Controversies Conference, Kidney Int, 97, 861, 10.1016/j.kint.2020.01.046 Pietribiasi, 2015, Kinetics of plasma refilling during hemodialysis sessions with different initial fluid status, ASAIO J, 61, 350, 10.1097/MAT.0000000000000206 Chamney P, Wabel P, Krämer M, Isermann R. Simulation of active vascular refilling in haemodialysis patients. Modelling and control in biomedical systems: workshop IFAC. Greifswald, 2000. Pietribiasi, 2016, Modelling transcapillary transport of fluid and proteins in hemodialysis patients, PLoS ONE, 11, 10.1371/journal.pone.0159748 Pietribiasi, 2018, Does the plasma refilling coefficient change during hemodialysis sessions?, Int J Artif Organs, 41, 706, 10.1177/0391398818803439 Possenti, 2019, Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system, Microvasc Res, 122, 101, 10.1016/j.mvr.2018.11.003 Mc Causland, 2020, Intradialytic hypotension and cardiac arrhythmias in patients undergoing maintenance hemodialysis: results from the monitoring in dialysis study, Clin J Am Soc Nephrol, 15, 805, 10.2215/CJN.06810619 Correa, 2020, Predictors of intradialytic symptoms: an analysis of data from the hemodialysis study, Am J Kidney Dis, 76, 331, 10.1053/j.ajkd.2020.01.004 Cavalcanti, 2006, Mathematical modeling of arterial pressure response to hemodialysis-induced hypovolemia, Comput Biol Med, 36, 128, 10.1016/j.compbiomed.2004.08.004 Pstras, 2020, Transcapillary transport of water, small solutes and proteins during hemodialysis, Sci Rep, 10, 18736, 10.1038/s41598-020-75687-1 Pstras, 2019, Hemodialysis-induced changes in hematocrit, hemoglobin and total protein: Implications for relative blood volume monitoring, PLoS ONE, 14, 10.1371/journal.pone.0220764 Pstras, 2020, Relative blood volume changes during haemodialysis estimated from haemoconcentration markers, Sci Rep, 10, 14809, 10.1038/s41598-020-71830-0 Pstras, 2021, Monitoring relative blood volume changes during hemodialysis: Impact of the priming procedure, Artif Organs, 45, 1189, 10.1111/aor.13972 Balter, 2015, Methods and challenges for the practical application of Crit-Line™ monitor utilization in patients on hemodialysis, Blood Purif, 39, 21, 10.1159/000368936 Alayoud, 2019, Utility of a blood volume monitor in the management of anemia in dialysis by computing the total hemoglobin mass, Hemodial Int, 23, 419, 10.1111/hdi.12776 Nesrallah, 2013, Biofeedback dialysis for hypotension and hypervolemia: a systematic review and meta-analysis, Nephrol Dial Transplant, 28, 182, 10.1093/ndt/gfs389 Mann, 2000, Sodium modeling, Kidney Int Suppl, 76, S79, 10.1016/S0085-2538(15)47404-6 Baigent, 2001, Mathematical modelling of profiled haemodialysis: A simplified approach, J Theor Med, 3, 10.1080/10273660108833070 Abohtyra, 2019, Individualization of ultrafiltration in hemodialysis, IEEE Trans Biomed Eng, 66, 2174, 10.1109/TBME.2018.2884931 Javed, 2010, Model predictive control of relative blood volume and heart rate during hemodialysis, Med Biol Eng Comput, 48, 389, 10.1007/s11517-010-0582-5 Javed, 2011, Identification and control for automated regulation of hemodynamic variables during hemodialysis, IEEE Trans Biomed Eng, 58, 1686, 10.1109/TBME.2011.2110650 Leung, 2017, Randomized crossover trial of blood volume monitoring-guided ultrafiltration biofeedback to reduce intradialytic hypotensive episodes with hemodialysis, Clin J Am Soc Nephrol, 12, 1831, 10.2215/CJN.01030117 Hecking, 2017, Feedback control in hemodialysis-much ado about nothing?, Clin J Am Soc Nephrol, 12, 1730, 10.2215/CJN.09770917 Maggiore, 1995, Thermal balance and dialysis hypotension, Int J Artif Organs, 18, 518, 10.1177/039139889501800908 Schneditz, 2001, Temperature and thermal balance in hemodialysis, Semin Dial, 14, 357, 10.1046/j.1525-139X.2001.00088.x van der Sande, 2009, Control of core temperature and blood pressure stability during hemodialysis, Clin J Am Soc Nephrol, 4, 93, 10.2215/CJN.01800408 Bullen, 2019, Individualized cool dialysate as an effective therapy for intradialytic hypotension and hemodialysis patients' perception, Ther Apher Dial, 23, 145, 10.1111/1744-9987.12761 Tentori, 2013, Association of dialysate bicarbonate concentration with mortality in the Dialysis Outcomes and Practice Patterns Study (DOPPS), Am J Kidney Dis, 62, 738, 10.1053/j.ajkd.2013.03.035 Tovbin, 2016, Correcting acidosis during hemodialysis: current limitations and a potential solution, Semin Dial, 29, 35, 10.1111/sdi.12454 Wolf, 2019, Physicochemical models of acid-base, Semin Nephrol, 39, 328, 10.1016/j.semnephrol.2019.04.003 Andreassen, 2005, Mathematical models of oxygen and carbon dioxide storage and transport: interstitial fluid and tissue stores and whole-body transport, Crit Rev Biomed Eng, 33, 265, 10.1615/CritRevBiomedEng.v33.i3.20 Rees, 2005, Mathematical models of oxygen and carbon dioxide storage and transport: the acid-base chemistry of blood, Crit Rev Biomed Eng, 33, 209, 10.1615/CritRevBiomedEng.v33.i3.10 Wolf, 2013, Whole body acid-base and fluid-electrolyte balance: a mathematical model, Am J Physiol Renal Physiol, 305, F1118, 10.1152/ajprenal.00195.2013 Ježek, 2018, Modern and traditional approaches combined into an effective gray-box mathematical model of full-blood acid-base, Theor Biol Med Modell, 15, 14, 10.1186/s12976-018-0086-9 Leypoldt, 2021, Modeling acid-base balance during continuous renal replacement therapy, J Clin Monit Comput Blaine, 2015, Renal control of calcium, phosphate, and magnesium homeostasis, Clin J Am Soc Nephrol, 10, 1257, 10.2215/CJN.09750913 Ott, 2013, Therapy for patients with CKD and low bone mineral density, Nat Rev Nephrol, 9, 681, 10.1038/nrneph.2013.182 KDIGO CKD-MBD Work Group, 2011, KDIGO 2017 clinical practice guideline update for the diagnosis, evaluation, prevention, and treatment of chronic kidney disease-mineral and bone disorder (CKD-MBD), Kidney Int Suppl, 2017, 1 Debowska, 2015, Phosphate kinetics during weekly cycle of hemodialysis sessions: application of mathematical modeling, Artif Organs, 39, 1005, 10.1111/aor.12489 Poleszczuk, 2016, Phosphate kinetics in hemodialysis: application of delayed pseudo one-compartment model, Blood Purif, 42, 177, 10.1159/000445934 di Filippo, 2018, Assessment of intradialysis calcium mass balance by a single pool variable-volume calcium kinetic model, Hemodial Int, 22, 126, 10.1111/hdi.12531 Hall, 2011 Bos, 1999, Effects of arteriovenous fistulas on cardiac oxygen supply and demand, Kidney Int, 55, 2049, 10.1046/j.1523-1755.1999.00433.x Savage, 2002, The impact of arteriovenous fistula formation on central hemodynamic pressures in chronic renal failure patients: a prospective study, Am J Kidney Dis, 40, 753, 10.1053/ajkd.2002.35686 Dundon, 2014, The deleterious effects of arteriovenous fistula-creation on the cardiovascular system: a longitudinal magnetic resonance imaging study, Int J Nephrol Renovasc Dis, 7, 337 MacRae, 2004, Arteriovenous fistula-associated high-output cardiac failure: a review of mechanisms, Am J Kidney Dis, 43, e17, 10.1053/j.ajkd.2004.01.016 Huberts, 2012, A pulse wave propagation model to support decision-making in vascular access planning in the clinic, Med Eng Phys, 34, 233, 10.1016/j.medengphy.2011.07.015 Caroli, 2013, Validation of a patient-specific hemodynamic computational model for surgical planning of vascular access in hemodialysis patients, Kidney Int, 84, 1237, 10.1038/ki.2013.188 Bozzetto, 2017, Clinical use of computational modeling for surgical planning of arteriovenous fistula for hemodialysis, BMC Med Inf Decis Making, 17, 26, 10.1186/s12911-017-0420-x Bozzetto, 2016, Transitional flow in the venous side of patient-specific arteriovenous fistulae for hemodialysis, Ann Biomed Eng, 44, 2388, 10.1007/s10439-015-1525-y Remuzzi, 2017, Is shear stress the key factor for AVF maturation?, J Vasc Access, 18, 10, 10.5301/jva.5000686 Gemert, 1984, Shunt haemodynamics and extracorporeal dialysis: an electrical resistance network analysis, Phys Med Biol, 29, 219, 10.1088/0031-9155/29/3/002 Georgianos, 2019, Systolic and diastolic hypertension among patients on hemodialysis: Musings on volume overload, arterial stiffness, and erythropoietin, Semin Dial, 32, 507, 10.1111/sdi.12837 Poleszczuk, 2018, Patient-specific pulse wave propagation model identifies cardiovascular risk characteristics in hemodialysis patients, PLoS Comput Biol, 14, 10.1371/journal.pcbi.1006417 Poleszczuk, 2018, Subject-specific pulse wave propagation modeling: Towards enhancement of cardiovascular assessment methods, PLoS ONE, 13, 10.1371/journal.pone.0190972 Debowska, 2018, Impact of hemodialysis on cardiovascular system assessed by pulse wave analysis, PLoS ONE, 13, 10.1371/journal.pone.0206446 Bos, 2000, Cardiac and hemodynamic effects of hemodialysis and ultrafiltration, Am J Kidney Dis, 35, 819, 10.1016/S0272-6386(00)70250-2 Ding, 2015, Three-dimensional simulation of mass transfer in artificial kidneys, Artif Organs, 39, E79, 10.1111/aor.12415 Annan, 2012, Mathematical modeling for hollow fiber dialyzer: blood and HCO3-dialysate flow characteristics, Int J Pure Appl Math, 79, 425 Rambod, 2010, An experimental and numerical study of the flow and mass transfer in a model of the wearable artificial kidney dialyzer, Biomed Eng Online, 9, 21, 10.1186/1475-925X-9-21 Eloot, 2002, Computational flow modeling in hollow-fiber dialyzers, Artif Organs, 26, 590, 10.1046/j.1525-1594.2002.07081.x Sigdell, 1974 Jaffrin, 1990, Simultaneous convective and diffusive mass transfers in a hemodialyser, J Biomech Eng, 112, 212, 10.1115/1.2891174 Sigdell, 1982, Calculation of combined diffusive and convective mass transfer, Int J Artif Organs, 5, 361, 10.1177/039139888200500609 Waniewski, 2015 Waniewski, 1991, Theoretical basis and experimental verification of the impact of ultrafiltration on dialyzer clearance, Artif Organs, 15, 70, 10.1111/j.1525-1594.1991.tb00763.x Waniewski, 1993, Alternative descriptions of combined diffusive and convective mass transport in hemodialyzer, Artif Organs, 17, 3, 10.1111/j.1525-1594.1993.tb00377.x Waniewski, 1994, Impact of ultrafiltration on back-diffusion in hemodialyzer, Artif Organs, 18, 933, 10.1111/j.1525-1594.1994.tb03346.x Galach, 2003, Impact of convective transport on dialyzer clearance, J Artif Organs, 6, 42, 10.1007/s100470300007 Depner, 2004, Dialyzer performance in the HEMO Study: in vivo K0A and true blood flow determined from a model of cross-dialyzer urea extraction, ASAIO J, 50, 85, 10.1097/01.MAT.0000104824.55517.6C Hörl WH, Koch K-M, Lindsay RM, Ronco C, Winchester JFe. Replacement of renal function by dialysis. 5th ed. Dordrecht: Springer Netherlands; 2004. Waniewski, 2020, Impact of solute exchange between erythrocytes and plasma on hemodialyzer clearance, Biocybern Biomed Eng, 40, 265, 10.1016/j.bbe.2019.04.003 Henderson, 1969, Altered permeability of the peritoneal membrane after using hypertonic peritoneal dialysis fluid, J Clin Invest, 48, 992, 10.1172/JCI106080 Morelle, 2021, ISPD Recommendations for the evaluation of peritoneal membrane dysfunction in adults: classification, measurement, interpretation and rationale for intervention, Perit Dial Int, 41, 352, 10.1177/0896860820982218 Oberg, 2017, Optimizing Automated Peritoneal Dialysis Using an Extended 3-Pore Model, Kidney Int Rep, 2, 943, 10.1016/j.ekir.2017.04.010 Rippe, 1989, Simulations of peritoneal solute transport during CAPD. Application of two-pore formalism, Kidney Int, 35, 1234, 10.1038/ki.1989.115 Ho-dac-Pannekeet, 1996, Peritoneal transport characteristics with glucose polymer based dialysate, Kidney Int, 50, 979, 10.1038/ki.1996.399 Parikova, 2006, Analysis of fluid transport pathways and their determinants in peritoneal dialysis patients with ultrafiltration failure, Kidney Int, 70, 1988, 10.1038/sj.ki.5001861 Stachowska-Pietka, 2019, Fluid tonicity affects peritoneal characteristics derived by 3-pore model, Perit Dial Int, 39, 243, 10.3747/pdi.2017.00267 Leypoldt, 1993, Interpreting peritoneal membrane osmotic reflection coefficients using a distributed model of peritoneal transport, Adv Perit Dial, 9, 3 Leypoldt, 1992, The effect of convection on bidirectional peritoneal solute transport: predictions from a distributed model, Ann Biomed Eng, 20, 463, 10.1007/BF02368137 Flessner, 1984, A distributed model of peritoneal-plasma transport: theoretical considerations, Am J Physiol, 246, R597 Heimburger, 1992, A quantitative description of solute and fluid transport during peritoneal dialysis, Kidney Int, 41, 1320, 10.1038/ki.1992.196 Waniewski, 1992, Aqueous solute concentrations and evaluation of mass transport coefficients in peritoneal dialysis, Nephrol Dial Transplant, 7, 50 Waniewski, 1996, Diffusive mass transport coefficients are not constant during a single exchange in continuous ambulatory peritoneal dialysis, ASAIO J, 42, M518, 10.1097/00002480-199609000-00040 Waniewski, 2005, Fluid and solute transport in CAPD patients before and after permanent loss of ultrafiltration capacity, Int J Artif Organs, 28, 976, 10.1177/039139880502801004 Waniewski, 1995, Diffusive and convective solute transport in peritoneal dialysis with glucose as an osmotic agent, Artif Organs, 19, 295, 10.1111/j.1525-1594.1995.tb02332.x Imholz, 1994, Fluid and solute transport in CAPD patients using ultralow sodium dialysate, Kidney Int, 46, 333, 10.1038/ki.1994.279 Imholz, 1998, Day-to-day variability of fluid and solute transport in upright and recumbent positions during CAPD, Nephrol Dial Transplant, 13, 146, 10.1093/ndt/13.1.146 Twardowski, 1987, Peritoneal equilibration test, Perit Dial Bull, 7, 138, 10.1177/089686088700700306 Heimbürger, 1995, Lymphatic absorption in CAPD patients with loss of ultrafiltration capacity, Blood Purif, 13, 327, 10.1159/000170217 Heimbürger, 1990, Peritoneal transport in CAPD patients with permanent loss of ultrafiltration capacity, Kidney Int, 38, 495, 10.1038/ki.1990.231 Van Biesen, 2006, The personal dialysis capacity test is superior to the peritoneal equilibration test to discriminate inflammation as the cause of fast transport status in peritoneal dialysis patients, Clin J Am Soc Nephrol, 1, 269, 10.2215/CJN.00820805 Sampimon, 2011, The time course of peritoneal transport parameters in peritoneal dialysis patients who develop encapsulating peritoneal sclerosis, Nephrol Dial Transplant, 26, 291, 10.1093/ndt/gfq343 Balafa, 2011, Peritoneal albumin and protein losses do not predict outcome in peritoneal dialysis patients, Clin J Am Soc Nephrol, 6, 561, 10.2215/CJN.05540610 Stachowska-Pietka, 2010, Changes in free water fraction and aquaporin function with dwell time during continuous ambulatory peritoneal dialysis, Artif Organs, 34, 1138, 10.1111/j.1525-1594.2010.01036.x Waniewski, 2004, A mathematical model of local stimulation of perfusion by vasoactive agent diffusing from tissue surface, Cardiovasc Eng, 4, 115, 10.1023/B:CARE.0000025138.71454.3c Waniewski, 2008, How accurate is the description of transport kinetics in peritoneal dialysis according to different versions of the three-pore model?, Perit Dial Int, 28, 53, 10.1177/089686080802800110 Fischbach, 2001, Dynamic changes of the total pore area available for peritoneal exchange in children, J Am Soc Nephrol, 12, 1524, 10.1681/ASN.V1271524 Haraldsson, 1998, How to evaluate and optimize peritoneal dialysis treatment, Nephrol Dial Transplant, 13, 112, 10.1093/ndt/13.suppl_6.112 Freida, 2007, Combination of crystalloid (glucose) and colloid (icodextrin) osmotic agents markedly enhances peritoneal fluid and solute transport during the long PD dwell, Perit Dial Int, 27, 267, 10.1177/089686080702700311 Olszowska, 2002, Comparison of peritoneal transport of solutes and water during CAPD with glucose or amino acids solutions. Preliminary report, Pol Merkur Lekarski, 13, 389 Park, 1993, Peritoneal transport during dialysis with amino acid-based solutions, Perit Dial Int, 13, 280, 10.1177/089686089301300404 Morelle, 2018, Mechanisms of crystalloid versus colloid osmosis across the peritoneal membrane, J Am Soc Nephrol, 29, 1875, 10.1681/ASN.2017080828 Leypoldt, 2015, Low-polydispersity glucose polymers as osmotic agents for peritoneal dialysis, Perit Dial Int, 35, 428, 10.3747/pdi.2013.00232 Rippe, 2008, Optimum electrolyte composition of a dialysis solution, Perit Dial Int, 28, S131, 10.1177/089686080802803s25 Rippe, 2000, Computer simulations of ultrafiltration profiles for an icodextrin-based peritoneal fluid in CAPD, Kidney Int, 57, 2546, 10.1046/j.1523-1755.2000.00114.x Galach, 2011, Mathematical modeling of the glucose-insulin system during peritoneal dialysis with glucose-based fluids, ASAIO J, 57, 41, 10.1097/MAT.0b013e3181fe5b76 Galach, 2012, Membrane transport of several ions during peritoneal dialysis: mathematical modeling, Artif Organs, 36, E163, 10.1111/j.1525-1594.2012.01484.x Coester, 2008, The relationship between effluent potassium due to cellular release, free water transport and CA125 in peritoneal dialysis patients, NDT Plus, 1, iv41 Imholz, 1993, Effect of an increased intraperitoneal pressure on fluid and solute transport during CAPD, Kidney Int, 44, 1078, 10.1038/ki.1993.351 Lindholm, 1989, Peritoneal ultrafiltration and fluid reabsorption during peritoneal dialysis, Nephrol Dial Transplant, 4, 805 Flessner, 2004, Effective lymphatic absorption rate is not a useful or accurate term to use in the physiology of peritoneal dialysis, Perit Dial Int, 24, 313, 10.1177/089686080402400403 Flessner, 2001, Transport of protein in the abdominal wall during intraperitoneal therapy. I. Theoretical approach, Am J Physiol Gastrointest Liver Physiol, 281, G424, 10.1152/ajpgi.2001.281.2.G424 Waniewski, 2013, Threefold peritoneal test of osmotic conductance, ultrafiltration efficiency, and fluid absorption, Perit Dial Int, 33, 419, 10.3747/pdi.2011.00329 Rippe, 1991, Computer simulations of peritoneal fluid transport in CAPD, Kidney Int, 40, 315, 10.1038/ki.1991.216 Pannekeet, 1995, The standard peritoneal permeability analysis: a tool for the assessment of peritoneal permeability characteristics in CAPD patients, Kidney Int, 48, 866, 10.1038/ki.1995.363 La Milia, 2007, Simultaneous measurement of peritoneal glucose and free water osmotic conductances, Kidney Int, 72, 643, 10.1038/sj.ki.5002405 La Milia, 2005, Mini-peritoneal equilibration test: A simple and fast method to assess free water and small solute transport across the peritoneal membrane, Kidney Int, 68, 840, 10.1111/j.1523-1755.2005.00465.x Smit, 2004, Quantification of free water transport in peritoneal dialysis, Kidney Int, 66, 849, 10.1111/j.1523-1755.2004.00815.x Venturoli, 2005, Validation by computer simulation of two indirect methods for quantification of free water transport in peritoneal dialysis, Perit Dial Int, 25, 77, 10.1177/089686080502500114 Waniewski, 2007, Ultrafiltration and absorption in evaluating aquaporin function from peritoneal transport of sodium, Perit Dial Int, 27, 687, 10.1177/089686080702700616 Krediet, 2018, Ultrafiltration failure is a reflection of peritoneal alterations in patients treated with peritoneal dialysis, Front Physiol, 9, 1815, 10.3389/fphys.2018.01815 Morelle, 2015, Interstitial fibrosis restricts osmotic water transport in encapsulating peritoneal sclerosis, J Am Soc Nephrol, 26, 2521, 10.1681/ASN.2014090939 Stachowska-Pietka, 2011, Distributed modeling of glucose induced osmotic fluid flow during single exchange with hypertonic glucose solution, Biocybern Biomed Eng, 31, 39, 10.1016/S0208-5216(11)70004-3 Stachowska-Pietka, 2011, Distributed models of peritoneal transport, 23 Stachowska-Pietka, 2006, Distributed model of peritoneal fluid absorption, Am J Physiol Heart Circ Physiol, 291, H1862, 10.1152/ajpheart.01320.2005 Stachowska-Pietka, 2012, Computer simulations of osmotic ultrafiltration and small-solute transport in peritoneal dialysis: a spatially distributed approach, Am J Physiol Renal Physiol, 302, F1331, 10.1152/ajprenal.00301.2011 Stachowska-Pietka, 2016, Concomitant bidirectional transport during peritoneal dialysis can be explained by a structured interstitium, Am J Physiol Heart Circ Physiol, 310, H1501, 10.1152/ajpheart.00925.2014 Waniewski, 2009, Distributed modeling of osmotically driven fluid transport in peritoneal dialysis: theoretical and computational investigations, Am J Physiol Heart Circ Physiol, 296, H1960, 10.1152/ajpheart.00121.2009 Waniewski, 2016, Peritoneal fluid transport rather than peritoneal solute transport associates with dialysis vintage and age of peritoneal dialysis patients, Comput Math Methods Med, 2016, 8204294, 10.1155/2016/8204294 Waniewski, 2002, Distributed modeling of diffusive solute transport in peritoneal dialysis, Ann Biomed Eng, 30, 1181, 10.1114/1.1519264 Cherniha, 2020, A mathematical model for transport in poroelastic materials with variable volume: derivation, lie symmetry analysis, and examples, Symmetry, 12, 396, 10.3390/sym12030396 Gotch, 1974, Individualized, quantified dialysis therapy of uremia, Proc Clin Dial Transplant Forum, 27 Gotch, 1985, A mechanistic analysis of the National Cooperative Dialysis Study (NCDS), Kidney Int, 28, 526, 10.1038/ki.1985.160 National Kidney F, 2015, KDOQI Clinical practice guideline for hemodialysis adequacy: 2015 update, Am J Kidney Dis, 66, 884, 10.1053/j.ajkd.2015.07.015 Tattersall, 2007, EBPG guideline on dialysis strategies, Nephrol Dial Transplant, 22, ii5 Dombros, 2005, European best practice guidelines for peritoneal dialysis. 7 Adequacy of peritoneal dialysis, Nephrol Dial Transplant, 20, ix24 Waniewski, 2010, Can the diverse family of dialysis adequacy indices be understood as one integrated system?, Blood Purif, 30, 257, 10.1159/000320764 Casino, 1996, The equivalent renal urea clearance: a new parameter to assess dialysis dose, Nephrol Dial Transplant, 11, 1574, 10.1093/oxfordjournals.ndt.a027616 Gotch, 1998, The current place of urea kinetic modelling with respect to different dialysis modalities, Nephrol Dial Transplant, 13, 10, 10.1093/ndt/13.suppl_6.10 Waniewski, 2016, Quantification of dialytic removal and extracellular calcium mass balance during a weekly cycle of hemodialysis, PLoS ONE, 11, 10.1371/journal.pone.0153285 Casino, 2017, The variable target model: a paradigm shift in the incremental haemodialysis prescription, Nephrol Dial Transplant, 32, 182 Casino, 2004, Simple and accurate quantification of dialysis in acute renal failure patients during either urea non-steady state or treatment with irregular or continuous schedules, Nephrol Dial Transplant, 19, 1454, 10.1093/ndt/gfh218 Vanholder, 2015, Once upon a time in dialysis: the last days of Kt/V?, Kidney Int, 88, 460, 10.1038/ki.2015.155 Chan, 2019, Dialysis initiation, modality choice, access, and prescription: conclusions from a Kidney Disease: Improving Global Outcomes (KDIGO) Controversies Conference, Kidney Int, 96, 37, 10.1016/j.kint.2019.01.017 Stachowska-Pietka, 2015, Peritoneal dialysis: principles and peritoneal physiology Gura, 2016, A wearable artificial kidney for patients with end-stage renal disease. JCI, Insight, 1 Salani, 2018, Innovations in wearable and implantable artificial kidneys, Am J Kidney Dis, 72, 745, 10.1053/j.ajkd.2018.06.005 Bazaev, 2016, A mathematical model of extrarenal purification of human blood using a wearable artificial kidney based on peritoneal dialysis, Biomed Eng, 50, 219, 10.1007/s10527-016-9624-0 Brunati, 2018, Phosphate and calcium control in short frequent hemodialysis with the NxStage system one cycler: mass balance studies and comparison with standard thrice-weekly bicarbonate dialysis, Blood Purif, 45, 334, 10.1159/000487123 Leypoldt, 2019, Volume of urea cleared as a therapy dosing guide for more frequent hemodialysis, Hemodial Int, 23, 42, 10.1111/hdi.12692 Michalec, 2016, Biomedical monitoring of phosphate removal by hemodialysis, J Pharm Biomed Anal, 126, 9, 10.1016/j.jpba.2016.04.034 Pilt, 2020, Online urea concentration estimation from spent dialysate using optical sensor, 1459 Britton, 1987, One-dimensional theory of haemofilters, Math Med Biol, 4, 59, 10.1093/imammb/4.1.59 Werynski, 1985, Theoretical formulation of sieving coefficient evaluation for membrane plasma separation, Artif Organs, 9, 250, 10.1111/j.1525-1594.1985.tb04387.x Patzer, 2003, Bound solute dialysis, ASAIO J, 49, 271, 10.1097/01.MAT.0000065378.73558.83 Magosso, 2006, A modeling study of bilirubin kinetics during Molecular Adsorbent Recirculating System sessions, Artif Organs, 30, 285, 10.1111/j.1525-1594.2006.00216.x Jung, 2012, Relationship between kinetics of albumin-bound bilirubin and water-soluble urea in extracorporeal blood purification, Nephrol Dial Transplant, 27, 1200, 10.1093/ndt/gfr413 Jung, 2020, Bile acid kinetic modeling in end-stage liver support patients, Biocybern Biomed Eng, 40, 764, 10.1016/j.bbe.2020.03.002 Werynski, 2000, Kinetic analysis of LDL apoB transport and metabolism in non-steady states, Control Cybern, 29, 405 Waniewski, 1992, Immune response after plasmapheresis, Biocybern Biomed Eng, 11, 61 Waniewski, 1991, Mathematical modeling of antigen and immune complex kinetics during extracorporeal removal of autoantibody, Int J Artif Organs, 14, 186, 10.1177/039139889101400312 Werynski, 2002, Mathematical modeling in blood purification processes, Biocybern Biomed Eng, 22, 69 Flessner, 2005, Resistance of tumor interstitial pressure to the penetration of intraperitoneally delivered antibodies into metastatic ovarian tumors, Clin Cancer Res, 11, 3117, 10.1158/1078-0432.CCR-04-2332 Stachowska-Pietka J, Waniewski J. Mathematical Models of Intraperitoneal Drug Delivery. In: Ceelen W, Levine E, editors. Intraperitoneal cancer therapy: Taylor & Francis Group; 2016. p. 153-69. Wientjes, 1993, Penetration of mitomycin C in human bladder, Cancer Res, 53, 3314 Gupta, 1995, Penetration kinetics of 2',3'-dideoxyinosine in dermis is described by the distributed model, Pharm Res, 12, 108, 10.1023/A:1016298906589 Flessner, 2006, Correlating structure with solute and water transport in a chronic model of peritoneal inflammation, Am J Physiol Renal Physiol, 290, F232, 10.1152/ajprenal.00211.2005 Canaud, 2020, The renal replacement therapy landscape in 2030: reducing the global cardiovascular burden in dialysis patients, Nephrol Dial Transplant, 35, ii51, 10.1093/ndt/gfaa005