3D simulation of solutes concentration in urinary concentration mechanism in rat renal medulla

• Published in: Mathematical biosciences 2019-02, Vol.308, p.59-69
• Main Authors: Mahdavi, S. Sharareh, Abdekhodaie, Mohammad J., Farhadi, Fatollah, Shafiee, Mohammad Ali
• Format: Article
• Language: English
• Subjects: Animals; Collecting duct; Computer Simulation; Experimental data; Kidney Concentrating Ability; Kidney Medulla; Kidney Tubules; Kidneys; Mathematical models; Models, Biological; Nephrons; Osmolality; Osmolar Concentration; Pictures; Rats; Renal medulla; Sodium; Solutes; Solutes concentration; Three dimensional models; Tubules; Urea; Urinary concentration mechanism
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2018.12.008

•The location of the tubules affects the solutes concentration.•The boot-shaped prebend segment significantly increased osmolality of collecting duct.•Collecting duct osmolality at the end of the IM is 1198 mOsmol/kg H2O which was close to.•Experimental data.•Osmolality of tubules at cortico-medullary boundary were lower than blood plasma (∼290 mOsmol/kg H2O) and close to experimental data. In this work, a mathematical model was developed to simulate the urinary concentration mechanism. A 3-D geometry was derived based on the detail physiological pictures of rat kidney. The approximate region of each tubule was obtained from the volume distribution of structures based on Walter Pfaller's monograph and Layton's region-based model. Mass and momentum balances were applied to solve for the change in solutes concentration and osmolality. The osmolality of short and long descending nephrons at the end of the outer medulla was obtained to be 530 mOsmol/kgH2O and 802 mOsmol/kgH2O, respectively, which were in acceptable agreement with experimental data. The fluid osmolality of the short and long ascending nephrons was also compatible with experimental data. The osmolality of CD fluid at the end of the inner medulla was determined to be 1198 mOsmol/kgH2O which was close the experimental data (1216 ± 118). Finally, the impact of the position of each tubule on the fluid osmolality and solutes concentration were obvious in the results; for example, short descending limb a1, which is the closest tubule to the collecting duct, had the highest urea concentration in all tubules. This reflects the important effect of the 3D modeling on the precise analysis of urinary concentration mechanism.