Severe Vesico-ureteral Reflux and Urine Sequestration: Mathematical Relations and Urodynamic Consequences

TL;DR

This paper introduces mathematical formulas to estimate urine sequestration volumes in the urinary system for VUR patients, highlighting differences between infants and older children and discussing implications for bladder function.

Contribution

It presents novel geometric and topological methods to quantify urine sequestration in VUR, linking anatomical measurements to urodynamic consequences.

Findings

Urine sequestration is greater in infants than in older children.

Mathematical models can estimate proximal urinary volumes from ultrasound and imaging data.

Primary VUR can cause urodynamic problems due to urine sequestration.

Abstract

Some simple mathematical formulae to calculate the volumes of proximal pyeloureteral reflexive systems are presented, and the results are compared to bladder capacity values. Using the results of the calculi, the author discusses possible implications of severe urinary sequestration in the pyeloureteral systems. Using geometrical and topological approximations we calculate the volumes of ureters and renal pelvises, applying in vivo measurements obtained from conventional ultrasound, retrograde cystourethrograms and topographic anatomic references. Approximations use 2 decimals and assumed $\pi$ value was 3.14. Ureteral and pyelic volumes are calculated, respectively, from the mathematical formula for the cylinder and cone volumes. Dolicomegaureter are compensated using proportional calculi. Bladder volumes are estimated from conventional formulae. Proximal urinary sequestration is compared between infants and older children with VUR. Mechanisms of direct induction of bladder urodynamic failure from VUR are suggested. Sequestration of urine in the ureter and renal pelvis can be estimated from mathematical formulae in patients with VUR. The values used derive from ultrasound examinations, CUM and topographical anatomical references. Primary VUR can determine urodynamic problems. Urine sequestration in the proximal urinary system is worse in infants than in older children.