In an attempt to improve the diagnostic accuracy of uroflowmetry by utilizing all the available information contained in the uroflow curve (voided volume, flow time, Qmax, Qave, time to peak flow), we developed a mathematical formula incorporating these parameters, to calculate Flow Resistive Forces Index (QRF), a novel measure of urethral resistance and assessed its clinical applicability vs Qmax.

Main idea was based on the concept that, in terms of hydrodynamics, voiding occurs when a resultant force produces the impulse required to change the momentum of a given volume of urine, triggering transition from the stationary to the flowing state. Central pillars of our theoretical model were, the impulse-momentum principle deriving from Newton's second law of motion which, when applied to liquids states that, the sum of forces acting on a flowing fluid volume relate to its acceleration by: Faverage= V x aaverage   and, the temporal profile of uroflow curve, that is bell shaped comprised of an ascending and a descending limb depicting the time sequence of events over the course of micturition, marked by steeply increasing/accelerating flow to a maximum value (Qmax) that then, gradually reduces/decelerates until termination. The resultant, that is net or total force applied to a given volume of urine during voiding, is composed of individual forces acting in opposite directions as: 1) Expulsive Forces (promote voiding/accelerate urine flow) and 2) Resistive Forces (impede voiding/decelerate flow). We regarded Detrusor pressure as the main impulsive force reflecting the pump function of the bladder and assumed that forces resisting outflow can be represented and quantified by Urethral resistance factor, that is considered the most reasonable estimate of urethral resistance, is applicable to both genders and can be calculated by the equation: URA=[(1+4dQ2Pdet)1/2-1]/2dQ2  deriving  Pdet=(2dQ2URA +1)2 -1/4dQ2  (d=3.8x10-4)  .Thus, total  Faverage : = Fexpulsive – Fresistive= average Detrusor Pressure (Pdet) – average Urethral Resistance (R).
The equation was developed in three consecutive steps. In 1&2, average acceleration was calculated by individually measuring flow acceleration and deceleration deriving Eq-1 (aave = Qmax(tft-2tpf)/2tft)  and by applying the impulse-momentum and Pdet formulas to extract Eq-2 (aave= dQave2 Rave2/V ) [Qmax=maximum flow rate, Qin=initial flow (onset of voiding)[≈0], t0=time of initiation of urination[≈0], tpf = time to peak flow, Qfin=final flow[termination of voiding ≈0], tft=flow time, d=3.8x10-4, Qave= average flow rate, Rave = average urethral resistance, V= voided volume]. In step3, combining Eqs 1&2 and solving for Rave, the QRFindex equation which expresses the mean resistance to urine was formulated . Subsequently, we applied QRF to a cohort of 84 patients (61 males-23 females) complaining of voiding dysfunction symptoms, who underwent uroflow test followed by pressure-flow study and were classified according to Schafer LinPURR nomogram as unobstructed (LinPURR: 0-1) or obstructed (LinPURR: 2-6). Although LinPURR grading is basically applicable to men, we decided to employ it in females, since there is no consensus on how to properly determine bladder outflow obstruction in women. Statistical analysis was performed by using the SPSS-22® and MedCalc® statistical packages (p<0,05).

Overall, urodynamic obstruction was diagnosed in 43,5%  of the patients:  50,8% males [1 in 2] and 25% [1 in 4] females (x2=4,67-p=0,03). On univariate analysis, QRF values were significantly higher in obstructed vs unobstructed patients while, bivariate linear correlations, binary logistic regression model & ROC curve analyses, showed that in both sexes (mostly in men), QRF was a strong independent predictor of bladder outflow obstruction, significantly differing from Qmax that was weakly associated to this condition. Optimal QRF cutoff points: >2,8 in men - > 3,4 in women.

In both sexes (predominantly in men), QRF index was a highly significant predictor of bladder outflow obstruction diagnosis (exhibited excellent diagnostic performance characteristics),significantly outperforming in discriminative accuracy Qmax, the currently most widely used urethral resistance estimator.

The proposed mathematical formula derives a novel index (QRF) that highly accurately predicts bladder outflow obstruction, significantly outperforming Qmax. Relatively small cohort size, single center origin, lack of control group and employment of Schafer nomogram in females, were potential limitations. As this index seems to markedly improve the diagnostic ability of uroflow testing, we anticipate that with further clinical evaluation and validation, it might become a valuable complement to urodynamics armamentarium.