Fig. 4: Time to detection of bacteriuria.

The detection time is defined as the time until the bacterial abundance in the urine exceeds a detection threshold of 10⁷ (light green), 10⁵ (mid green), or 10³ (dark green) cells/mL, mimicking tests of different sensitivity. Also plotted(pink dashed) is the theoretically predicted time for the FKPP wave to travel the length of the catheter \(L/2\sqrt{{r}_{S}{D}_{S}}\). a Time to detection of bacteriuria for different values of the urine production rate. For the high-sensitivity test (threshold 10³mL⁻¹), bacteriuria is eventually detected, no matter how high the urine production rate, because even in the washout regime, the presence of the catheter ensures that there are some bacteria in the urine. In contrast, low sensitivity tests do not detect bacteriuria when the model is run for high urine production rates, because the bacterial abundance in the urine is very low in the no bacteriuria regime (Fig. 3a). For CAUTI diagnosis, clinical guidelines⁵ require both clinical symptoms and bacterial counts > 10³ colony forming units (CFU) mL⁻¹ while a diagnosis of significant bacteriuria requires a higher bacterial count > 10⁵ CFU mL⁻¹. b Time to detection of bacteriuria for different values of the urethral length. The time for bacteriuria to develop increases linearly with the urethral length. The vertical axis scale is the same as in (a). Note that in this case, there is no significant difference between different testing sensitivities, as the urethral length dominates the timescale. All model parameters are as given in Table 1 (for comparison with Fig. 3, note that the urine production rate is 1 mL/min).