Predicting the risk of kidney stone formation in the nephron by ‘reverse engineering’

Abstract

Although most kidney stones are found in the calyx, they are usually initiated upstream in the nephron by precipitation there of certain incipient mineral phases. The risk of kidney stone formation can thus be indicated by changes in the degree of saturation of these minerals in the nephron fluid. To this end, relevant concentration profiles in the fluid along the nephron have been calculated by starting with specified urine compositions and imposing constraints from the corresponding, much less variable, blood compositions. A model for supersaturation within ten sections of both long and short nephrons has accordingly been developed based on this ‘reverse engineering’ of the necessary substance concentrations coupled with chemical speciation distributions calculated by our Joint Expert Speciation System (JESS). This allows the likelihood of precipitation to be assessed based on Ostwald’s ‘Rule of Stages’. Differences between normal and stone-former profiles have been used to identify sections in the nephron where conditions seem most likely to induce heterogeneous nucleation.

Appendix

A computer program has been developed using the programming language Ada to simulate the ultrafiltration and reabsorption processes in the kidney. A matrix of reabsorption factors has been constructed from published data to quantify what proportion of the original amount of the substances under consideration entering the Bowman’s space via ultrafiltration is reabsorbed [8]. Every substance is associated with a sequence of values representing the reabsorption quantity in each of the ten segments of the nephron. The following function is used to work out the change in amount of substance, y, in the fluid in the lumen using the values in the matrix, R:

$$\begin{aligned} y^i_{s} = y^i_{s-1} - {\frac{R[s,i]}{100}}y^i_0 \quad 1 \le s \le 10, \end{aligned}$$

where $y^i_0$ is the amount of substance i that enters the Bowman’s space via ultrafiltration; $y^i_{s}$ is the amount of substance i at the end of the nephron section under consideration; $y^i_{s-1}$ is the amount of substance i at the end of the previous nephron section; R[s, i] is the percentage of substance i reabsorbed in the nephron section under consideration.

An analogous equation applies to the total volume of the solution which is needed to calculate the concentrations of the substances under consideration.

The calculations given in this paper represent a particular snap shot of current knowledge and it is important to understand that changes will no doubt be made in future to deal with matters such as improved equilibrium constants, changes in the reabsorption factors and other areas where improved information becomes available.

To implement the ‘reverse model’, adjustments are made to the values in the reabsorption matrix, the value of the adjustment applied is calculated from the ratio of concentration in the urine under consideration and the urine concentrations produced using the standard reabsorption values, to alter the final result for the urine values to the specified value.

Tables 3, 4 and 5 show the total concentrations of the substances under consideration along the length of the nephron for the three sets of subjects used in this paper.

A copy of the computer program may be requested by contacting the corresponding author.

Table 3 Long nephron concentrations UK N (mmol/L)

Table 4 Long nephron concentrations UK RSF (mmol/L)

Table 5 Long nephron concentrations KSA RSF (mmol/L)