In FY 2014-2015 effort, an analytical Population Balance Equation model was developed to predict the steady state size distribution of nucleating, growing, and agglomerating renal calculi during their transit through the kidney in 1g and microgravity based solely on using the renal biochemical profile of the subject as input.
This deterministic model for renal stone formation was developed using the rigorous frame work of the Population Balance Equation (PBE). The model is amenable to analytical solutions based on two simplifying but acceptable assumptions. Therefore, it can provide fast solutions to accommodate the numerous Monte Carlo generated parametric simulations that are required in future by the Probabilistic Risk Assessment (PRA) analyses.
The model was verified through comparison with the published results provided by several MSRPP crystallization experiments including an in-vitro calcium oxalate experiment related to renal stone formation. Four subjects were considered based on their published 1g and microgravity biochemical profiles, namely--1g normal, microgravity astronaut, and 1g recurrent and microgravity stone-formers.
The research was carried out in two phases. In Phase I, simulations were performed to assess the impact of biochemical alterations induced by Space travel on development of renal stones and risk of a critical renal formation for the astronauts. In Phase II, numerical simulations were performed to examine and assess the efficacy of several dietary countermeasures such as use of citrates and increased hydration in reducing the risk of critical renal stone development for the astronauts.
From the results of the comprehensive Phase I case studies involving the four above-mentioned subjects the following assessments were made:
1. The model was successful in clearly distinguishing between a 1g normal and a 1g recurrent stone-former based on their published 24 hr urine biochemical profiles.
2. The predicted stone size distribution and maximum stone size for a microgravity astronaut were closer to those of a recurrent stone-former on Earth than a normal risk free subject in 1g underscoring the detrimental effect of space altered renal biochemistries.
3. Due to microgravity renal biochemical alterations, the relative change in risk level for developing renal stone in microgravity was more significant for a normal person going to space than a stone former -- an important issue to consider for astronaut screening.
4. For stone-formers both on Earth and in Space depletion of calcium and oxalate is an important factor to be considered and points to the shortcoming of the relative supersaturation levels determined by the 24 hr urine measurements performed distal to the growth process as a definitive measure of the risk.
5. Agglomeration was found to be a crucial mechanism for stone size enhancement both in 1g and microgravity.
In the Phase II research, the renal stone formation model was used to assess the impact of citrate and pyrophosphate dietary supplements and increased hydration as countermeasures for reducing the risk of critical renal stone development for the astronauts during their future long-duration missions. The results of the comparative Phase II numerical case studies indicate the following assessments for the microgravity astronaut subject:
1. Citrate was found to be an effective inhibitor of both growth and agglomeration. Our numerical predictions indicate that urine, due to its normal citrate content, is already, to a large extent, inhibited against growth and agglomeration of CaOx crystals. Any additional increase in citrate beyond the average normal 1g urinary levels through dietary supplements is beneficial but only to a limited extent. However, the model also predicts that any decline in the citrate levels below the normal 1g urinary values during space travel could easily move the microgravity astronaut subject into the stone-forming risk category. So the current results strongly recommend for use of citrate as a dietary countermeasure to prevent the adverse effect of any space-induced hypocitraturia during the future missions.
2. Pyrophosphate was also found to be an effective direct inhibitor of growth. Results indicate that minimal pyrophosphate concentrations in urine can move the maximum stone size predicted for the microgravity astronaut from a near critical value of 140 microns to a definitively safe range below 10 microns. These promising predictions suggest that more comprehensive experimental assessment of use of pyrophosphate and other similar inhibitors such as phytic acid, and osteopontin as dietary countermeasures for the space program are warranted.
3. Hydration can act as an effective promoter or inhibitor of renal stone development in 1g and microgravity. Our results indicate that dehydration below the level of 1.5 liters/day urinary output during space travel can easily move a preflight non-stone-former to the stone population densities and renal stone size ranges resembling 1-g recurrent stone formers. Augmented hydration up to 3 liters/day urinary output levels were also simulated and numerical results indicate that hydration levels from 2.5-3 liters/day can serve as excellent and effective countermeasure. Thus based on our results, a ½ liter increase in hydration level from the current guideline level of 2.0 liters/day to 2.5 liters/day is recommended because it is predicted that it will provide considerable inhibitive benefits, moving the astronaut well into a risk free range.
There are two main factors that will determine whether a critical stone incident will occur or not. First is the renal biochemistry that dictates the rate of stone size enhancement due to growth and agglomeration and the second is the residence time of renal calculi that is determined by their transport through the nephron by the urinary flow. The lag that might occur due to nonslip boundary condition (in both 1g and microgravity) or due to gravity effects in upward flowing tubules (only in 1g) could not be included in the present “lumped” transport analysis. In order to consider these important transport effects the PBE renal stone model needs to be coupled to a two-phase CFD model for stone and urine transport through the nephron. While a coupled CFD-PBE analysis was outside the scope of the analytical model it is part of our ongoing parallel CFD renal stone model development effort.
Finally, we only investigated the effect of variation in the direct inhibitive action by citrate and pyrophosphate. For the citrate case there is also an indirect inhibition due to speciation. This contribution was included in our model only at a fixed level as for an average urine. In order to consider the impact of indirect inhibition as a function of citrate concentration, the use of speciation codes such as JESS or Equil2 is required to account for the bounding of calcium ions with citrate in forming soluble complexes that lowers the supersaturation levels of CaOx. Coupling of JESS computations with the current PBE renal stone model will be undertaken as part of our ongoing work in this area with the goal of providing a more comprehensive assessment of both direct and indirect inhibition potentials of the citrate and hydration countermeasures in near future.
Two papers have been submitted to American Journal of Physiology - Renal Physiology:
Kassemi, M. and Thompson, P. "Prediction of Renal Stone Size Distributions in Microgravity Using a PBE Analytical Model: 1. Effect of Space-Induced Biochemical Alterations " Submitted AJP-Renal, Sep-2015
Kassemi, M. and Thompson, D. "Prediction of Renal Stone Size Distributions in Microgravity Using a PBE Analytical Model: 2. Effect Dietary Countermeasures" Submitted AJP-Renal, Sep-2015