In this work analytical Population Balance Equation (PBE) and Computational Fluid Dynamics (CFD) models were developed to predict the steady state size distribution of nucleating, growing, and agglomerating calcium oxalate (CaOx) renal calculi during their transit through the kidney in 1g and microgravity based solely on the renal biochemical profile of the subject as input. The PBE 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 with excellent agreements.
For the PBE renal stone formation simulation studies, 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. Parametric simulations were performed to assess the impact of alterations in renal biochemistry of the astronauts due to microgravity exposure on the risk of critical CaOx renal stone formation during long duration missions and to quantify the efficacy of using citrate and pyrophosphate dietary supplements and increased hydration as possible countermeasures for reducing this risk.
Through comprehensive numerical case studies performed by the PBE model the following assessments were made:
1. The PBE 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 CaOx crystal aggregate size distribution 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 increase in risk level for developing renal stone in microgravity was relatively more significant for a normal person going to space than a stone former. However, numerical predictions also clearly underscore that the stone-former subject has still by far the highest absolute risk of critical stone formation during space travel.
4. For stone-formers both on Earth and in Space depletion of calcium and oxalate is an important factor to be considered. This 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.
6. 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 its average normal urinary levels on Earth through dietary supplements is beneficial but only to a limited extent. However, the model also predicts that any decline in the citrate levels during space travel below its normal urinary values on Earth 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.
7. Pyrophosphate was also found to be an effective direct inhibitor of growth. Results indicate that minimal pyrophosphate concentrations in urine can move the maximum CaOx aggregate 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.
8. Hydration can act as an effective promoter or inhibitor of renal stone development in 1g and microgravity. Our results indicate that dehydration during space travel that may cause astronaut urinary volumes below 1.5 liters/day can easily move a preflight non-stone-former to the population densities and renal stone size ranges resembling the 1-g recurrent stone formers. Augmented hydration levels that produce up to 3 liters/day urinary output were also simulated and numerical results indicate that urinary volumes from 2.5 - 3 liters/day can serve as an excellent and effective countermeasure. Thus based on our results, a ½ liter increase in urine output 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.
In this work, 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 representative of a standard urine biochemistry. 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.
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) or due to nucleation and growth on Randall plaque surfaces or on injured sections of the nephron could not be included in the present “lumped” PBE transport analysis.
In order to consider these important transport effects, a two-phase PBE-CFD Renal Calculi Formation & Transport model was developed by coupling the PBE for nucleating, growing, and agglomerating renal calculi to a CFD model that solves for flow of urine, conservation of species, and transport of renal calculi in the nephron using a Eulerian two-phase mathematical framework.
Parametric simulations were performed using the PBE-CFD model to study steady state stone size and volume fraction distributions in the four main sections of the nephron under weightlessness conditions. These sections are: the tubule (distal, tube of Henle, proximal); the Inner Medullary Collecting Duct (IMCD); the Outer Medullary Collecting Duct (OMCD); and the Duct of Bellini (DoB). The CFD results reiterated that agglomeration has a profound effect on the renal stone size distributions by decreasing the population of smaller stones and increasing the number and sizes of the larger stones in all four segments of the nephron. More importantly, it was found that due to the retarding effect of the wall on the urinary flow, the volume fraction of the CaOx crystals is dramatically increased at the walls of tubule and IMCD segments. Thus for these first two nephron segments, a mixed-suspension mixed-product removal (MSMPR) continuous crystallizer model as adopted by many of the previous theoretical work is not valid.
Our numerical results further show that mixing due to the cascading transition between the nephron segments produces quite uniform volume fraction distributions in the OMCD, and DoB nephron segments. Simulations using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, our results also imply that since the highest stone volume fraction occurs next to the tubule and duct walls, there may be an increased propensity for wall adhesion, for example, on existing Randall Plaque surfaces or injured sections of the nephron, with a greater risk of evolution towards critical sizes. More detailed CFD models that can rigorously capture the urine-crystal-wall interactions are needed to provide a deeper understanding of renal stone formation that leads to a critical retention scenario.