A quantitative systems pharmacology model of plasma potassium regulation by the kidney and aldosterone

Maddah, Erfan; Hallow, K. Melissa

doi:10.1007/s10928-022-09815-x

Cited by 10 publications

(9 citation statements)

References 42 publications

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“…The model currently includes limited physiological detail (e.g., GI compartments) and limited detail on the complexity of K + regulation; this could be expanded upon in the future using information from literature based on detailed physiological experiments and data from large trials of drugs that influence K + handling (e.g., aldosterone antagonists), as explored by Stadt et al 18 . and Maddah and Hallow 17 . Such refinement would improve the fidelity of the model in capturing sK + trends at the highest and lowest ends, where underlying regulatory systems are likely not working optimally.…”

Section: Discussionmentioning

confidence: 99%

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

Clegg,

Chu,

Nagard

et al. 2023

CPT Pharmacom & Syst Pharma

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Potassium (K+) is the main intracellular cation in the body. Elevated K+ levels (hyperkalemia) increase the risk of life‐threatening arrhythmias and sudden cardiac death. However, the details of K+ homeostasis and the effects of orally administered K+ binders, such as sodium zirconium cyclosilicate (SZC), on K+ redistribution and excretion in patients remain incompletely understood. We built a fit‐for‐purpose systems pharmacology model to describe K+ homeostasis in hyperkalemic subjects and capture serum K+ (sK+) dynamics in response to acute and chronic administration of SZC. The resulting model describes K+ distribution in the gastrointestinal (GI) tract, blood, and extracellular and intracellular spaces of tissue, renal clearance of K+, and K+–SZC binding and excretion in the GI tract. The model, which was fit to time‐course sK+ data for individual patients from two clinical trials, accounts for bolus delivery of K+ in meals and oral doses of SZC. The virtual population of patients derived from fitting the model to these trials was then modified to predict the SZC dose–response and inform clinical trial design in two new applications: emergency lowering of sK+ in severe hyperkalemia and prevention of hyperkalemia between dialysis sessions in patients with end‐stage chronic kidney disease. In both cases, the model provided novel and useful insight that was borne out by the now completed clinical trials, providing a concrete case study of fit‐for‐purpose, model‐informed drug development after initial approval of a drug.

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Section: Discussionmentioning

confidence: 99%

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

Clegg,

Chu,

Nagard

et al. 2023

CPT Pharmacom & Syst Pharma

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“…Youn et al [33] used two-compartment and three-compartment models to analyze fluxes of K + between the extracellular and intracellular space as well as K + uptake by red blood cells. Maddah and Hallow [34] developed a quantitative systems pharmacology model that captures the effect of aldosterone on K + homeostasis to simulate the effects of spironolactone treatment in patients with hyperaldosteronism.…”

Section: Discussionmentioning

confidence: 99%

A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

Stadt

Leete

Devinyak

2022

Preprint

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Maintaining normal potassium (K+) concentration in the extra- and intracellular fluid is critical for cell function. K+ homeostasis is achieved by ensuring proper distribution between extra- and intracellular fluid compartments and by matching K+ excretion with intake. The Na+-K+-ATPase pump facilitates K+ uptake into the skeletal muscle, where most K+ is stored. Na+-K+-ATPase activity is stimulated by insulin and aldosterone. The kidneys regulate long term K+ regulation by controlling the amount of K+ excreted through urine. Renal handling of K+ is mediated by a number of regulatory mechanisms, including an aldosterone-mediated feedback control, in which high extracellular K+ concentration stimulates aldosterone secretion which enhances urine K+ excretion, and a gastrointestinal feedforward control mechanism, in which dietary K+ intake increases K+ excretion. Recently, a muscle-kidney cross talk signal has been hypothesized, where the K+ concentration in skeletal muscle cells directly affects urine K+ excretion, without changes in extracellular K+ concentration. To understand how these mechanisms coordinate under different K+ challenges, we have developed a compartmental model of whole-body K+ regulation. The model represents the intra- and extracellular fluid compartments in a human (male) as well as a detailed kidney compartment. We included (i) the gastrointestinal feedforward control mechanism, (ii) the effect of insulin, and (iii) aldosterone on Na+-K+-ATPase K+ uptake, and (iv) aldosterone stimulation of renal K+ secretion. We used this model to investigate the impact of regulatory mechanisms on K+ homeostasis. Model predictions showed how the regulatory mechanisms synthesize to ensure that the extra- and intracellular fluid K+ concentrations remain in normal range in times of K+ loading and fasting. Additionally, we predict that without the hypothesized muscle-kidney cross talk signal, the model was unable to predict a return to normal extracellular K+ concentration after a period of high K+ loading or depletion.

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“…To model [ALD], denoted by C al , we use the approach developed by Maddah & Hallow [11]: where m K − aldo is a fitting parameter and is the total extracellular fluid [K + ] given by and is the baseline extracellular [K + ]. We capture the effect of [ALD] on Na + -K + -ATPase abundance by the scaling factor ρ al (see Eq.…”

Section: Methodsmentioning

confidence: 99%

A mathematical model of whole-body potassium regulation: Global parameter sensitivity analysis^*

Stadt,

Layton

2023

Preprint

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Potassium (K+) is an essential electrolyte that is tightly regulated by various complex physiological mechanisms. In this study, we analyze a mathematical model of whole-body K+regulation to investigate the sensitivity of different model outcomes to parameter values. We used the Morris method, a global sensitivity analysis technique, to evaluate the impact of the parameters on both steady state results and transient simulations during a single-meal. Our results shows that the most influential parameters and processes depend on what you are measuring. Specifically, steady state results relied primarily on parameters that were involved in kidney function, while transient results relied on hormonal feedback mechanisms. This study shows that our mathematical model of whole-body potassium regulation captures known physiological function of potassium regulation despite a large number of uncertain parameters.MSC codes68Q25, 68R10, 68U05

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A quantitative systems pharmacology model of plasma potassium regulation by the kidney and aldosterone

Cited by 10 publications

References 42 publications

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

A mathematical model of whole-body potassium regulation: Global parameter sensitivity analysis^*

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A quantitative systems pharmacology model of plasma potassium regulation by the kidney and aldosterone

Cited by 10 publications

References 42 publications

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

A mathematical model of whole-body potassium regulation: Global parameter sensitivity analysis*

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A mathematical model of whole-body potassium regulation: Global parameter sensitivity analysis^*