Use of Artificial Intelligence to Identify New Mechanisms and Approaches to Therapy of Bone Disorders Associated With Chronic Kidney Disease

Chronic kidney disease (CKD) leads to clinically severe bone loss, resulting from the deranged mineral metabolism that accompanies CKD. Each individual patient presents a unique combination of risk factors, pathologies, and complications of bone disease. The complexity of the disorder coupled with our incomplete understanding of the pathophysiology has significantly hampered the ability of nephrologists to prevent fractures, a leading comorbidity of CKD. Much has been learned from animal models; however, we propose in this review that application of multiple techniques of mathematical modeling and artificial intelligence can accelerate our ability to develop relevant and impactful clinical trials and can lead to better understanding of the osteoporosis of CKD. We highlight the foundational work that informed our current model development and discuss the potential applications of our approach combining principles of quantitative systems pharmacology, model predictive control, and reinforcement learning to deliver individualized precision medical therapy of this highly complex disorder.

Development of a quantitative systems pharmacology model of chronic kidney disease: metabolic bone disorder

Chronic kidney disease mineral bone disorder (CKD-MBD) is a virtually universal complication of kidney diseases, starting early in the course of disease and resulting in devastating clinical consequences ranging from bone fragility to accelerated atherosclerosis and early cardiovascular death. Guidelines for therapeutic goals for CKD-MBD have been published, and achievement of these guidelines is associated with improved survival. However, the incomplete understanding of CKD-MBD and the individual variability in the manifestations of CKD-MBD have made it difficult to achieve these guidelines. We hypothesized that the progression of MBD through all stages of CKD, including end-stage kidney disease, could be represented by a quantitative systems pharmacology/systems biology (QSP) model. To address this hypothesis, we constructed a QSP model of CKD-MBD, building on an open-source model of calcium and phosphorus metabolism. Specifically, we estimated and validated the model using data from 5,496 patients with CKD enrolled in the Chronic Renal Insufficiency Cohort study. Our model accurately predicted changes in markers of mineral metabolism related to progressing CKD. We demonstrated that the incorporation of fibroblast growth factor 23 and the soft tissue compartment is essential for accurate modeling of the changes in calcium, phosphorus, intact parathyroid hormone, and calcitriol in CKD-MBD. We conclude that our systems biology model accurately represents CKD-MBD disease progression and can be used as a test bench for improving therapeutic interventions.

A mathematical model of parathyroid gland biology

Altered parathyroid gland biology in patients with chronic kidney disease (CKD) is a major contributor to chronic kidney disease-mineral bone disorder (CKD-MBD). This disorder is associated with an increased risk of bone disorders, vascular calcification, and cardiovascular events. Parathyroid hormone (PTH) secretion is primarily regulated by the ionized calcium concentration as well as the phosphate concentration in the extracellular fluid and vitamin D. The metabolic disturbances in patients with CKD lead to alterations in the parathyroid gland biology. A hallmark of CKD is secondary hyperparathyroidism, characterized by an increased production and release of PTH, reduced expression of calcium-sensing and vitamin D receptors on the surface of parathyroid cells, and hyperplasia and hypertrophy of these cells. These alterations happen on different timescales and influence each other, thereby triggering a cascade of negative and positive feedback loops in a highly complex manner. Due to this complexity, mathematical models are a useful tool to break down the patterns of the multidimensional cascade of processes enabling the detailed study of subsystems. Here, we introduce a comprehensive mathematical model that includes the major adaptive mechanisms governing the production, secretion, and degradation of PTH in patients with CKD on hemodialysis. Combined with models for medications targeting the parathyroid gland, it provides a ready-to-use tool to explore treatment strategies. While the model is of particular interest for use in hemodialysis patients with secondary hyperparathyroidism, it has the potential to be applicable to other clinical scenarios such as primary hyperparathyroidism or hypo- and hypercalcemia.

Bridging adults and paediatrics with secondary hyperparathyroidism receiving haemodialysis: a pharmacokinetic-pharmacodynamic analysis of cinacalcet

AIMS

The aims of this study were to develop a pharmacokinetic (PK) and PK-pharmacodynamic (PK/PD) model of cinacalcet in adults and paediatrics with secondary hyperparathyroidism (SHPT) on dialysis, to test covariates of interest, and to perform simulations to inform dosing in paediatrics with SHPT.

METHODS

Cinacalcet PK, intact parathyroid hormone (iPTH) and corrected calcium (cCa) time courses following multiple daily oral doses (1-300 mg) were modelled using a nonlinear mixed effects modelling approach using data from eight clinical studies. Model-based trial simulations, using adult or paediatric titration schemas, predicted efficacy (iPTH change from baseline and proportion achieving iPTH decrease ≥30%) and safety (cCa change from baseline and proportion achieving cCa ≤8.4 mg/dL) endpoints at 24 weeks.

RESULTS

Cinacalcet PK parameters were described by a two-compartment linear model with delayed first-order absorption-elimination (apparent clearance = 287.74 L h-1 ). Simulations suggested that paediatric starting doses (1, 2.5, 5, 10 and 15 mg) would provide PK exposures less than or similar to a 30 mg adult dose. The titrated dose simulations suggested that the mean (prediction interval) proportion of paediatric and adult subjects achieving ≥30% reduction in iPTH from baseline at Week 24 was 49% (36%, 62%), and 70.1% (62.5%, 77%), respectively. Additionally, the mean (confidence interval) proportion of paediatric and adult subjects achieving cCa ≤8.4 mg dL-1 at Week 24 was 8% (2%, 18%) and 23.6% (17.5%, 30.5%), respectively.

CONCLUSIONS

Model-based simulations showed that the paediatric cinacalcet starting dose (0.2 mg kg-1 ), titrated to effect, would provide the desired PD efficacy (PTH suppression <30%) while minimizing safety concerns (hypocalcaemia).

Population Pharmacokinetic and Pharmacodynamic Modeling of Etelcalcetide in Patients with Chronic Kidney Disease and Secondary Hyperparathyroidism Receiving Hemodialysis

INTRODUCTION

Etelcalcetide is a novel calcimimetic that binds and activates calcium-sensing receptors (CaSRs) for the treatment of secondary hyperparathyroidism (SHPT).

METHODS

To assess titrated dosing regimens, population pharmacokinetic (PK) and PK/pharmacodynamic (PKPD) modeling of etelcalcetide was performed using NONMEM 7.2. In this analysis, plasma etelcalcetide, serum parathyroid hormone (PTH) and calcium (Ca) concentration-time data were collected from five phase I, II, and III clinical trials following single or multiple intravenous doses of etelcalcetide ranging from 2.5 to 60 mg. A semi-mechanistic model was used to describe the relationship between etelcalcetide, PTH, and Ca. This model included the role of PTH in Ca regulation, the feedback of Ca onto PTH production via the CaSR, and the activity of etelcalcetide plasma levels in increasing the sensitivity of the CaSR to Ca via the cooperative binding model. The impact of relevant covariates was evaluated by stepwise forward/backward selection. Model evaluation was based on standard goodness-of-fit plots and prediction-corrected visual predictive checks (pcVPCs). Simulation was conducted to evaluate titrated dosing regimens.

RESULTS AND DISCUSSION

The time courses of etelcalcetide, PTH, and Ca were well-described by the model. The clearance and central volume of distribution (Vc) of etelcalcetide were 0.472 L/h and 49.9 L, respectively, while estimates of the turnover half-lives of PTH and Ca were 0.36 and 23 h, respectively. The extent of interindividual variability in model parameters was low to moderate (6-67%), and no covariates were identified as significant predictors of PK and PD variability. pcVPCs confirmed the predictive ability of the model.

CONCLUSIONS

The current analysis confirms the putative mechanism of action of etelcalcetide as an allosteric activator of CaSR. Simulations showed that dose titration of etelcalcetide, rather than fixed dose, is needed to effectively decrease the PTH level in patient populations.

Pharmacology of bisphosphonates

The biological effects of the bisphosphonates (BPs) as inhibitors of calcification and bone resorption were first described in the late 1960s. In the 50 years that have elapsed since then, the BPs have become the leading drugs for the treatment of skeletal disorders characterized by increased bone resorption, including Paget's disease of bone, bone metastases, multiple myeloma, osteoporosis and several childhood inherited disorders. The discovery and development of the BPs as a major class of drugs for the treatment of bone diseases is a paradigm for the successful journey from "bench to bedside and back again". Several of the leading BPs achieved "blockbuster" status as branded drugs. However, these BPs have now come to the end of their patent life, making them highly affordable. The opportunity for new clinical applications for BPs also exists in other areas of medicine such as ageing, cardiovascular disease and radiation protection. Their use as inexpensive generic medicines is therefore likely to continue for many years to come. Fifty years of research into the pharmacology of bisphosphonates have led to a fairly good understanding about how these drugs work and how they can be used safely in patients with metabolic bone diseases. However, while we seemingly know much about these drugs, a number of key aspects related to BP distribution and action remain incompletely understood. This review summarizes the existing knowledge of the (pre)clinical and translational pharmacology of BPs, and highlights areas in which understanding is lacking.

Pharmacometrics and systems pharmacology for metabolic bone diseases

Mathematical modelling and simulation (M&S) of drug concentrations, pharmacologic effects and the (patho)physiologic systems within which they interact can be powerful tools for the preclinical, translational and clinical development of drugs. Indeed, the Prescription Drug User Fee Act (PDUFA VI), incorporated as part of the FDA Reauthorization Act of 2017 (FDARA), highlights the goal of advancing model-informed drug development (MIDD). MIDD can benefit development across many drug classes, including for metabolic bone diseases such as osteoporosis, cancer-related and numerous rare metabolic bone diseases; conditions characterized by significant morbidity and mortality. A drought looms in terms of the availability of new drugs to better treat these devastating diseases. This review provides an overview of several M&S approaches ranging from simple pharmacokinetic to integrated pharmacometric and systems pharmacology modelling. Examples are included to illustrate the use of these approaches during the development of several drugs for metabolic bone diseases such as bisphosphonates, denosumab, teriparatide and sclerostin inhibitors (romosozumab and blosozumab).

Dynamics of Bone Cell Interactions and Differential Responses to PTH and Antibody-Based Therapies

We propose a mathematical model describing the dynamics of osteoblasts and osteoclasts in bone remodeling. The goal of this work is to develop an integrated modeling framework for bone remodeling and bone cell signaling dynamics that could be used to explore qualitatively combination treatments for osteoporosis in humans. The model has been calibrated using 57 checks from the literature. Specific global optimization methods based on qualitative objectives have been developed to perform the model calibration. We also added pharmacokinetics representations of three drugs to the model, which are teriparatide (PTH(1-34)), denosumab (a RANKL antibody) and romosozumab (a sclerostin antibody), achieving excellent goodness-of-fit of human clinical data. The model reproduces the paradoxical effects of PTH on the bone mass, where continuous administration of PTH results in bone loss but intermittent administration of PTH leads to bone gain, thus proposing an explanation of this phenomenon. We used the model to simulate different categories of osteoporosis. The main attributes of each disease are qualitatively well captured by the model, for example changes in bone turnover in the disease states. We explored dosing regimens for each disease based on the combination of denosumab and romosozumab, identifying adequate ratios and doses of both drugs for subpopulations of patients in function of categories of osteoporosis and the degree of severity of the disease.

A survey of renal impairment pharmacokinetic studies for new oncology drug approvals in the USA from 2010 to early 2015: a focus on development strategies and future directions

The US Food and Drug Administration (FDA) issued a guidance document in 2010 on pharmacokinetic (PK) studies in renal impairment (RI) on the basis of observations that substances such as uremic toxins might result in altered drug metabolism and excretion. No specific recommendations for oncology drugs were included. We surveyed the publicly available FDA review documents of 29 small molecule oncology drugs approved between 2010 and the first quarter of 2015. The objectives were as follows: (i) summarize the impact of RI on PK at the time of the initial new drug application; (ii) identify limitations of the guidance; and (iii) outline an integrated approach to study the impact of RI on these drugs. Our survey indicates that the current FDA guidance does not appear to provide clear strategic or decision pathways for RI studies in terms of small molecule oncology drugs. The FDA review documents indicate an individualized approach to the review because of the complex pharmacologic nature of these drugs and patient populations. Overall, the strategy for carrying out a RI study during clinical development or as a postmarketing study requires integration with the totality of data, including mass balance, absolute bioavailability, drug–drug interaction, hepatic dysfunction, population PK, exposure–response analysis, the therapeutic window for best guidance, and determination of the optimal doses for special oncology populations.

Population Pharmacokinetics and Pharmacodynamics of the Calcimimetic Etelcalcetide in Chronic Kidney Disease and Secondary Hyperparathyroidism Receiving Hemodialysis

Etelcalcetide is a novel calcimimetic in development for the treatment of secondary hyperparathyroidism (SHPT). A population pharmacokinetic/pharmacodynamic (PK/PD) model was developed relating etelcalcetide exposures to markers of efficacy (parathyroid hormone [PTH]) and safety (calcium) using data from three clinical studies. The semimechanistic model was developed that included allosteric activation pharmacology and understanding of calcium homeostasis. The temporal profiles for all biomarkers were well described by the model. The cooperativity constant was 4.94, confirming allosteric activation mechanism. Subjects with more severe disease (higher PTH baseline) were predicted to experience less pronounced reduction in PTH (percentage change from baseline), but more reduction in calcium (Ca; percentage change from baseline). There was no evidence that dose adjustment by any covariate was needed. Model‐based simulations provided quantitative support to several elements of dosing, such as starting dose, monitoring, and titration timing for registration trials.

Multiscale models of compact bone

This work is concerned about multiscale models of compact bone. We focus on the lacuna–canalicular system. The interstitial fluid and the ions in it are regarded as solvent and others are treated as solute. The system has the characteristic of solvation process as well as non-equilibrium dynamics. The differential geometry theory of surfaces is adopted. We use this theory to separate the macroscopic domain of solvent from the microscopic domain of solute. We also use it to couple continuum and discrete descriptions. The energy functionals are constructed and then the variational principle is applied to the energy functionals so as to derive desirable governing equations. We consider both long-range polar interactions and short-range nonpolar interactions. The solution of governing equations leads to the minimization of the total energy.

Application of a Systems Pharmacology-Based Placebo Population Model to Analyze Long-Term Data of Postmenopausal Osteoporosis

Osteoporosis is a progressive bone disease characterized by decreased bone mass resulting in increased fracture risk. The objective of this investigation was to test whether a recently developed disease systems analysis model for osteoporosis could describe disease progression in a placebo-treated population from the Early Postmenopausal Intervention Cohort (EPIC) study. First, we qualified the model using a subset from the placebo arm of the EPIC study of 222 women who had similar demographic characteristics as the 149 women from the placebo arm of the original population. Second, we applied the model to all 470 women. Bone mineral density (BMD) dynamics were changed to an indirect response model to describe lumbar spine and total hip BMD in this second population. This updated disease systems analysis placebo model describes the dynamics of all biomarkers in the corresponding datasets to a very good approximation; a good description of an individual placebo response will be valuable for evaluating treatments for osteoporosis.

FDA Advisory Meeting Clinical Pharmacology Review Utilizes a Quantitative Systems Pharmacology (QSP) Model: A Watershed Moment?

In the evolving discipline of quantitative systems pharmacology (QSP), QSP model (QSPM) applications are expanding. Recently, a QSPM was used by US Food and Drug Administration (FDA) clinical pharmacologists to evaluate the appropriateness of a proposed dosing regimen for a new biologic. This application expands the use-horizon for QSPMs into the regulatory domain. Here we retrace the evolution of the model and suggest a question-based approach to directing model scope, identifying applications, and understanding overall QSPM value.

Issues, challenges, and opportunities in model-based drug development for monoclonal antibodies

Over the last two decades, there has been a simultaneous explosion in the levels of activity and capability in both monoclonal antibody (mAb) drug development and in the use of quantitative pharmacologic models to facilitate drug development. Both of these topics are currently areas of great interest to academia, the pharmaceutical and biotechnology industries, and to regulatory authorities. In this article, we summarize convergence of these two areas and discuss some of the current and historical applications of the use of mathematical-model-based techniques to facilitate the discovery and development of mAb therapeutics. We also consider some of the current issues and limitations in model-based antibody discovery/development and highlight areas of further opportunity.

Predicting nonlinear changes in bone mineral density over time using a multiscale systems pharmacology model

A mathematical model component that extends an existing physiologically based multiscale systems pharmacology model (MSPM) of calcium and bone homeostasis was developed, enabling prediction of nonlinear changes in lumbar spine bone mineral density (LSBMD). Data for denosumab, a monoclonal antibody osteoporosis treatment, dosed at several levels and regimens, was used for fitting the BMD component. Bone marker and LSBMD data extracted from the literature described on/off-treatment effects of denosumab over 48 months [Miller, P.D. et al. Effect of denosumab on bone density and turnover in postmenopausal women with low bone mass after long-term continued, discontinued, and restarting of therapy: a randomized blinded phase 2 clinical trial. Bone 43, 222–229 (2008)]. An indirect model linking bone markers to LSBMD was embedded in the existing MSPM, reasonably predicting nonlinear increases in LSBMD during treatment (24 months); LSBMD declines following discontinuation and increases upon treatment reinstitution. This study demonstrates the utility of MSPM extension to describe a phenomena of interest not originally in a model, and the ability of this updated MSPM to predict nonlinear longitudinal changes in the clinically relevant endpoint, LSBMD, with denosumab treatment.

Integrated pharmacometrics and systems pharmacology model-based analyses to guide GnRH receptor modulator development for management of endometriosis

Endometriosis is a gynecological condition resulting from proliferation of endometrial-like tissue outside the endometrial cavity. Estrogen suppression therapies, mediated through gonadotropin-releasing hormone (GnRH) modulation, decrease endometriotic implants and diminish associated pain albeit at the expense of bone mineral density (BMD) loss. Our goal was to provide model-based guidance for GnRH-modulating clinical programs intended for endometriosis management. This included developing an estrogen suppression target expected to provide symptomatic relief with minimal BMD loss and to evaluate end points and study durations supportive of efficient development decisions. An existing multiscale model of calcium and bone was adapted to include systematic estrogen pharmacologic effects to describe estrogen concentration-related effects on BMD. A logistic regression fit to patient-level data from three clinical GnRH agonist (nafarelin) studies described the relationship of estrogen with endometrial-related pain. Targeting estradiol between 20 and 40 pg/ml was predicted to provide efficacious endometrial pain response while minimizing BMD effects.