WO2010148411A1 - Procédé et appareil pour modélisation informatique de l'hypertension - Google Patents

Procédé et appareil pour modélisation informatique de l'hypertension Download PDF

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WO2010148411A1
WO2010148411A1 PCT/US2010/039388 US2010039388W WO2010148411A1 WO 2010148411 A1 WO2010148411 A1 WO 2010148411A1 US 2010039388 W US2010039388 W US 2010039388W WO 2010148411 A1 WO2010148411 A1 WO 2010148411A1
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ang
raas
model
computer
representation
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PCT/US2010/039388
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Jennifer Beh
Hector De Leon
Stuart Friedman
Manoj Rodrigo
Arthur Lo
Serguei Ermako
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Entelos, Inc.
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H10/00—ICT specially adapted for the handling or processing of patient-related medical or healthcare data
    • G16H10/20—ICT specially adapted for the handling or processing of patient-related medical or healthcare data for electronic clinical trials or questionnaires

Definitions

  • the present invention relates generally to the field of computer simulation of hypertension and its associated disease risks, particularly, loss of kidney function, heart failure and stroke.
  • Hypertension the medical condition of elevated blood pressure
  • NHANES National Health and Nutrition Examination Survey
  • Ml myocardial infarction
  • PVD peripheral vascular disease
  • HF renal failure and heart failure
  • Other risk factors contributing to the complex etiology of hypertension include age, weight, race/ethnicity, genetic predisposition, diabetes and dietary sodium intake.
  • vasoconstrictors e.g., Angiotensin Il (Ang II) and endothelin
  • vasoconstrictors e.g., Angiotensin Il (Ang II) and endothelin
  • vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI2).
  • a variety of endogenous vasodilators including Ang (1-7), calcitonin gene-related peptide (CGRP), substance P and adrenomedullin, to name a few, have all been implicated in the development and maintenance of high blood pressure.
  • the hypertensinogenic mechanisms mediated by an increased SNS activity involve perturbed baroreflex and chemoreflex pathways at both central and peripheral levels. Indirect clinical evidence of the contribution of the sympathetic nervous system activity to hypertension is the lowering blood pressure effect of centrally acting sympatholytic agents (alpha-adrenergic antagonists).
  • Peripheral resistance is elevated in hypertension due to structural alterations. Remodeling of small arteries and arterioles contributes to the development and maintenance of high blood pressure and the ensuing organ damage. Elevated resistance in these arterioles is caused by an increased wall-to-lumen ratio. Additional pathophysiological mechanisms have been proposed to explain the increased resistance observed in hypertensive subjects including hyperuricemia, arterial stiffness, increased oxidative stress, vascular inflammation and endothelial dysfunction.
  • the Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance (Korner and Angus (1997) Vascular remodeling. Hypertension 29:1065-1066; and Korner, et al. (1992) Are cardiac and vascular "amplifiers" both necessary for the development of hypertension? Kidney lnt Suppl 37:S38- S44).
  • the model of hypertension described herein allows one to investigate different hypotheses about the role of angiotensin Il (Ang II) in the physiological function of the kidney, in addition to its recognized role in blood pressure regulation.
  • hypertensive patients receiving therapies that affect renin-angiotensin aldosterone system (RAAS) may experience delay in onset of glomerulosclerosis and interstitial tubulofibrosis.
  • RAAS renin-angiotensin aldosterone system
  • the model is a powerful tool for quickly testing multiple hypotheses about the physiology that can help answer a wide range of drug development questions.
  • it can be used to predict the expected changes in blood pressure for specific therapies in clinical trials, or to identify patient types that are most likely to benefit from anti-hypertensive therapies based on specific characteristics or biomarkers (and thus enrich a clinical trial). It can be used to test mechanistic hypotheses that are infeasible or impractical to test clinically, or to test the impact of known or hypothesized drug characteristics (e.g. localization in the kidney, ability to access specific receptors) on end-organ protection, possibly providing support for drug differentiation claims.
  • drug characteristics e.g. localization in the kidney, ability to access specific receptors
  • the current disclosure provides the first model to integrate systemic RAAS, renal RAAS, renal function and blood pressure regulation into a single system.
  • the present model can be used to confidently test hypotheses underlying the effects of different diseases on renal disease progression.
  • the relative contributions of glucose, MAP and Ang Il on disease progression in the model are realistic assumptions based on clinical measurements, published data and phenomenological observations.
  • One aspect of the invention provides computer models of hypertension comprising a) a RAAS pathway module; b) a renal function module; and c) a blood pressure regulation module.
  • the RAAS pathway module comprises a representation of RAAS in systemic circulation, and a representation of RAAS in the kidney.
  • the RAAS pathway module can also comprise a representation of RAAS in heart tissue.
  • the renal function module can comprise a representation of glomerular filtration rate and/or a representation of renal sodium regulation.
  • the renal function module can additional include a representation of disease effects.
  • the blood pressure regulation module comprises a representation of cardiac output and a representation of vascular resistance.
  • Another aspect of the invention provides systems for simulating hypertension comprising: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of hypertension with the data to generate a set of outputs describing the result of the simulation of hypertension; and c) a computer-executable report generator capable of reporting the set of outputs.
  • the computer model comprises i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module.
  • the computer-executable data editor further is capable of accepting a set of parameters describing a virtual patient.
  • the computer- executable integrator further is capable of executing the computer model with the set of parameters describing the subject.
  • the computer-executable data editor further is capable of accepting a virtual protocol and the computer-executable integrator is capable of executing the computer model with the virtual protocol.
  • Yet another aspect of the invention provides systems comprising: a) a processor including computer-readable instructions stored thereon that, upon execution by a processor, cause the processor to simulate atherosclerosis; b) a first user terminal, the first user terminal operable to receive a user input specifying one or more parameters associated with one or more mathematical representations defined by the computer readable instructions; and c) a second user terminal, the second user terminal operable to provide the set of outputs to a second user.
  • the computer readable instructions comprise: i) a RAAS pathway module comprising a mathematical representation of a plurality of biological processes associated with RAAS, wherein the plurality of biological processes comprises RAAS in systemic circulation, RAAS in kidney, and optionally, RAAS in cardiac tissue; ii) a renal function module comprising a mathematical representation of a plurality of biological processes associated with renal function, wherein the plurality of biological processes comprises glomerular filtration rate and albuminuria; iii) a blood pressure regulation module comprising a mathematical representation of a plurality of biological processes associated with blood pressure regulation, wherein the plurality of biological processes comprises cardiac output and vascular resistance; iv) defining a set of mathematical relationships between the representations of biological processes associated with RAAS, renal function and blood pressure regulation; and v) applying a virtual protocol to the set of mathematical relationships to generate a set of outputs.
  • the first user may be the same as or different than the second user.
  • the model of hypertension can be a tool for investigating the effects of a variety of antihypertensive therapies on lower MAP and the progressive loss of renal function.
  • the limited human data on renal enzyme rates, peptide concentrations and the biology underlying the longitudinal progression of disease was a challenge in constructing the model.
  • Development of the model clearly relies on multiple assumptions of the underlying physiology, but these assumptions have been constrained by both data in the literature and clinical observations of renal function.
  • Figure 1 provides a Summary Diagram of the computer model of hypertension.
  • Figure 2 provides an Effect Diagram of the RAAS pathway in systemic circulation.
  • Figure 3 provides an Effect Diagram of the RAAS pathway module in kidney, particularly the glomerulus.
  • Figure 4 provides an Effect Diagram of the RAAS pathway module in kidney, particularly in tubular tissue.
  • Figure 5 provides an Effect Diagram of the RAAS pathway in cardiac (heart) tissue.
  • Figure 6 provides an Effect Diagram of disease representation and progression in the renal function module.
  • Figure 7 provides an Effect Diagram of albumin and creatinine calculations in the renal function module.
  • Figure 8 provides an Effect Diagram of systemic blood circulation, baroreceptor activity, and ADH secretion in the blood pressure regulation module.
  • Figure 9 provides an Effect Diagram of glomerular filtration, sodium filtration, water handling and renal hemodynamics in the blood pressure regulation module.
  • Figure 10 provides an Effect Diagram of calculations relating to RAAS and non- RAAS therapies.
  • Figure 11 provides an Effect Diagram of calculations relating to clinical outputs.
  • Figure 12 provides an Effect Diagram of additional characteristics and conversions for the model.
  • Figure 13 illustrates the effect of various non-RAAS therapies on mean arterial pressure.
  • NT normotensive VP
  • HT-1 hypertensive VP with increased preglomerular resistance
  • HT-2 hypertensive VP with nephropathy
  • HT-3 hypertensive patient with altered Na+ reabsorption
  • HT-4 hypertensive patient with increased TPR.
  • Figure 14 illustrates the effect of different RAAS therapies on mean arterial pressure for normotensive and hypertensive patients. Patient phenotypes as described in Figure 14.
  • the invention encompasses novel computer models of hypertension and systems for predicting development and progression of hypertension and associated risk for developing diseases, such as heart failure, stroke and kidney disease.
  • the computer model of hypertension comprises a RAAS pathway module, a renal function module, and a blood pressure regulation module.
  • a "biological system” can include, for example, a collection of cells such as a cell culture, an organ, a tissue, a multi-cellular organism such as an individual human patient, a subset of cells of a multi-cellular organism, or a population of multi-cellular organisms such as a group of human patients or the general human population as a whole.
  • a biological system can also include, for example, a multi-tissue system such as the nervous system, immune system, or an organ, such as a kidney.
  • biological component refers to a portion of a biological system.
  • a biological component that is part of a biological system can include, for example, an extracellular constituent, a cellular constituent, an intra-cellular constituent, or a combination of them.
  • suitable biological components include, but are not limited to, metabolites, DNA, RNA, proteins, surface and intracellular receptors, enzymes, hormones, cells, organs, tissues, portions of cells, tissues, or organs, subcellular organelles, chemically reactive molecules like H + , superoxides, ATP, as well as combinations or aggregate representations of these types of biological variables.
  • biological components can include therapeutic agents such as an ACE inhibitor or diuretic.
  • biological process is used herein to mean an interaction or series of interactions between biological components.
  • suitable biological processes include, but are not limited to, activation, apoptosis or recruitment of certain cells (such as macrophages), inflammation, cytokine production, and the like.
  • biological process can also include a process comprising one or more therapeutic agents, for example an ACE inhibitor or diuretic.
  • Each biological variable of the biological process can be influenced, for example, by at least one other biological variable in the biological process by some biological mechanism, which need not be specified or even understood.
  • parameter is used herein to mean a value that characterizes the interaction between two or more biological components.
  • parameters include affinity constants, K m , K 0 , /c cat , half life, or net flux of water, sodium or proteins.
  • variable refers to a value that characterizes a biological component.
  • variables include protein concentrations, such as circulating Ang I or plasma renin concentration, physical measures, such as vascular capacity or extracellular fluid volume.
  • phenotype is used herein to mean the result of the occurrence of a series of biological processes. As the biological processes change relative to each other, the phenotype also undergoes changes.
  • One measurement of a phenotype is the level of activity of variables, parameters, and/or biological processes at a specified time and under specified experimental or environmental conditions.
  • a phenotype can include, for example, the state of an individual cell, an organ, a tissue, and/or a multi-cellular organism. Organisms useful in the methods and models disclosed herein include animals. The term "animal" as used herein includes mammals, such as humans. A phenotype can also include, but is not limited to, behavior of the system as a whole, e.g. mean arterial pressure. The conditions defined by a phenotype can be imposed experimentally, or can be conditions present in a patient type. For example a normal phenotype can include a certain amount of circulating Ang Il and sodium and a certain mean arterial pressure. In another example, a disease phenotype can include increased sympathetic nervous activity, increased preglomerular resistance.
  • the phenotype can include the amount of sodium absorption by a nephron or diabetic nephropathy.
  • simulation is used herein to mean the numerical or analytical integration of a mathematical model.
  • biological characteristic is used herein to refer to a trait, quality, or property of a particular phenotype of a biological system.
  • biological characteristics of the biological systems related to hypertension include clinical signs and diagnostic criteria associated with blood pressure and kidney function.
  • the biological characteristics of a biological system can be measurements of biological variables, parameters, and/or processes. Suitable examples of biological characteristics associated with RAAS include, but are not limited to, measurements of glomerular filtration rates (GFR), mean arterial pressure (MAP) and concentration of certain circulating proteins.
  • GFR glomerular filtration rates
  • MAP mean arterial pressure
  • computer-readable medium is used herein to include any medium which is capable of storing or encoding a sequence of instructions for performing the methods described herein and can include, but not limited to, optical and/or magnetic storage devices and/or disks.
  • the present invention provides a mathematical model of hypertension as part of an integrated in s/V/co/experimental approach to the assessment of cardiovascular risk, particularly of heart failure or stroke.
  • the exemplified computer model of hypertension is a large-scale nonlinear ordinary differential equation-based representation of the key biological mechanisms involved in the RAAS pathway, kidney function and blood pressure regulation.
  • a computer model can be designed to model one or more biological processes or functions.
  • the computer model can be built using a "top-down" approach that begins by defining a general set of behaviors indicative of a biological condition, e.g. blood pressure.
  • the behaviors are then used as constraints on the system and a set of nested subsystems are developed to define the next level of underlying detail. For example, given a behavior such mean arterial pressure, the specific mechanisms inducing the behavior can each be modeled in turn, yielding a set of subsystems, which can themselves be deconstructed and modeled in detail.
  • the control and context of these subsystems is, therefore, already defined by the behaviors that characterize the dynamics of the system as a whole.
  • the deconstruction process continues modeling more and more biology, from the top down, until there is enough detail to replicate a given biological behavior.
  • the model is capable of modeling biological processes that can be manipulated by a drug or other therapeutic agent.
  • the methods used to develop computer models of hypertension typically begin by identifying one or more biological processes associated with the RAAS pathway in specific tissues (such as systemic circulation, kidney tissue and/or cardiac tissue), one or more biological processes associated with kidney function and one or more biological processes associated with blood pressure regulation. The identification of these biological processes can be informed by data relating to a metabolic, hormonal or organ system or any portion thereof.
  • the method can also comprise the step of identifying one or biological processes associated with stability of heart tissue and cardiovascular risk, particularly with myocardial tissue damage.
  • the method next comprises the step of mathematically representing each identified biological process.
  • FIG. 1 provides an overview of the modules that can be utilized in designing a computer model of hypertension.
  • identifying a biological process associated with the RAAS pathway comprises identifying one or more biological processes related the RAAS pathway in systemic circulation, identifying one or more biological processes associated with the RAAS pathway in the kidney, and optionally identifying one or more biological processes associated with the RAAS pathway in heart tissue.
  • the RAAS pathway in kidney can be separately represented by glomerular RAAS and tubular RAAS.
  • the biological processes related to the RAAS pathway can comprise one or more of angiotensinogen production, processing of angiotensinogen to Ang I, the action of chymase or ACE to generate Ang II, the production of Ang (1-7), inactivation of Ang Il and binding of AT-1 or AT-2 to Ang Il (see Fig. 2-5).
  • the representation of systemic RAAS pathway in a preferred embodiment, represents the feedback regulation of prorenin synthesis and processing and the equilibrium between prorenin and renin.
  • the biological processes related to the glomerular RAAS pathway comprise Ang I influx and efflux in the kidney, the interaction between changes of Ang I and/or Ang Il in the kidney on blood volume, or the interaction between blood volume on Ang I and Ang Il synthesis and degradation in the kidney (see Fig. 3).
  • identifying a biological process associated with renal function comprise identifying a biological process related to disease progression (see, e.g. Fig. 6) or a biological process related to albumin/creatinine processing (see, e.g. Fig. 7).
  • the biological processes related to disease progression can include, but are not limited to blood pressure effect on filtration, plasma glucose effect on K f and filtration, glomerular Ang Il effect on K f and filtration, glomerular pressure effects on nephron loss and the sieving membrane, the rate of disease damage to sieving, rate of sieving membrane repair, reversible and/or permanent damage to the sieving membrane, Ang Il effect on tubular fibrosis, and excess albumin reabsorption and the effect on tubular fibrosis.
  • the biological processes related to albumin/creatinine processing can relate to a single glomerulus and/or the whole kidney.
  • These processes can include, but are not limited to, SNGFR, glomerular albumin sieving coefficient, glomerular filtrate albumin concentration, reabsorption capacity and fraction, tubular fibrosis level, fibrosis effect on albumin reabsorption, fraction of functional nephrons, albumin excretion rate, creatinine clearance rate, creatinine synthesis rate, serum creatinine concentration, and age effect on GFR.
  • identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to ADH secretion, peripheral resistance, cardiac output, extracellular fluid volume and/or vascular capacity (see, e.g. Fig. 8).
  • identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to water filtration, renal hemodynamics and/or sodium filtration (see, e.g. Fig. 9).
  • the biological processes related to water filtration can include, but are not limited to, urine flow rate, the effect of aldosterone concentration and/or ADH concentration on tubular water reabsorption rate.
  • the biological processes related to sodium filtration can include, but are not limited to, total sodium amount, extracellular fluid volume, filtered sodium load, proximal tubule and LoH reabsorption, macular densa sodium flows, distal sodium reabsorption, distal tubule sodium outflow, macula densa signal accumulation, and sodium excretion via urine.
  • the biological processes related to renal hemodynamics can include, efferent arteriole resistance, afferent arteriole resistance, renal blood flow, renal vascular resistance, renal sympathetic nerve activity, tubule-glomerular feedback effect and glomerular pressure autoregulation
  • each biological process is mathematically represented.
  • the computer model can represent a first biological process using a first mathematical relation and a second biological process using a second mathematical relation.
  • a mathematical relation typically includes one or more variables, the behavior (e.g., time evolution) of which can be simulated by the computer model.
  • mathematical relations of the computer model can define interactions among variables describing levels or activities of various biological components of the biological system as well as levels or activities of combinations or aggregate representations of the various biological components.
  • variables can represent various stimuli that can be applied to the physiological system.
  • the mathematical model(s) of the computer-executable software code represents the dynamic biological processes related to RAAS pathway including kidney function and blood pressure.
  • the form of the mathematical equations employed may include, for example, partial differential equations, stochastic differential equations, differential algebraic equations, difference equations, cellular automata, coupled maps, equations of networks of Boolean or fuzzy logical networks, etc.
  • the parameters are used to represent intrinsic characteristics (e.g., genetic factors) as well as external characteristics (e.g., environmental factors) for a biological system.
  • the phenotype can be mathematically defined by the values of x and p at a given time. Once a phenotype of the model is mathematically specified, numerical integration of the above equation using a computer determines, for example, the time evolution of the biological variables x ⁇ t) and hence the evolution of the phenotype over time.
  • the methods further can comprise methods for validating the computer models described herein.
  • the methods can include generating a simulated biological characteristic associated with development or progression of hypertension, and comparing the simulated biological characteristic with a corresponding reference biological characteristic measured in vivo. The result of this comparison in combination with known dynamic constraints may confirm some part of the model, or may point the user to a change of a mathematical relationship within the model, which improves the overall fidelity of the model.
  • Methods for validating the various models described herein are taught in U.S. Patent Publication 2002-0193979, entitled “Apparatus And Method For Validating A Computer Model," and in U.S. Patent No. 6,862,561 , entitled “Method and Apparatus for Computer Modeling a Joint.”
  • the computer model hypertension provides predictive power to rapidly assess, e.g., the efficacy of novel therapeutics prior to investment in large-scale clinical trials.
  • the model contains three modules: an RAAS pathway module, a renal function module and a blood pressure regulation module.
  • the model can be used to establish a population of virtual patients (representing a variety of clinical phenotypes) to rapidly assess the effects of modulating highly-sensitive target pathways on key clinical endpoints.
  • researchers can assess the efficacy of novel therapeutics, and identify biomarker patterns for predicting long-term clinical efficacy.
  • the goal of a model is to speed up the development process along the drug development pipeline.
  • Novel therapies can be prioritized based on efficacy early in the drug development process, with multiple dosing regimens and protocols tested and results returned prior to recruiting the first patient in a clinical trial.
  • Combination therapies can also be evaluated in the model to look for potential non-additive effects, and to identify the most potent approach in lowering blood pressure in patients with multiple disease etiologies.
  • a set of biomarkers could be determined that can identify the best responders to different therapeutic approaches for treating hypertension.
  • the model is to provide a versatile tool for pharmaceutical research and development to optimize current approaches to drug development, and to provide new insight into the physiology to reduce the time to bring an effective novel therapy to the market.
  • Hypertension is postulated to result from numerous pathophysiological mechanisms including increased peripheral resistance, increased sympathetic nervous system activity, overproduction of sodium-retaining factors and vasoconstrictors (e.g., Ang Il and endothelin), increased sodium reabsorption by the kidneys, deficiencies of vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI 2 ), or from an imbalance in the regulation of glomerular pressure - all of which are difficult to isolate as the cause of hypertension.
  • vasoconstrictors e.g., Ang Il and endothelin
  • vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI 2 )
  • ANP atrial natriuretic peptide
  • NO nitric oxide
  • PKI 2 prostacyclin
  • Ang Il has been the focus of intensive research aimed at elucidating its role in the control of blood pressure, extracellular fluid and electrolyte homeostasis.
  • Ang Il is a peptide with potent vasoconstricting effects. It is part of the RAAS pathway, a cascade of bioactive peptides and regulatory enzymes.
  • the classical systemic RAAS pathway has been described to start with the synthesis and release of angiotensinogen (AGT) into the systemic circulation by the liver.
  • AGT angiotensinogen
  • Renin a proteolytic enzyme synthesized by the juxtaglomerular cells in the kidney, cleaves AGT to form the decapeptide angiotensin I (Ang I).
  • Angiotensin-converting enzyme cleaves Ang I to form Ang II, which is the octapeptide hormone that regulates blood pressure by the modulation of sodium reabsorption in the kidney and by effecting central and peripheral nervous system activity to increase cardiac output and systemic vascular resistance.
  • RAAS-modulating therapies directly manipulate this pathway to alter the levels of Ang Il in the systemic circulation to reduce blood pressure.
  • Three classes of RAAS- modulating pharmacological therapies are currently available on the market.
  • Direct renin inhibitors (DRIs) target renin activity; ACE inhibitors block the conversion from Ang I to Ang II; angiotensin-receptor blockers (ARBs) prevent the binding of Ang Il to the Angiotensin 11-1 receptors (AT1 ). All three reduce the systemic activity of Ang II, which leads to vasodilation, decreased renal sodium reabsorption and reduced secretion of vasopressin (from the brain) and aldosterone (from the adrenal cortex).
  • Figure 10 illustrates various modes of representing therapeutic interventions in the present computer model of hypertension.
  • the model can account for ACE inhibitor effect on systemic and/or renal chymase activity, on systemic and/or glomerular ACE activity, and on Ang(1-7) clearance.
  • the model can account for direct renin inhibitor effects on plasma and glomerular renin activity and the resulting glomerular Ang I production, peritubular ang I synetheis and tubular tissue synthesis of Ang I.
  • the model can account for angiotensin receptor blockers on AT1 receptor binding, renal At1 receptor binding, Ang Il clearance and degradation rate, and Ang III clearance and degradation rate.
  • the computer model accounts for diuretic effects on distal tubule sodium reabsorption, proximal tubule and LoH sodium reabsorption and macula densa signaling.
  • the computer model accounts for the effect of calcium channel blockers on efferent arteriole resistance, preglomerular arteriole resistance and systemic arterial resistance.
  • the computer model accounts for beta blocker effects on renal sympathetic nerve activity.
  • the computer model described herein represents biological processes at multiple levels and then evaluates the effect of the biological processes on biological processes across all levels.
  • the computer model provides a multi-variable view of a biological system.
  • the computer model also, preferably, provides cross-disciplinary observations through synthesis of information from two or more disciplines into a single computer model or through linking a plurality of computer models that represent different disciplines.
  • An exemplary computer model reflects a particular biological system, e.g., the vascular system, and anatomical factors relevant to issues to be explored by the computer model.
  • the level of detail incorporated into the model is often dictated by a particular intended use of the computer model.
  • biological components being evaluated often operate at a subcellular level; therefore, the subcellular level can occupy the lowest level of detail represented in the model.
  • the subcellular level includes, for example, biological components such as DNA, proteins, peptides therapeutic agents, and subcellular organelles.
  • the model can be evaluated at the multicellular level or even at the level of a whole organism. Because an individual biological system, e.g.
  • a single human is a common entity of interest with respect to the ultimate effect of the biological components, the individual biological system (e.g., represented in the form of clinical outcomes) is the highest level represented in the system.
  • Chemical and therapeutic interventions are introduced into the model through changes in parameters at lower levels, with clinical outcomes being changed as a result of those lower level changes, as opposed to representing effects by directly changing the clinical outcome variables.
  • the model represents evolving dynamics of cell populations, rather than the sequence of events for a single cell.
  • This higher level of abstraction can show, for example, major physiological subsystems and their interconnections, but need not report certain detailed elements of the computer model - at least not without the user explicitly deciding to view the detailed elements.
  • This higher level of abstraction can provide a description of the virtual patient's phenotype and underlying physiological characteristics, but need not include certain parametric settings used to create that virtual patient in the computer model.
  • this higher level of abstraction can describe what the therapy does but need not include certain parametric settings used to simulate that exposure in the computer model.
  • a subset of outputs of the computer model that is particularly relevant for subjects and doctors can be made readily accessible.
  • the output can comprise an identification of one or more biological processes that most significantly affect whether hypertension develops or whether a certain patient might respond to a selected therapy.
  • the output may suggest biological assays that can be used to assess the likelihood that a subject may develop high blood pressure.
  • the model of hypertension described herein can be used to generate a model for simulating development and progression of high blood pressure and the associated increased risk of adverse effects, such as heart failure, stroke and kidney damage.
  • the simulation model may include hundreds or even thousands of objects, each of which can include a number of parameters.
  • it is useful to access and observe the input values of certain key parameters prior to performance of a simulation operation, and also possibly to observe output values for these key parameters at the conclusion of such an operation.
  • many parameters are included in the expression of, and are affected by, a relationship between two objects, one may also need to examine certain parameters at either end of such a relationship.
  • the computer model is configured to allow visual representation of mathematical relations as well as interrelationships between variables, parameters, and biological processes.
  • This visual representation includes multiple modules or functional areas that, when grouped together, represent a large complex model of a biological system.
  • simulation modeling software is used to provide a computer model, e.g., as described in U.S. Pat. No. 5,657,255, issued Aug. 12, 1997, titled “Hierarchical Biological Modeling System and Method”; U.S. Pat. No. 5,808,918, issued Sep. 15, 1998, titled “Hierarchical Biological Modeling System and Method”; U.S. Pat. No. 6,051 ,029, issued Apr.
  • FIG. 1 Various Diagrams can be used to illustrate the dynamic relationships among the elements of the model of skin sensitization. Examples of suitable diagrams include Effect and Summary Diagrams.
  • a Summary Diagram can provide an overview of the various pathways modeled in the methods and models described herein.
  • the Summary Diagram illustrated in FIG. 1 provides an overview of modules that can form the present model of hypertension.
  • a Summary Diagram also can provide an overview of pathways modeled in a particular module and/or provide links to individual modules of the model.
  • the models represent the relevant components of the phenotype through the use of "state” and “function” nodes whose relations are defined through the use of diagrammatic arrow symbols.
  • An Effect Diagram can be a visual representation of the model equations and illustrate the dynamic relationships among the elements of the model.
  • FIG. 3 provides an example of an Effect Diagram illustrating the glomerular RAAS Pathway. The Effect
  • Diagram is organized into functional areas, which when grouped together represent the large complex physiology of the phenotype being modeled.
  • State and function nodes show the names of the variables they represent and their location in the model. The arrows and modifiers show the relationship of the state and function nodes to other nodes within the model. State and function nodes also contain the parameters and equations that are used to compute the values of the variables the represent in simulated experiments. In some embodiments, the state and function nodes are represented according to the method described in U.S. Patent No. 6,051 ,029, entitled “Method of Generating a Display for a Dynamic Simulation Model Utilizing Node and Link Representations," incorporated herein by reference. Examples of state and function nodes are further discussed below.
  • State nodes are represented by single-border ovals and represent variables in the system, the values of which are determined by the cumulative effects of inputs over time.
  • “Input” refers to any parameter that can affect the variable being modeled by the state node.
  • input for a state node representing glomerular Ang Il mass can be glomerular Ang Il synthesis and glomerular Ang I mass, regulated by total glomerular ACE activity and chymase activity.
  • State node values are defined by differential equations.
  • the predefined parameters for a state node include its initial value (S 0 ) and its status.
  • state nodes can have a half-life. In these embodiments, a circle containing an "H" is attached to the node that has a half-life.
  • Function nodes are represented by double-border ovals and represent variables in the system, the values of which, at any point in time, are determined by inputs at the same point in time. Function nodes are defined by algebraic functions of their inputs.
  • the predefined parameters for a function node include its initial value (F 0 ) and its status. Setting the status of a node effects how the value of the node is determined.
  • the status of a state or function node can be: 1 ) Computed, i.e., the value is calculated as a result of its inputs; 2) Specified-Locked, i.e., the value is held constant over time; or 3) Specified Data, i.e., the value varies with time according to predefined data points.
  • State and function nodes can appear more than once in the module diagram as alias nodes. Alias nodes are indicated by one or more dots (see, e.g., state node
  • State and Function nodes are also defined by their position, with respect to arrows and other nodes, as being source nodes (S) and/or target nodes (T). Source nodes are located at the tails of arrows and target nodes are located at the heads of arrows. Nodes can be active or inactive.
  • Arrows link source nodes to target nodes and represent the mathematical relationship between the nodes. Arrows can be labeled with circles that indicate the activity of the arrow. A key to the annotations in the circles is located in the upper left corner of each effect Diagram. If an arrowhead is solid, the effect is positive. If the arrowhead is hollow, the effect is negative.
  • the fully-integrated computer model of hypertension preferably is capable of representing a breadth of patient phenotypes in terms of their physiological status, additional risk factors for high blood pressure, and alternate genetic and/or hypothesized mechanistic variants.
  • the resulting virtual patients can be used to predict the effect of therapeutic and/or dietary intervention on hypertension and the risk of adverse endpoints, such as heart failure or stroke.
  • the methods disclosed herein can be used to form a computer model capable of simulating patient phenotypes and further can incorporate the addition of new components, as well as increased detail in components already modeled. For example, computer models predicting changes in filtration capacity in the kidneys of a diabetic or aging patient.
  • the RAAS pathway module incorporates the enzymatic pathways involved in the synthesis and conversion of AGT to Ang I, Ang Il and downstream metabolites, such as Ang(1-7) and Ang IV.
  • the activity of enzymes including renin, ACE, a chymase-like enzyme, and neutral endopeptidase (NEP) were included in the model in addition to the binding rates of Ang Il to the two Ang Il receptors (AT1 and AT2).
  • the inclusion of these peptides and enzymes allows for the investigation antihypertensive therapies that target the RAAS.
  • Figs. 2, 3 and 4 provide a diagrammatic representation of the pathway model, in systemic circulation, glomerulus and tubule, respectively.
  • the Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance
  • GC Guyton/Coleman
  • Karaaslan et al published a modified version of the GC model that added the influence of the renal sympathetic nervous activity on the synthesis and release of renin and the afferent arteriolar tone.
  • the model that describes the dynamics of the renin-angiotensin system is represented using a system of ordinary differential equations (1 )-(8).
  • Each biochemical reaction has zero th -order components of production (k n ) and first order degradation kinetics expressed through half-life parameters (h n ).
  • Binding or enzymatic reactions can be expressed as first-order reactions with parameters (c n ).
  • a feedback function, f relating plasma renin activity (PRA) to ATI-bound Ang Il is also included in the model.
  • PRA is assumed to be proportional to the concentration of its substrate, AGT, because the concentration of AGT is comparable to the Michaelis-Menten constant (Km).
  • ACE and chymase activity in the vasculature were determined to have V m values of 222 and 154 pmol/ml/hr, respectively, which was considerably greater than rates (-0.3 pmol/ml/hr) measured in humans (Takai, et al. (1997) Characterization of chymase from human vascular tissues. CHn Chim Acta 265:13-20; Meng, et al. (1995) Sensitive method for quantitation of angiotensin-converting enzyme (ACE) activity in tissue. Biochem
  • ACE was assumed to be responsible for >95% of the conversion of Ang I to Ang II.
  • Human and animal data support the hypothesis of ACE being the primary enzyme responsible for Ang I to Ang Il conversion in normotensive humans.
  • ACE expression and systemic conversion of AGT to Ang I take place primarily in the pulmonary circulation.
  • Ang Il binds preferentially to AT1 rather than AT2 receptors.
  • Data from human smooth muscle cells and renal tissue indicate that AT2 receptors are expressed at lower levels compared to AT1 receptors (Haulica, et al. (2005) Angiotensin peptides and their pleiotropic actions. J Renin Angiotensin Aldosterone Syst 6:121-131 ).
  • Ang I and Ang Il have half lives of approximately 30 seconds in the systemic circulation.
  • For Ang IV the model assumes a half-life of 10 minutes, which is between the reported half lives of Ang Il and Ang(1-7). The concentrations of Ang IV and Ang(1-7) in the systemic circulation were calculated based on the solution of the steady-state equilibrium equations.
  • PRA increases via a regulatory feedback mechanism in response to a reduction in blood pressure, in a relationship that reflects a reduction in Ang Il binding to the AT1 receptors.
  • An analysis of clinical data from trials testing therapies that modulate the RAAS pathway suggests a rapid increase in PRA 24 hours post-treatment, which correlated with the reductions in Ang Il bound to AT1 receptors and blood pressure.
  • the model divides the kidney into two regions: the renal vasculature compartment, comprised of all vascular structures within the kidney (including the blood volume within those structures) and the renal tissue compartment, comprised of all tissue external to vascular structures (including the tubules and interstitial tissue).
  • the model makes the following assumptions and simplifications:
  • RAAS peptides are arterially delivered from the circulation to the renal vascular compartment at concentrations equal to systemic levels, and the peptides flow out of the renal vascular compartment back to the systemic circulation at concentration equal to renal vasculature levels.
  • All angiotensin peptides and all enzymes in the RAAS pathway are also produced locally within each compartment, although the rates of production and enzymatic conversion can vary greatly from those in systemic circulation, as discussed below.
  • a concentration gradient exists between the renal tissue and renal vasculature, such that RAAS peptides produced in the renal tissue diffuse into the renal vasculature. Biopsy data shows that renal tissue levels of Ang I and Ang
  • Kidney lnt Kidney lnt
  • Ang IV and Ang(1-7) levels in the kidney were not specifically modeled because of the limited availability of data. Instead, rates of conversion of Ang I and Ang IV to Ang(1-7) and Ang IV were assumed to be incorporated into the degradation rates of Ang I and Ang II. • Since limited data is available on any changes in the concentrations of AGT and renin within the renal tubules and interstitium, the rate of Ang I synthesis in the renal tissue compartment was assumed to be at equilibrium levels.
  • the model accounts for: 1 ) arterially delivered Ang I and Ang Il peptides and return of these peptides to the systemic circulation; 2) production and utilization of Ang I and Ang Il in the renal vascular bed; 3) diffusion of Ang I and Ang Il from the renal tissue into the renal vasculature; and 4) binding of Ang Il to its receptors.
  • the model takes into consideration: 1 ) production and utilization of Ang I and Ang Il in the renal tissue; 2) diffusion of locally produced peptides into the renal vasculature, and 3) binding of Ang Il to its receptors.
  • Equations (10-13) for the renal vascular RAAS are shown below. These equations are almost identical to those for systemic RAAS sub-module, but the rates are specific for the renal circulation, include additional terms have been added to describe the flow of angiotensin peptides in and out of the kidney at a rate F k , and include the diffusion of angiotensin peptides from the renal tissue compartment to the renal vasculature at a rate of D k .
  • Equations (14-17) for RAAS within the renal tissue compartment are as shown above.
  • the concentration of Ang I at the renal vein is approximately 50% higher than the concentration at the renal artery.
  • the concentration of Ang Il at the renal vein is approximately 50% lower than the concentration at the renal artery.
  • the rate of blood flow to the kidney (F k ) is ⁇ 1 L/min at rest and the blood volume of the kidney is 70 ml, equivalent to a residence time of 4 seconds. • The rate of local Ang I and Ang Il degradation in the kidney is significantly increased over the systemic degradation rate to account for the high rate of angiotensin peptide removal in the renal circulation.
  • the chosen parameters yielded a solution for the dynamical system that satisfied the known constraints of the renal vascular bed.
  • the renal vascular parameters with the same value as their systemic counterpart are not listed in the table.
  • the RAAS pathway within the renal tissue i.e. the tubular compartment
  • the RAAS pathway within the renal tissue was implemented in a similar fashion as the renal vascular RAAS, with identical enzymes, peptides and receptors. Although the concentration and activities of the enzymes were assumed to differ, there is minimal quantitative data for these rates in the published literature.
  • the primary constraint for the renal tissue RAAS is the assumption that the renal tissue should function as a source of Ang I and Ang Il that enters into the renal vasculature.
  • the parameters describing the activity of the renal tissue RAAS pathway was parameterized such that: (i) the equilibrium concentrations of the angiotensin peptides in the tissue pathway were a source of Ang I and Ang Il in the renal vascular compartment; and (ii) the constraints on Ang I and Ang Il concentrations measured by Danser were satisfied.
  • a validation of any model consists of the agreement between model predictions and one or more experimental data sets that were not used to determine the initial parameterization of the model.
  • a validation of the model parameters describing the normotensive Virtual Patient was conducted using a series of published radio-labeled angiotensin peptide infusion experiments (Danser, et al. (1998) Angiotensin l-to-ll conversion in the human renal vascular bed. J Hypertens 16:2051- 2056; and Admiraal, et al. (1993) Regional angiotensin Il production in essential hypertension and renal artery stenosis. Hypertension 21 :173-184).
  • ACE inhibitors were simulated by changing the effect of the rate constant C ACE
  • ARBs angiotensin Il type I receptor blockers
  • DRIs direct renin inhibitors
  • AT1 receptors mediate the majority of Ang Il actions involved in the regulation of blood pressure and blood volume.
  • ACEI blocks the action of ACE competitively and thus the conversion of Ang I to Ang II, thereby reducing circulating and local levels of Ang II.
  • ACEI therapy is associated with a decrease in Ang II, a reactive increase in plasma renin concentration and an increase in plasma Ang I.
  • the reactive increase in plasma renin concentration was also observed in response to ARB and DRI therapy.
  • the simulated ACEI in the model predicted increased concentrations and Ang I and Ang(1-7) and decreased concentrations of Ang II, consistent with reported clinical data (Manhem, et al. (1985) A dose-response study of HOE 498, a new non-sulphydryl converting enzyme inhibitor, on blood pressure, pulse rate and the renin-angiotensin- aldosterone system in normal man. Br J Clin Pharmacol 20:27-35).
  • the time course of the Ang I and Ang Il response predicted an equilibration in the angiotensin peptide concentrations after 5 hours, in agreement with short-term measurements taken in the studies highlighted in Table 5.
  • ARBs act by blocking the binding of Ang Il to the AT1 receptor rather than by inhibiting Ang Il synthesis, their use results in an increase in plasma Ang Il levels.
  • the blockade of AT1 receptors increases renin secretion and the corresponding concentration of plasma Ang I.
  • DRIs have a significant and sustained effect on PRA to reduce the concentration of both Ang I and Ang Il in the circulation.
  • the simulated effects of DRIs in the model predict a decreased concentration of circulating Ang I, Ang Il and Ang(1-7), consistent with results reported in clinical studies (Nussberger, et al. (2007) Plasma renin and the antihypertensive effect of the orally active renin inhibitor aliskiren in clinical hypertension. Int J CHn Pract 61 :1461-1468).
  • Table 2 summarized the wide range of reported clinical values of enzyme activities in the RAAS pathway cascade to reflect the intrinsic variability between human subjects.
  • the values summarized in Table 3 described only one set of parameters for the system of equations that yields a feasible solution.
  • the parameter values in Table 2 can be changed within the observed ranges to generate a new Virtual Patient hypothesis.
  • changing the parameters may yield a mathematically correct steady solution for a new Virtual Patient, the combination of parameter values may not result in steady state concentrations or enzyme activity rates that are consistent with the physiological data. For example, decreasing the rate of Ang Il clearance from the circulation will increase the time it takes for Ang Il to reach an equilibrium. If the resulting Ang Il concentration at equilibrium increases significantly beyond physiological range determined by the infusion studies, then the chosen set of parameters for the Virtual Patient was considered invalid.
  • the verification of the simulated results against plausible data is a valuable step during the process of model building.
  • a collection, or cohort, of multiple feasible Virtual Patients can be generated using a systematic process to explore the parametric space and a method for testing the feasibility criteria of each parameterization.
  • Table 6 summarizes one such method for exploring the parametric space that varies the half lives and enzyme activity rates around the nominal values of the first virtual patient (VP1).
  • a patient hypothesis may be generated by simulating with parameters within the nominal range where the value of 100% is equal to the values chosen for the first Virtual Patient.
  • Table 7 summarizes a set of feasibility criteria for the concentration of angiotensin peptides based on a survey of the literature.
  • the cohort of feasible Virtual Patients can be modified depending on criteria to describe a particular disease phenotype. For example, the feasibility criteria for plasma renin activity can be increased accordingly in patients that exhibit exaggerated renal production of renin leading to increased concentrations of plasma renin. It is important to note that the cohort of Virtual Patients may not follow the same distribution as the clinical population and additional refinement of the patient-generation procedure may be required.
  • Chymase is another enzyme that can convert Ang I to Ang II. Therapy that focuses on the inhibition of ACE activity does not affect the continued conversion of Ang I to Ang Il by chymase. Based on the clinically measured changes in circulating Ang I and Ang Il and the assayed reduction in ACE activity in response to moderate doses of ACEI, the model predicts that ACE is responsible for greater than 95% of Ang Il synthesis in the representative normotensive patient. If the role of ACE in the synthesis of Ang Il was reduced to ⁇ 95%, the model was unable to reproduce the clinically measured reduction in Ang II. [0107] PRA increases in response to ARB or ACEI therapy can be represented by establishing a relationship between decreased Ang Il binding to AT1 receptors and PRA.
  • the kidney possesses all the RAAS components and enzymatic machinery required for the local tissue generation of Ang Il and other RAAS-related peptides.
  • the models described herein comprise a renal function module.
  • the renal module includes a representation of the kidney as an assembly of single nephrons and associated fluid dynamics processes that influence glomerular filtration rate.
  • the renal function module also can comprise a representation of glomerular filtration rate (GFR) and a representation of albuminuria.
  • GFR glomerular filtration rate
  • glomerular filtration permeability is distributed between fenestrated endothelium, GBM and the slit diaphragm.
  • the model represents albumin transport across the glomerular basement membrane as a function, independently, of diffusion and convection (water filtration).
  • GFR is represented as a function of glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (K f ).
  • K f in turn, can be represented as a result of integration of multiple effects of physical barriers to filtration in one simplified term representing: podocyte slit diaphragm length, quantity of slits, diaphragm composition, GBM thickness and composition, endothelium integrity and function, and total (capillary) surface area.
  • glomerular hydrostatic pressure can be determined based on afferent and efferent arteriole resistance and blood pressure at the renal artery.
  • the glomerular filter present in the capillary tuft located inside the Bowman's capsule is responsible for the formation of ⁇ 180 L/day of primary urine devoid of macromolecules. This primary filtrate is then modified by the nephron's tubular system and its volume reduced to -1.5 L/day excreted in urine.
  • the glomerular filter/barrier consists of 3 distinct layers 1 ) a fenestrated endothelium, 2) a glomerular basement membrane (GBM) and 3) a slit diaphragm located between the interdigitating foot processes of epithelial podocytes.
  • GBM glomerular basement membrane
  • the anti-clogging capacity of the glomerulus has prompted investigators to postulate various mechanisms where the GBM (gel permeation), the podocyte (size selectivity) and the endothelium (size and charge selectivity) are the relevant components behind the barrier's filtering capacity.
  • GBM gel permeation
  • podocyte size selectivity
  • endothelium size and charge selectivity
  • GFR and albuminuria are the clinical measures used to define normal kidney function and to diagnose renal disease. Both parameters result from a variety of physiological phenomena, some of which are not fully understood and therefore their quantitative nature and relevance cannot be derived directly from the scientific literature.
  • Glomerular filtration rate can be represented as the sum of single nephron GFR (SNGFR) of N nephrons, where N is 2x10e6.
  • SNGFR single nephron GFR
  • the SNGFR of the n th nephron is a flow (in nl/min) that is commonly calculated from the Starling equation: where K f is the hydrostatic conductance , P represents a physical pressure in either the glomerular capillaries or the Bowman's space and ⁇ represents the oncotic pressure (exerted by plasma proteins).
  • the reflection coefficient ( ⁇ ), is often thought as a correction factor for the differences in permeability of body capillaries to large proteins and their contribution to the interstitial fluid oncotic pressure; ⁇ can take values between 0 and 1.
  • Glomerular capillaries have a very low permeability to proteins including albumin, therefore a ⁇ value close to 1 is typically used.
  • hepatic sinusoids are highly permeable to albumin produced by hepatocytes and therefore have a low ⁇ . Strictly speaking, each of the N nephrons would have its own set of these 5 parameters producing a unique SNGFR for each nephron.
  • the glomerular hydrostatic pressure of a specific nephron can be calculated from basic fluid dynamic principles (e.g., a pipe and valve calculation) and will depend on renal perfusion pressure, total renal blood flow resistance, and the resistance presented by the afferent and efferent arterioles of the nephron.
  • the degree of vasodilation / vasoconstriction of the arterioles is of significant interest for this modeling effort as it will be regulated by various factors, most particularly by Ang II.
  • K f The hydrostatic conductance, K f , is the term most closely associated with what are traditionally viewed as the physiological properties of the glomerular membrane determining GFR.
  • Eq (19) demonstrates that K f is the ratio of the flow through a resistance to the pressure difference between the two sides of the resistance.
  • K f represents the effects of a number of complex biological phenomena, including:
  • the model represents GFR as follows:
  • albumin in urine albuminuria
  • albuminuria is typically measured in mg/day. Similar to GFR, albuminuria is represented as the sum of albumin excretion by N nephrons (as for GFR, a single typical nephron manifesting the mean excretion is used as the basis for the model).
  • Excreted albumin is represented as the amount of protein delivered to the proximal tubule that is not reabsorbed, where the amount reabsorbed is a fraction (f) of the amount that enters the tubular system.
  • Albumin tubular reabsorption is a saturable process, thus, loads that exceed the saturation level will be excreted in urine.
  • Single nephron albumin excretion rate (1 - f) * filtered load (22) where the filtered load is the rate at which albumin is delivered from the Bowman's space into the tubule (mg/min).
  • Mass conservation requires that the flow of albumin into the tubule is the product of the albumin concentration in the Bowman's space and the flow rate of fluid into the tubule (SNGFR).
  • the concentration in the Bowman's space is determined using the concept of the sieving coefficient ( ⁇ ) that is the ratio of the Bowman's space concentration to the plasma concentration.
  • albumin excretion rate N*( 1 - f) * SNGFR * ⁇ * [Alb] plasma (23)
  • albuminuria is proportional to GFR. If GFR doubles, albuminuria doubles. Additionally, per Eq (23), albuminuria is proportional to the plasma albumin concentration. While Eq (23) clearly indicates that albuminuria is dependent on GFR, other scenarios in which albuminuria might not depend on GFR should be considered.
  • filtered load is the product of flow and concentration.
  • the sieving coefficient ( ⁇ ) and f are defined empirically: there is an albumin concentration difference between the glomerular Bowman's space and plasma, and for any set of concentrations that ratio is defined as ⁇ .
  • some fraction of albumin (f) is reabsorbed in the proximal tubule.
  • Eq (23) the albumin excretion rate might not depend on GFR. So far, ⁇ and f are assumed to be fixed, yet experimental data suggest otherwise.
  • the filtration coefficient ⁇ is also likely to change with changes in SNGFR.
  • the direction of the change is indeed to decrease with increasing SNGFR in order to maintain albuminuria levels.
  • the changes in ⁇ with SNGFR will partially mitigate the changes in albuminuria induced by changes in SNGFR in Eq (21).
  • ⁇ would need to vary with (1/SNGFR) to cancel the SNGFR in Eq (23).
  • the present model for albuminuria leads to an explicit dependence of albuminuria on SNGFR (Eq (23)) that is a function of the sieving coefficient ( ⁇ ) and tubular readsorption (f) on SNGFR. Furthermore, within the constraints of normal physiological changes in the nephron, the expected dependencies of ⁇ and fon SNGFR will not cancel the dependence of albumin excretion on SNGFR in Eq (23) — the changes in ⁇ may reduce the dependence partially and the changes in f will augment the dependence. The available data do not support the idea that the filtered load of albumin is nearly independent of GFR. Haraldsson et al., Properties of the glomerular barrier and mechanisms of proteinuria. Physiol Rev 2008 April;88(2):451-87.
  • Glomerular filter permeability / selectivity is distributed among the 3 main components of the glomerular filtration barrier (fenestrated endothelium / GBM / slit diaphragm of podocyte foot processes). Other theoretical models of filtration are centered around one layer (e.g., GBM). Smithies, Why the kidney glomerulus does not clog: a gel permeation/diffusion hypothesis of renal function. Proc Natl Acad Sci U S A 2003 April 1 ;100(7):4108-13.
  • GFR is determined by glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (K f ).
  • K f is the result of integrating the multiple effects of a series of physical barriers to filtration into one simplified term.
  • the determinants of glomerular hydrostatic pressure are: o afferent and efferent arteriole resistance, o the blood pressure at the renal artery.
  • the sieving coefficient of any solute is the concentration in the filtrate divided by the concentration in the retentate. In the case of glomerular filtration, it is defined as the concentration in the Bowman's capsule by that in plasma.
  • the sieving coefficient of plasma solutes being filtered by the glomerular membrane is determined by a number of factors including 1 ) the intrinsic selectivity of the membrane given by solute size, charge and shape; 2) the filtration rate of water; 3) the solute concentration; and 4) the arrangements of the layers involved in filtration (fenestrated endothelium, GBM and slit diaphragm).
  • albuminuria represented a single-layer glomerular membrane that factors in the sieving coefficient of albumin and implicitly represents the various factors influencing that sieving coefficient.
  • the model treats N, K f , P gbm , and [Alb] p ⁇ aSm a as inputs that will vary in response to various acute and chronic changes in a given patient.
  • the model additionally includes functions for ⁇ and f that have as arguments various values generated by the model:
  • clinical behaviors can be mechanistically modulated to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies.
  • the key renal components represented in the model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin.
  • the cardiovascular hemodynamic components represented in the platform include mean arterial pressure (MAP), cardiac output (CO), total peripheral resistance (TPR), sympathetic nervous activity (SNA), and vascular capacitance.
  • the humoral components with vascular and renal effects can include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium.
  • Ang II Angiotensin Il
  • ADH anti-diuretic hormone
  • ADP atrial natriuretic peptide
  • sodium and potassium Compared to the Guyton- Coleman model, the integrated hypertension model disclosed herein comprises a more detailed representation of systemic RAAS-related peptides including Ang I and Ang (1- 7); glomerular and tubular RAAS compartments; renal function (GFR and albuminuria) and the representation of the mechanistic effects of RAAS- and non RAAS-based therapies.
  • the blood pressure regulation module tracks sodium balance and total sodium amount. It also calculates water intake and integrates and tracks water balance and extracellular fluid volume (ECFV).
  • ECFV extracellular fluid volume
  • the blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it calculates MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses.
  • RAP right atrial pressure
  • the foundation of the blood pressure regulation module is the renal function curve or 'pressure natriuresis'. Pressure natriuresis relates mean arterial pressure (MAP) to blood volume and establishes a steady-state equilibrium for MAP. The equilibrium point between blood volume and MAP is attained through the renal excretion of sodium and water.
  • RAAS and other hormonal factors allow pressure natriuresis to occur over a wider range of blood pressure by up-regulating sodium excretion when the plasma sodium concentration is high and increasing sodium reabsorption when plasma sodium levels are low.
  • the tubuloglomerular feedback pathway participates in regulating these effects and is represented in Figure 9.
  • Sodium levels are sensed by the macula densa, a cellular structure located after the proximal tubule and loop of Henle but before the distal tubule and collecting duct.
  • Low levels of sodium in the glomerular filtrate induce renin release, which promotes Ang Il and aldosterone synthesis.
  • Ang Il acts in the proximal tubule to increase reabsorption of sodium and water to increase blood volume.
  • Aldosterone increases sodium reabsorption in the distal tubule and therefore its actions are physiologically similar to those of Ang II. Increased levels of Ang Il in response to low sodium concentration by the macula densa also result in vasoconstriction of the afferent and efferent arterioles, with a greater effect on the efferent arteriole that results in increased single nephron glomerular filtration rate (SNGFR). High levels of sodium sensed by the macula densa will have the opposite effect - block renin release, lower sodium reabsorption and thus promote further sodium excretion while also lowering SNGFR.
  • SNGFR single nephron glomerular filtration rate
  • MAP is a product of cardiac output (CO, defined as the rate at which blood is ejected by the left ventricle) and arterial (arteriolar) resistance (total peripheral resistance, TPR).
  • CO cardiac output
  • TPR total peripheral resistance
  • RSNA renal sympathetic nervous activity
  • the added representation of the RSNA takes into consideration the more accurate connection between the regulation of arterial pressure and arterial blood volume. This approach allows for the simulation of alternative disease etiologies leading to hypertension. Such profiles will be generated in response to various SNS activity- mediated perturbations of individual vascular bed resistances.
  • the addition of the RSNA to the GC model is a closer approximation to 'essential' hypertension.
  • Clinical behaviors can be mechanistically modulated in the blood pressure regulation module to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies.
  • the key renal components represented in the blood pressure regulation model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin.
  • the cardiovascular hemodynamic components represented in the platform include mean arterial pressure, cardiac output, total peripheral resistance, sympathetic nervous activity, and vascular capacitance.
  • the humoral components with vascular and renal effects include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium.
  • the main biological blocks include cardiovascular, renal and signaling (humoral) variables.
  • the primary clinical behaviors that can be mechanistically modulated include • generation of high blood pressure,
  • the key renal components include
  • the blood pressure regulation module can track sodium balance and total sodium amount. It also can calculate water intake to track water balance and extracellular fluid volume (ECFV).
  • ECFV extracellular fluid volume
  • the blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it can calculate MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses.
  • Figures 8 and 9 delineates the key functions and relationships implemented in the model.
  • the blood pressure regulation module comprises both systemic cardiovascular (Fig. 8) and renal (Fig. 9) aspects.
  • the renal aspect represented in the blood pressure regulation module can be broken down into three functions. The first function is the determination of GFR.
  • GFR is largely dominated by MAP, afferent arteriole resistance and efferent arteriole resistance. Afferent resistance is driven by the external rSNA input and by an internal feedback from the macula densa. GFR determines the load of water entering the tubule, and in conjunction with the externally determined sodium concentration, it determines the sodium entering the tubule.
  • the second function is water reabsorption, which is represented by a single reabsorption process (the sum of proximal tubule, loop of Henle, distal tubule, and collecting duct reabsorption). The reabsorption fraction preferably is modulated by aldosterone and ADH. Urine flow is simply the non-reabsorbed filtrate.
  • the third component of renal sub- module is the reabsorption of sodium, which is handled in three separate regions.
  • the first region is labeled "proximal tubule & LOH Na+ reabsorption" and includes the representation of the reabsorption that occurs in the LoH.
  • Sodium reabsorption also occurs in the distal tubule and the collecting duct.
  • the various reabsorption processes are modulated by Ang II, rSNA, aldosterone and ANP. Note that the reabsorption fraction also depends on the sodium load. Often the sodium load dependence can dominate over the humoral modulators.
  • renin secretion and afferent arteriole resistance are determined based on sodium flow at the macula densa (located just before the entrance to the distal tubule).
  • the effects of the primary hormones involved in the regulation of sodium including ADH, ANP, Ang Il and aldosterone are also represented.
  • the model also includes the modulation of rSNA by MAP, right atrial pressure RAP and the effects of rSNA on renin secretion by the kidney.
  • the present model includes the vascular resistance of interlobar, arcuate, and interlobular arteries (collectively called 'preglomerular resistance'), as well as the resistance of peritubular capillaries and veins. This additional granularity allows one to more accurately describe intrarenal vascular resistance and its effects on blood pressure.
  • Ang Il is a potent vasoconstrictor that has effects both in the kidney and throughout the systemic circulation
  • some implementations include a representation of the effects of Ang Il on the renal vasculature.
  • Ang Il has effects on both renal and systemic circulations.
  • the contribution of Ang Il to the systemic arterial resistance was compared to results obtained using the Quantitative Human Physiology (QHP) software.
  • QHP is a publicly available simulation software from the University of Mississippi developed and maintained by Coleman and colleagues (Hester, et al. A multilevel open source integrative model of human physiology. FASEB J 2008 March 1 ;22(1_MeetingAbstracts):756).
  • QHP version 2008b3 was used to obtain the functional dependence of arterial resistance on Ang Il concentration.
  • the effects of Ang Il on afferent arteriole and total preglomerular resistance were represented as a linear relationship:
  • R R 0 (a + b - C AngII )
  • R 0 is the nominal vascular resistance
  • C An gi ⁇ is the concentration of Ang Il (circulating or bound to a receptor)
  • a and b are fitting constants such that for physiological C An gi ⁇ values the modifier in parenthesis is close to 1.
  • TPR does not explicitly include renal vascular resistance and does not account for its contribution to TPR.
  • certain implementations of the model described here in considers systemic and renal components as parallel resistances with an appropriate calculation of their effect on mean arterial pressure and cardiac output to differentiate between the renal and systemic effects on hypertension. The changes are reflected in the "total peripheral resistance" node.
  • Renal blood flow can be calculated by taking into account that actual pressure drop in the kidney is less than mean arterial pressure.
  • the contribution of renal vein resistance corresponds to a measured value of approximately 4 mm Hg.
  • the current model preferably includes an additional autoregulatory mechanism that constrains GFR values by reducing changes in glomerular pressure that occur in response to changes in MAP. The effect can be implemented via "glomerular pressure autoregulation". When calculated, theoretical glomerular pressure can be adjusted by multiplying it to a transform function.
  • GFR is a function of the number of effective functional nephrons. Functional nephrons may change because of disease progression or simply through the aging process. To account for these effects, total GFR can be computed as a product of an average SNGFR and the total number of nephrons.
  • Sodium reabsorption mechanisms can be added by 1 ) implicitly representing the Loop of Henle, and 2) modifying the effect of the macula densa on the tubuloglomerular feedback. These modifications were implemented to represent the effects of diuretic therapy, particularly loop diuretics (furosemide).
  • the Karaaslan model includes no specific mechanism(s) to account for this regulation.
  • One implementation of the model includes additional feedback to renal water reabsorption in the RAAS model. This feedback mechanism helps to keep plasma sodium concentration within feasible (physiological and pathological) constraints.
  • the reabsorption regulator the following form was chosen:
  • Q and Q 0 is sodium reabsorption rate and its nominal value, respectively.
  • C, Cmax, and Cref are current sodium concentration, and its physiologically maximal and nominal values respectively, S and G are scale and gain factors allowing to fine tune the effect.
  • This feedback has a nonstandard form, similar but not identical to proportional control, whereby a rapid compensatory mechanism is activated as sodium concentrations increase and approach an upper limit.
  • the feedback's gain can be adjusted to prevent oscillatory/unstable behaviors while still maintaining sufficiently tight control over sodium concentration.
  • a more common controller, one that increases water reabsorption proportionately to the sodium concentration relative to a "set-point" could also be implemented as it may also correct for reductions in sodium concentration.
  • This alternate form may be less effective at keeping a "maximum" concentration limit, which was the original issue detected in the Karaaslan model.
  • the invention also provides methods and systems for simulating hypertension.
  • the system of the invention comprises: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of atherosclerosis with the data to generate a set of outputs describing the result of the simulation of atherosclerosis; and c) a computer-executable report generator capable of reporting the set of outputs.
  • the computer model comprises: i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module.
  • Methods of simulating RAAS comprise executing the models of the invention, optionally in conjunction with a virtual stimulus.
  • Methods of simulating RAAS can comprise applying a virtual protocol to the computer model to generate a set of outputs to represent a phenotype of the biological system.
  • the phenotype can represent a normal state or a disease state.
  • the methods can further include accepting user input specifying one or more parameters or variables associated with one or more mathematical representations prior to executing the computer model.
  • the user input comprises a definition of a virtual patient or a definition of the virtual protocol, such as administration of a therapy.
  • Running the computer model produces a set of outputs for a biological system represented by the computer model.
  • the set of outputs can represent one or more phenotypes of the biological system, i.e., the simulated subject, and includes values or other indicia associated with variables and parameters at a particular time and for a particular execution scenario.
  • a phenotype is represented by values at a particular time.
  • the behavior of the variables is simulated by, for example, numerical or analytical integration of one or more mathematical relations to produce values for the variables at various times and hence the evolution of the phenotype over time.
  • the level of detail of the output can vary dependent upon the level of sophistication of the target user.
  • Exemplary outputs can range from an exhaustive report including all parameters of the computer model to a simple indicator of likelihood of hypertension or a normotensive blood pressure at a particular point in time. Additional clinically relevant outputs include therapeutic effects on circulating angiotensinogen, glomerular ACE activity or blood volume.
  • the computer executable software code numerically solves the mathematical equations of the model(s) under various simulated experimental conditions. Furthermore, the computer executable software code can facilitate visualization and manipulation of the model equations and their associated parameters to simulate different patients subject to a variety of stimuli. See, e.g., U.S. Patent Number 6,078,739, entitled “Managing objects and parameter values associated with the objects within a simulation model," the disclosure of which is incorporated herein by reference. Thus, the computer model(s) can be used to rapidly test hypotheses and investigate potential drug targets or therapeutic strategies.
  • the computer model can represent a normal state as well as a disease (e.g., hypertensive or diabetic) state of a biological system.
  • the computer model includes parameters that are altered to simulate a disease state or a progression towards the disease state.
  • the parameter changes to represent a disease state are typically modifications of the underlying biological processes involved in the disease state, for example, to represent the genetic or environmental effects of a condition on the underlying physiology.
  • selecting and altering one or more parameters a user modifies a normal state and induces a phenotype of interest. In one implementation, selecting or altering one or more parameters is performed automatically.
  • various mathematical relations of the computer model, along with a modification defined by the virtual stimulus can be solved numerically by a computer using standard algorithms to produce values of variables at one or more times based on the modification. Such values of the variables can, in turn, be used to produce the first set of results of the first set of virtual measurements.
  • the virtual stimulus is a representation of administration of a therapy.
  • One or more virtual patients in conjunction with the computer model can be created based on an initial virtual patient that is associated with initial parameter values.
  • a different virtual patient can be created based on the initial virtual patient by introducing a modification to the initial virtual patient.
  • modification can include, for example, a parametric change (e.g., altering or specifying one or more initial parameter values), altering or specifying behavior of one or more variables, altering or specifying one or more functions representing interactions among variables, or a combination thereof.
  • a parametric change e.g., altering or specifying one or more initial parameter values
  • altering or specifying behavior of one or more variables altering or specifying one or more functions representing interactions among variables, or a combination thereof.
  • other virtual patients e.g., patients possessing certain risk factors for developing high blood pressure, may be created based on the initial virtual patient by starting with the initial parameter values and altering one or more of the initial parameter values.
  • Alternative parameter values can be defined as, for example, disclosed in U.S. Pat. No. 6,078,739. These alternative parameter values can be grouped into different sets of parameter values that can be used to define different virtual patients of the computer model. For certain applications, the initial virtual patient itself can be created based on another virtual patient (e.g., a different initial virtual patient).
  • one or more virtual patients in the computer model can be created based on an initial virtual patient using linked simulation operations as, for example, disclosed in the following publication: "Method and Apparatus for Conducting Linked Simulation Operations Utilizing A Computer-Based System Model", (U.S. Application Publication No. 20010032068, published on October 18, 2001 ).
  • This publication discloses a method for performing additional simulation operations based on an initial simulation operation where, for example, a modification to the initial simulation operation at one or more times is introduced.
  • additional simulation operations can be used to create additional virtual patients in the computer model based on an initial virtual patient that is created using the initial simulation operation.
  • a virtual patient can be customized to represent a particular subject.
  • one or more simulation operations may be performed for a time sufficient to create one or more "stable" virtual patient of the computer model.
  • a "stable" virtual patient is characterized by one or more variables under or substantially approaching equilibrium or steady-state condition.
  • Various virtual patients of the computer model can represent variations of the biological system that are sufficiently different to evaluate the effect of such variations on how the biological system responds to a given scenario.
  • one or more biological processes represented by the computer model can be identified as playing a significant role in modulating biological response to a therapy, and various virtual patients can be defined to represent different modifications of the one or more biological processes.
  • the identification of the one or more biological processes can be based on, for example, experimental or clinical data, scientific literature, results of a computer model, or a combination thereof.
  • various virtual patients can be created by defining different modifications to one or more mathematical relations included in the computer model, which one or more mathematical relations represent the one or more biological processes.
  • a modification to a mathematical relation can include, for example, a parametric change (e.g., altering or specifying one or more parameter values associated with the mathematical relation), altering or specifying behavior of one or more variables associated with the mathematical relation, altering or specifying one or more functions associated with the mathematical relation, or a combination of them.
  • the computer model may be run based on a particular modification for a time sufficient to create a "stable" configuration of the computer model.
  • the model of RAAS is executed while applying a virtual stimulus or protocol representing, e.g., a change in diet or a therapeutic regimen.
  • a virtual stimulus can be associated with a stimulus or perturbation that can be applied to a biological system.
  • Different virtual stimuli can be associated with stimuli that differ in some manner from one another.
  • Stimuli that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents, treatment regimens, and medical tests. Additional examples of stimuli include exercise and diet. Further examples of stimuli include environmental changes such as those relating to changes in level of exposure to an environmental agent.
  • a virtual protocol e.g., a virtual therapy, representing an actual therapy can be applied to a virtual patient in an attempt to predict how a real-world equivalent of the virtual patient would respond to the therapy.
  • Virtual protocols that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents and treatment regimens, mere passage of time, changes in lifestyle and the like.
  • a virtual protocol can be created, for example, by defining a modification to one or more mathematical relations included in a model, which one or more mathematical relations can represent one or more biological processes affected by a condition or effect associated with the virtual protocol.
  • a virtual protocol can define a modification that is to be introduced statically, dynamically, or a combination thereof, depending on the particular conditions and/or effects associated with the virtual protocol.
  • the detailed model of hypertension presented herein is the foundation of a platform to investigate the response of this system to multiple RAAS-modulating therapies.
  • the model can be used to predict the relative effects of the different therapies on entities that are difficult to measure clinically and can be used to predict the response to combination therapies for which clinical data is not available.
  • the model also highlights any differences between circulating and renal peptide concentrations, and how therapies that localize in the renal tissue may have different effects than therapies that remain only in the systemic circulation.
  • the predicted concentrations of renal peptides may also yield insight into the changes in local Ang Il in response to therapies without requiring invasive and difficult tissue sampling.
  • the model can be used to investigate questions around the effect of therapies on local tissue Ang Il that, in turn, has an effect on renal function.
  • Using combinations of different classes of RAAS-modulating therapies to treat hypertension is of interest in drug development. Since none of the currently prescribed therapies can block 100% of Ang Il production, it is thought that inhibiting the pathway at multiple points in the pathway and within the tissue may provide a more complete blockade and have a better effect on reducing blood pressure. While there is a large body of RAAS biomarker data available for monotherapies, there is less complete data on the corresponding biomarker response to combination therapy due to a lack of resources to pursue all potential combinations and cost factor attached with any clinical trial.
  • ATI-bound Ang Il is the actual effector of the RAAS pathway and is not measured in the clinic. Instead, the changes in upstream biomarkers are used to estimate and compare the effectiveness of different classes of RAAS modulating therapies.
  • plasma renin activity (PRA) and plasma renin concentration (PRC) are typically measured in clinical trials but different classes of RAAS drugs affect these phenotypic data in different ways (e.g. DRIs reduce PRA, while ARBs and ACEi increase PRA) while still achieve measurable decreases in blood pressure. This makes it difficult to compare the relative level of the reduction in AT-1 bound Ang Il achieved by different mono and combination therapies.
  • the model described herein can be used to fill this gap, by predicting the relative % change in ATI-bound Ang Il (i.e., the effector of downstream changes in blood pressure, glomerular filtration rate, end-organ protection, etc) for different monotherapies and for combination therapies even in the absence of any direct measure or marker of drug efficacy.
  • the model was rigorously calibrated with phenotypic data (PRA and PRC) from a large number of studies for a range of RAAS-modulating monotherapies (e.g. aliskiren, valsartan, losartan, irbesartan, enalapril, ramipril).
  • the model was able to predict the phenotypic (PRA/PRC) response to combinations of RAAS drugs for which data was available, (e.g. aliskiren + valsartan), with no additional changes in model parameters.
  • the model can be used with confidence to predict the change in phenotype for different combination therapies when sufficient clinical data is not available to us. For example, it has been used to predict the phenotypic response for aliskiren 300mg + ramipril 10mg. In addition, the model predicts the relative % inhibition of ATI-bound Ang Il for the different doses and types of RAAS-modulating therapies. The strength of this integrated model lies in the prediction of ATI-bound Ang Il levels, a valuable measure of the primary effector of the downstream response of the RAAS pathway that is difficult to measure in vivo, and even more difficult to measure in the tissue.
  • This invention can include a single computer model that serves a number of purposes.
  • this invention can include a set of large-scale computer models covering a broad range of physiological systems.
  • the system can include complementary computer models, such as, for example, epidemiological computer models or models of related systems, e.g. atherosclerosis and its associated cardiovascular risk.
  • computer models can be designed to analyze a large number of subjects and chemicals.
  • the computer models can be used to create a large number of validated virtual patients and to simulate their responses to a large number of therapeutic regimens or changes in lifestyle.
  • the invention and all of the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structural means disclosed in this specification and structural equivalents thereof, or in combinations of them.
  • the invention can be implemented as one or more computer program products, i.e., one or more computer programs tangibly embodied in an information carrier, e.g., in a machine readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, e.g., a programmable processor, a computer, or multiple computers.
  • a computer program (also known as a program, software, software application, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
  • a computer program does not necessarily correspond to a file.
  • a program can be stored in a portion of a file that holds other programs or data, in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code).
  • a computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.
  • processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer.
  • a processor will receive instructions and data from a read only memory (ROM) or a random access memory (RAM) or both.
  • the essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data.
  • a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks.
  • Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks.
  • semiconductor memory devices e.g., EPROM, EEPROM, and flash memory devices
  • magnetic disks e.g., internal hard disks or removable disks
  • magneto optical disks e.g., CD ROM and DVD-ROM disks.
  • the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
  • the invention can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and/or a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer.
  • a display device e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor
  • a keyboard and/or a pointing device e.g., a mouse or a trackball
  • Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.
  • the invention can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the invention, or any combination of such back end, middleware, or front end components.
  • the components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN”) and a wide area network (“WAN”), e.g., the Internet.
  • LAN local area network
  • WAN wide area network
  • the computing system can include clients and servers.
  • a client and server are generally remote from each other and typically interact through a communication network.
  • the relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
  • Example 1 Hypertensive virtual patients [0170] In the context of one implementation of the invention, four exemplary hypertensive virtual patients were developed.
  • HT-1 an essential hypertensive patient with local vasoconstriction and atherosclerosis: Increased preglomerular resistance is a known cause of hypertension, and may be caused by increased sympathetic nervous activity and/or widespread atherosclerosis. While these disease etiologies have a systemic effect, HT-1 was represented in as a local increase in the renal afferent arteriole resistance leading to decreased perfusion of the kidneys to represent patients who may have plaques, obstructions or other factors leading to constriction of the renal artery. Simulations with the present model demonstrated that as the resistance of the afferent arteriole is increased, the GFR initially decreases due to a reduction of perfusion pressure into the glomerulus resulting in decreased sodium and water excretion.
  • HT-2 a diabetic hypertensive patient with diabetic nephropathy/glomerular damage:.
  • K f is the hydrostatic conductance of the glomerular membrane. It is a product of k (specific filtration coefficient), and S (the available surface area for filtration). Patients with nephropathy typically have a reduced K f due to the reduction of both k and S. Loss of endothelial fenestrae, a thickened glomerular basement membrane, and loss of epithelial slits between podocyte foot processes all change the filters integrity by reducing k and the ability to filter water and solutes. Similarly, mesangial expansion and glomerulosclerosis decrease the surface area available for filtration.
  • K f can also increase in the early stages of diabetic nephropathy; the structural change(s) responsible for hyperfiltration in the diabetic setting are unclear, although glomerular
  • K f glomerular filtration coefficient
  • HT-3 an essential hypertensive patient with increased sodium absorption in nephron.
  • a defective increase in sodium reabsorption in the descending portion of the loop of Henle is commonly associated with sodium-insensitive hypertension. Since these sections of the nephron are located upstream of the macula densa it is subjected to regulation by tubuloglomerular feedback (TGF) mechanisms.
  • TGF tubuloglomerular feedback
  • sodium reabsorption is increased in tubular segments located before the macula densa (e.g. LoH), a specialized group of epithelial cells part of the juxtaglomerular apparatus (JGA).
  • the JGA is located in the portion of the distal tubule that comes in close contact with the afferent and efferent arterioles. Increased sodium reabsorption delivers less sodium to the distal tubule and this is sensed by the macula densa. As a result, 1 ) afferent arteriole resistance is decreased (most likely mediated by local production of vasodilators) and, 2) renin production by JG cells is increased. Local generation of Ang Il causes an increase in efferent arteriole resistance. Together, the effects on pre- and post-glomerular resistance increase GFR and bring it back to normal. Direct effects of Ang Il on sodium reabsorption also contribute to restore sodium homeostasis.
  • each nephron excretes less than the amount required to maintain sodium homeostasis.
  • Sodium accumulates slowly over time and eventually suppresses renin release in an effort to increase excretion.
  • the abnormally high level of distal sodium and water reabsorption will continue and increase mean arterial pressure.
  • HT-4 an essential hypertensive patient with increased systemic vascular resistance: Essential hypertension has been traditionally viewed to be a result of increased arterial resistance. Early studies on the use of central antihypertensive agents (e.g. clonidine) demonstrated that a reduction in the central sympathetic outflow translated into reductions in mean arterial pressure. Initial attempts using an increased tubuloglomerular resistance (TPR) to generate hypertension was not successful. The kidney was capable of compensating for any changes in the resistance by altering water volume and ultimately affecting cardiac output. In order to reproduce hypertension due to increased TPR, HT-4 virtual patient is represented by all systemic arteries (including the renal artery) having increased resistance.
  • TPR tubuloglomerular resistance
  • TPR can be expanded to include renal resistance and the actions of Ang Il on both renal and systemic arteries.
  • a representative of essential hypertension was created by modulating total peripheral and renal resistances. Although this hypertensive patient is similar to HT- 1 , this patient will respond differently to therapies that target the total peripheral resistance
  • Atenolol Similar mechanistic grounds were utilized to implement additional non-RAAS and RAAS-based therapies. Renal, vascular and hormonal mechanisms were utilized including handling of sodium by the nephron, direct or indirect effects on renal hemodynamics, and effects on arterial vasoreactivity.
  • the effect of a drug is implemented according to the reported inhibition of a specific pathway, as well as a function of the drug concentration.
  • the latter is approximated by a temporal profile when concentration transitions from its minimal to its maximal value.
  • the normalized profile is multiplied by a certain dose resulting in a net effect.
  • concentration increases from 0 to 1 in the course of 24 hours.
  • the shape of the curve can be adjusted/customized using the appropriate object parameters. Specific functional forms are presented for each drug class.
  • thiazides e.g. hydrochlorotiazide, HCT
  • HCT hydrochlorotiazide
  • thiazide lowers the value of Q re abso P by a factor of (1 - C Th *i) where C is the thiazide normalized concentration and / is the level of inhibition.
  • Parameter / is dependent on the dose and could be calibrated to fit specific data on Na+ reabsorption or high level behavior.
  • the factor (1 - C*i) should be set at values between 0 and 1.
  • thiazides may affect other pathways.
  • the acute effects of thiazide therapy include a reduction of plasma and extracellular fluid volume.
  • prolonged treatment i. e. > 1 month
  • plasma volume and extracellular fluid volume return close to pre-treatment levels. Therefore, the effect on systemic hemodynamics do not fully account for the reduction in blood pressure.
  • a hypothesis formulated in the literature ascribes long-term effects of thiazide therapy to changes in vascular resistance. In the platform, both pathways are represented; their separate or combined action is defined by their respective value sets. Fig.
  • Furosemide is a loop diuretic which acts predominately at the apical membrane in the thick ascending limb of the loop of Henle (LoH); it inhibits Na + and Cl " reabsorption.
  • the furosemide-mediated diuretic effect is represented by reducing Na + reabsorption in the proximal nephron.
  • the filtered sodium load in the proximal tubule is split into two fractions, one of them, F LoH , is ascribed to the LoH; this portion of the sodium reabsorption fraction is affected only by furosemide, (eq. 29). It is known that about 25% of sodium reabsorption happens in the LoH, thus the following range was chosen 0.2 ⁇ F LoH ⁇ 0.3 .
  • ⁇ -Blockers [0185] ⁇ -Blockers (BBs).
  • the antihypertensive action of BBs involves reductions in cardiac output and renin release from the kidneys.
  • Beta blockers also have a central nervous system effect that reduces the activity of the sympathetic nervous system (sympathetic activity outflow).
  • renin release is stimulated by increases in renal sympathetic activity (rSNA), whereas Na+ flow is sensed by the macula densa.
  • rSNA renal sympathetic activity
  • Na+ flow is sensed by the macula densa.
  • rSNA is represented as a normalized baseline value N ⁇ SNA multiplied by the effect of MAP on rSNA and the effect of right atrial pressure (RAP) on rSNA.
  • Beta blockers therapy reduces the value of rSNA, its representation in the platform is similar to thiazide, see Eq (30).
  • the rSNA value was reduced by therapy by 25%.
  • mean arterial pressure was reduced by 5-14 mm Hg in simulations ran in the set of VP treated, and the reductions were in agreement with reported data.
  • CCBs Calcium channel blockers
  • CCB based drugs have multiple effects on the cardiovascular system including reduction in the force of contraction of the myocardium, reduction in heart rate, as well as vasodilation.
  • calcium channel blocker effects are implemented as a reduction in systemic arterial resistance, and renal arterial resistance. Renal arterial resistance is represented as three compartments considered separately preglomerular (pre-afferent arteriole) resistance, and afferent and efferent arteriole resistances. It is assumed that the CCB effect is more pronounced on the efferent arteriole compared to the afferent, allowing more blood filtering through the glomerulus.
  • pre-afferent arteriole preglomerular resistance
  • FIG. 13 shows a mean arterial pressure reduction of approximately 10 mmHg with a CCB therapy applied to a hypertensive VP with elevated preglomerular resistance.
  • the therapy reduced efferent arteriole resistance by 50%, while afferent arteriole resistance was reduced by 15%.
  • ACE inhibitors in the RAAS PhysioLab platform affect several pathways involving different enzymatic activities A mempy . Mathematically, they are all similarly represented as a product of uninhibited activity A 0 and therapy effect, which in turn is defined by the degree of activity inhibition / [0188]
  • ACE inhibition therapy directly affects the activity of ACE, an enzyme that catalyzes the conversion of Ang I to Ang Il both in the systemic circulation and the intrarenal glomerular and tubular compartments. It is hypothesized that peritubular tissue may also contribute to the pool of Ang Il production in the kidney and that fraction also is affected by ACE inhibition therapy.
  • a T1 receptor blocker (ARB) ARBs block the activation of type I Ang Il receptors (AT1 ). In the model disclosed herein, AT1 receptors are split between three compartments.
  • ARB therapy affects Ang Il binding rates and have a similar functional form in all compartments: where r and r 0 are binding rates with and without therapy, T is therapy inhibition effect and C ARB is the concentration of the drug.
  • the values of 7 are selected from calibration experiments and specified in the parameter set describing ARB effects, the values of r 0 are calculated at equilibrium.
  • Additional mechanisms affected by AT1 receptor blocking therapy are included in the model. For instance, ARB therapy may affect Ang Il clearance rate by altering Ang Il degradation time constants.
  • Fig. 14 shows an example on how AT1 receptor blocking therapy changes mean arterial pressure in various virtual patients when binding rates were reduced a factor of 200, while degradation rates were reduced by a factor of only 5.
  • DRIs interrupt the RAAS system by binding and preventing the action of renin and thereby inhibiting the formation of Ang I and Ang II.
  • DRI therapy effects are split into two compartments, a systemic circulation compartment and an intrarenal compartment. In the latter, DRI therapy affects glomerular and tubular angiotensinogen conversion to Ang I by membrane bound renin.
  • inhibition of plasma renin activity by DRI therapy was implemented according to the following equation:
  • Aldosterone Antagonists were lumped into one effect that alters aldosterone secretion rate: CW, where Q° a ido is the nominal aldosterone secretion rate, T a ⁇ d0 is the inhibition effect of the therapy, and C a/(to is the concentration of the drug.
  • Fig. 14 depicts simulation results on MAP changes with an aldosterone antagonist that reduced the normalized secretion rate by 90%.
  • Type 2 diabetic (T2D) disease nephropathy and progression of renal damage was calibrated using clinical data from a study conducted by Nelson et al in Pima Indians (N Eng J Med 335(22): 1636-42 (1996). The study recruited 6 groups of adult subjects with pre-defined characteristics including
  • ITT impaired glucose-tolerance
  • Urinary albumin was measured in mg/l and creatinine in g/l. Microalbuminuria was defined as UACRs of 30-299, whereas macroalbuminuria as UACRs >300. GFR and albumin excretion rates were used to match the reported clinical behavior.
  • RAAS-related peptides in the kidney was simulated using a mathematical model of renal and systemic RAAS kinetics according to the present invention.
  • the model accounts for the renal production and release of Ang I, Ang II, Ang 1-7 and Ang IV.
  • Systemic and local levels of RAAS- related peptides were estimated based on published plasma and whole renal tissue data.
  • the model considers a single renal compartment localized to the glomerulus. Local glomerular rate of renin activity, angiotensin converting enzyme activity (ACE) and degradation rates are different than in the circulation to satisfy constraints observed in radiolabeled Ang I studies by Danser et al., 1998.
  • ACE angiotensin converting enzyme activity
  • renin-angiotensin aldosterone system plays a critical role in blood pressure regulation, renal function and fluid homeostasis.
  • Ang Il concentration in renal tissue is -10 times higher than that of plasma and raises questions about the contribution of intrarenal Ang Il to renal function and disease progression.
  • the model predicted that degradation of locally synthesized Ang I as well as circulating Ang I entering the kidney lowers the local levels of Ang Il but has little measurable impact on their circulating levels.
  • Pharmacological stimulation of renal Ang I degradation and/or inhibition of Ang I to Ang Il paracrine conversion may have therapeutic implications in preventing progression of diabetic and hypertensive nephropathy.

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Abstract

L'invention concerne de nouveaux modèles informatiques de l'hypertension et des systèmes pour prédire le développement et la progression de l'hypertension et des états pathologiques associés, notamment l'insuffisance cardiaque, les accidents cérébrovasculaires et les maladies rénales. En particulier, le modèle informatique de l'hypertension comprend un module de voie RAAS, un module de fonction rénale, et un module de régulation de la pression sanguine.
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Cited By (2)

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CN110738927A (zh) * 2019-10-29 2020-01-31 中南大学湘雅医院 一种多功能高灵敏度肾小球滤过率显示器
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