Techniques for modeling parathyroid function and calcimimetic drug activity

Abstract

The described techniques may include processes for modeling parathyroid gland (PTG) function and / or calcimimetic administration to patients with health abnormalities that affect PTG function. In one embodiment, a method may include providing a PTG function model configured to simulate the function of the PTG of a patient with at least one health abnormality that affects PTG function, the model may receive parameters configured to modulate calcium sensing receptor (CaSR) activity, the parameters may include calcium concentration, vitamin D concentration, and phosphorus concentration, simulate CaSR expression and vitamin D receptor (VDR) expression via a positive feedback loop between CaSR expression and VDR expression and inhibit CaSR expression and VDR expression through P, initiate at least one PTG adaptation based on the multiple parameters, and determine a model output comprising parathyroid hormone (PTH) concentration at one or more time intervals. Other embodiments are also described.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application Ser. No. 62 / 747,540, filed on October 18, 2018, entitled “Models, Multi-Compartment Models, and Techniques for Modeling Pharmacokinetics of the Calcimimetic Cinacalcet,” the contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates generally to processes for modeling the function of parts of the human body to generate healthcare recommendations, and more specifically to techniques for modeling the function of the parathyroid gland (PTG) and the activity of calcimimetic compounds. Background Art

[0004] The concentration of extracellular ionized calcium is maintained within a narrow physiological range via a biological system of negative and positive feedback regulators involving the major organs that transport calcium and phosphate, including the intestines, kidneys, bones, and endocrine glands with the parathyroid glands (PTG) being the most prominent regulator. In patients with certain abnormal health conditions, such as chronic kidney disease (CKD), the loss of regulatory renal function triggers a series of processes that ultimately lead to disruption of the ionized calcium regulatory system and associated health conditions, such as secondary hyperparathyroidism.

[0005] Clinical research is an important tool for understanding the calcium ion regulatory system in patients, especially those with abnormal health conditions. However, clinical research is expensive, time-consuming and resource-intensive. Therefore, in some cases, virtual models of biological systems, such as PTG, can be used to evaluate function and treatment without the need for actual patients, regulations and costs. In addition, virtual models can provide a large amount of biological information in a smaller time frame. Although some conventional models for modeling PTG function have been described, such modeling is limited. For example, conventional models cannot accurately reflect PTG function in patient populations with health abnormalities that affect PTG, such as CKD.

[0006] With regard to these and other considerations, improvements of the present invention may be useful. Summary of the invention

[0007] This Summary is provided to introduce some concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to necessarily identify key features or essential features of the claimed subject matter, nor is it intended to be an aid in determining the scope of the claimed subject matter.

[0008] According to various aspects of the described embodiments, a computer-implemented method for virtual parathyroid gland (PTG) function analysis may include providing a PTG function model via a processor of a computing device, the PTG function model being configured to simulate the PTG function of a patient having at least one health abnormality affecting the PTG function, the model being operable to: receive a plurality of parameters configured to modulate the activity of a calcium-sensing receptor (CaSR), the plurality of parameters comprising calcium concentration, vitamin D concentration, and phosphorus concentration; simulate CaSR expression and vitamin D receptor (VDR) expression via a positive feedback loop between CaSR expression and VDR expression and inhibiting CaSR expression and VDR expression by P; initiate at least one PTG adaptation based on the plurality of parameters; and determine a model output comprising a parathyroid hormone (PTH) concentration at one or more time intervals.

[0009] In some embodiments of the method, the at least one health abnormality includes one of chronic kidney disease (CKD), hypoparathyroidism, hyperparathyroidism, hypocalcemia, hypercalcemia, or hyperphosphatemia. In various embodiments of the method, the model is operable to downregulate at least one of the PTH release rate, production rate, or proliferation rate in response to calcium concentration, vitamin D concentration, and phosphorus concentration being within an optimal range. In some embodiments of the method, the model is operable to initiate at least one PTG adaptation in response to one of the multiple parameters being outside the optimal range for a critical time period. In various embodiments of the method, the calcium concentration includes one of ionized calcium (Ca2+) or a calcimimetic concentration determined via a calcimimetic model. In an exemplary embodiment of the method, the model can be used to promote at least one PTG adaptation using at least one stimulation function in response to a deviation from the optimal range for one of the multiple parameters.

[0010] In some embodiments of the method, the at least one stimulation function is determined based on:

[0011]

[0012] Among them, K w and W1 is a constant,

[0013] Among them, C is the calcium concentration, D is the vitamin D concentration, and P is the phosphorus concentration.

[0014] In various embodiments of the method, CaSR expression and VDR expression can be determined based on:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Among them, Ca opt Including optimal blood values ​​for calcium, D opt Including optimal blood values ​​of vitamin D, P opt Includes optimal blood values ​​for phosphorus, P includes serum phosphate concentration,

[0021] Among them, p Ca and p D Determine the intensity of stimulation and feedback, p Ca and n Ca and p D and n D The relationship between determines the equilibrium of the system, where Ca in , D in and P in is the factor that determines the effect of stimulation on CaSR expression and VDR expression, where τ c , τ D and τ P is the time constant that can be used to determine the rate of convergence to a steady state following a step change in calcium, vitamin D, or phosphate concentration.

[0022] In various embodiments of the method, the PTG functional model determines the sensed calcium concentration (CS) based on:

[0023]

[0024]

[0025] (8) sens(x) = A S +(1-A S )·(x / 2),

[0026] Where C is the calcium concentration, D is the vitamin D concentration,

[0027] Among them, A S is the maximum decay rate.

[0028] In an exemplary embodiment of the method, the method may include determining at least one treatment recommendation based on the model output.

[0029] According to various aspects of the described embodiments is a computer-implemented method for virtual parathyroid gland (PTG) function analysis, the method may include providing a calcimimetic model via a processor of a computing device, the calcimimetic model being configured to simulate the administration of a calcimimetic compound to a patient having at least one health abnormality affecting PTG function, the calcimimetic model being operable to: receive a calcimimetic dose; determine a concentration of the calcimimetic compound in at least one of a plurality of physiological compartments, each of the plurality of physiological compartments being respectively related to an adjacent physiological compartment via at least one constant rate function; and determine an output of a total calcimimetic concentration for at least one time period.

[0030] In some embodiments of the methods, the calcimimetic compound can comprise cinacalcet.

[0031] In various embodiments of the methods, the plurality of physiological compartments includes an absorption compartment, a first-pass metabolism compartment, a plasma free drug compartment, a plasma protein binding compartment, a fast tissue compartment, and a slow tissue compartment.

[0032] In some embodiments of the method, the absorption compartment is arranged adjacent to the first-pass metabolism compartment and is connected via k a In various embodiments of the method, the calcimimetic model can be used to simultaneously determine multiple pharmacokinetic parameters, including C max ,t max 、Bio、CL / F、t 1 / 2 , and VD. In an exemplary embodiment of the method, the output is provided as a calcium concentration input to a PTG functional model. In some embodiments of the method, the output is provided as a calcium concentration input to a PTG functional model via an allosteric operational model configured to shift calcium concentration based on the amount of free drug in plasma.

[0033] In various embodiments of the methods, the calcimimetic model can be used to determine the amount of calcimimetic compound in each compartment based on:

[0034]

[0035] In some embodiments of the method, corresponds to the amount of calcimimetic compound in the absorptive compartment, corresponds to the amount of calcimimetic compound in the first-pass metabolic compartment, corresponds to the amount of calcimimetic compound in the plasma free drug compartment, corresponds to the amount of calcimimetic compound in the plasma protein binding compartment, Corresponds to the amount of calcimimetic compound in the fast tissue compartment.

[0036] In various embodiments of the method, the coefficient matrix A may be configured as follows:

[0037] BRIEF DESCRIPTION OF THE DRAWINGS

[0038] By way of example, certain embodiments will now be described with reference to the accompanying drawings, in which:

[0039] Figure 1 A first exemplary operating environment according to the present disclosure is shown;

[0040] Figure 2A A first block diagram of a parathyroid gland (PTG) functional model according to the present disclosure is shown;

[0041] Figure 2B shows a second block diagram of a PTG functional model according to the present disclosure;

[0042] Figure 3A A first block diagram of a calcimimetic model according to the present disclosure is shown;

[0043] Figure 3B shows a second block diagram of a calcimimetic model according to the present disclosure;

[0044] Figure 4 Plotted the release rate of parathyroid hormone (PTH) as a function of ionized calcium (Ca) according to the present disclosure. 2+ )Changed graph;

[0045] Figure 5 A table depicting an illustrative basic parameter set for PTG, PTH release and intracellular degradation according to the present disclosure;

[0046] Figure 6 A table depicting an illustrative basic parameter set for stimulation functions according to the present disclosure;

[0047] Figure 7 depicts a table of exemplary basic parameter sets for time constants and intensity parameters for stimulation functions according to the present disclosure;

[0048] Figure 8 depicts a graph of the sensitivity of PTH prediction according to the present disclosure to changes in various parameters;

[0049] Fig. 9 Depicts the effect of time on Ca according to the present disclosure 2+ and plots of predicted PTH concentrations;

[0050] Fig.10 Depicts the effect of time on Ca according to the present disclosure 2+ and plots of predicted PTH concentrations;

[0051] Fig.11 Depicts the time versus relative Ca according to the present disclosure. 2+ and plots of relative PTH concentrations;

[0052] Fig.12 Depicts the effect of time on Ca according to the present disclosure 2+ and plots of predicted PTH concentrations;

[0053] Fig.13 depicts a graph of time versus PTH concentration according to the present disclosure;

[0054] Fig.14 depicts a graph of time versus relative phosphorus (P) and vitamin D (1,25D) and relative PTH concentrations according to the present disclosure;

[0055] Fig.15 depicts a graph of time versus Cinacalcet (C) concentration according to the present disclosure;

[0056] Fig.16 depicts a graph of time versus Cinacalcet (C) concentration according to the present disclosure;

[0057] Fig.17 depicts a graph of time versus Cinacalcet (C) concentration according to the present disclosure;

[0058] Fig.18 depicts a graph of time versus Cinacalcet (C) concentration according to various dosing regimens of the present disclosure;

[0059] Fig.19 a table depicting model parameters for a calcimimetic model according to the present disclosure;

[0060] Fig. 20 depicts results generated via simulations using a calcimimetic model in accordance with the present disclosure;

[0061] Fig.21 An embodiment of a computing architecture according to the present disclosure is shown. DETAILED DESCRIPTION

[0062] The present embodiment will now be described more fully below with reference to the accompanying drawings, in which several exemplary embodiments are shown. However, the subject matter of the present disclosure can be implemented in many different forms and should not be construed as being limited to the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure will be thorough and complete, and the scope of the subject matter will be conveyed to those skilled in the art. In the accompanying drawings, similar reference numerals always refer to similar elements.

[0063] Altered parathyroid biology in patients with chronic kidney disease (CKD) is a major contributor to chronic kidney disease-mineral bone disease (CKD-MBD). The disease is associated with bone disease, vascular calcification, and an increased risk of cardiovascular events. The secretion of parathyroid hormone (PTH) is primarily regulated by calcium concentration (Ca or Ca2+) in the extracellular fluid and calcitriol, the biologically active form of vitamin D (D or 1,25D). 2+ ) and the regulation of phosphate concentration (P). Metabolic disturbances in CKD patients may lead to altered parathyroid gland (PTG) biology. The hallmark of CKD is secondary hyperparathyroidism, which is characterized by increased production and release of parathyroid hormone, decreased expression of calcium-sensitive and vitamin D receptors on the surface of parathyroid cells, and hyperplasia and hypertrophy of these cells. These changes occur on different time scales and influence each other, triggering a highly complex cascade of negative and positive feedback loops. Due to this complexity, models can be used, among other things, to decompose the patterns of multidimensional cascades of processes and to conduct detailed studies of subsystems.

[0064] In some embodiments, the PTG analysis process may use a PTG functional model that includes the primary adaptive mechanisms that control the production and secretion of PTH in patients with certain health abnormalities, such as CKD (e.g., and in hemodialysis (HD)). In addition, the PTG analysis process may include or use a model of a parathyroid targeted drug, such as a calcimimetic model that simulates the administration of a calcimimetic compound (e.g., a cinacalcet compound). Although the PTG analysis process (including the PTG functional model and / or the calcimimetic model) may be used in the example of HD patients with secondary hyperparathyroidism described herein, the embodiments are not limited thereto as they are applicable to other clinical situations, such as primary hyperparathyroidism, hypocalcemia, and / or hypercalcemia, etc. In addition, although cinacalcet is used as an exemplary calcimimetic compound, the embodiments are not limited thereto as any calcimimetic compound, such as eticlipide, that is capable of operating according to some embodiments is contemplated herein.

[0065] The concentration of extracellular ionized calcium is maintained within a narrow physiological range by a biological system of negative and positive feedback regulators involving the major organs that transport calcium and phosphate, such as the intestine, kidney, bone, endocrine glands, and most prominently the PTG. Under normal conditions, the extracellular ionized calcium concentration (Ca 2+ ) is maintained in a narrow range of approximately 1-2%.

[0066] Serum Ca 2+The key endocrine regulator of calcium is PTH, which increases serum calcium levels by enhancing tubular calcium reabsorption, stimulating net bone resorption, and increasing the production of activated vitamin D (1,25-dihydroxyvitamin D3 or 1,25(OH)2D3), which increases net calcium absorption in the intestine. PTH is produced, stored, and ultimately released by PTG. PTG consists of two cell populations: active secretory cells and quiescent cells, which are capable of either proliferation or apoptosis. Active secretory cells produce, store, and release PTH. PTG activity itself is primarily regulated by the calcium-sensing receptor (CaSR) on the surface of PTG cells.

[0067] The CaSR is integrally involved in PTG function and biology and is therefore key to understanding pathologies such as secondary hyperparathyroidism. 2+ To activate CaSR, several signaling pathways are initiated that downregulate the release and production of PTH and the proliferation rate of PTG cells. In addition, CaSR regulates the stability of PTH mRNA, thereby mediating its degradation rate. In addition to controlling the secretion, synthesis, degradation of PTH and PTG proliferation, CaSR can also upregulate the expression of vitamin D receptor (VDR).

[0068] PTG is able to rapidly adapt to conditions that require enhanced PTH secretion, such as hypocalcemia. Different adaptive responses are manifested on significantly different time scales, ranging from minutes to hours, days to weeks. For example, in the case of acute hypocalcemia, PTG responds rapidly by releasing stored PTH within seconds to minutes. If hypocalcemia persists, the intracellular PTH degradation rate will decrease within 20 minutes, thereby increasing the amount of intact PTH that can be released. If normal blood calcium levels are still not reached, the rate of PTH production will increase within an hour. Subsequently, PTG will increase its cell proliferation rate within two days. In chronic hypokalemia, the increased proliferation rate will lead to hyperplasia, thereby increasing the mass of PTG by 10-100 times or more.

[0069] In patients with chronic kidney disease (CKD), loss of regulatory renal function triggers a cascade of processes that culminate in secondary hyperparathyroidism, an abnormality characterized by increased PTH synthesis and secretion and proliferation of PTG cells. A hallmark of CKD is impaired renal synthesis of 1,25-dihydroxyvitamin D3 (1,25D), the major bioactive form of vitamin D, and markedly impaired renal clearance of phosphate. Both 1,25D and phosphate significantly affect CaSR regulation, which in turn affects PTH synthesis and release and PTG proliferation. A positive feedback loop exists between CaSR and vitamin D receptor (VDR) expression, which is inhibited by high phosphate levels. The pathological effects of high phosphate levels are significant. For example, studies in uremic rats have shown that a high phosphate diet enhances PTG proliferation within a few days. Low calcium intake has similar results, but over a significantly longer period of time. Importantly, the positive feedback loop between CaSR and VDR is effectively attenuated under high phosphate levels.

[0070] In CKD, PTH stimulates bone resorption during bone formation, leading to Ca 2+ As a result, PTH and phosphate levels increase even further, and the expression of CaSR and VDR is suppressed, thereby reducing PTG's response to Ca 2+ and 1,25D sensitivity. Altered biology ultimately leads to PTG hyperplasia and secondary hyperparathyroidism.

[0071] Due to the complexity of the biological adaptability of PTG in CKD patients on hemodialysis, some embodiments may provide a PTG analysis process that may include a PTG functional model to analyze, evaluate, simulate, or otherwise examine PTG under abnormal health conditions, such as secondary hyperparathyroidism, and determine the best treatment strategy. Combined with mathematical models such as bone turnover, intestinal calcium absorption, and / or phosphate absorption, the PTG analysis process according to some embodiments may provide key elements of a bioinformatics model of PTG abnormalities such as secondary hyperparathyroidism in CKD and HD patients, for example. Therefore, the PTG analysis process according to some embodiments may be used to generate predictions about the development of CKD-MBD and / or the treatment of CKD-MBD.

[0072] Although there are multiple models of PTH activity in humans, conventional techniques fail to capture the key adaptive mechanisms of the complex network that regulates PTH and calcimimetic activity, particularly in patients with CKD or other health abnormalities that may affect PTG function. In addition, due to the widespread clinical use of calcimimetic agents, such as cinacalcet, practical CKD-MBD models should be characterized by the use of calcimimetic agents and their effects. In addition, calcimimetic models should be easily adaptable to various situations in the clinic, such as cinacalcet exposure enhanced by liver injury, and should be able to reflect different dosing regimens, including patient compliance with calcimimetic treatment regimens, but they perform poorly due to various issues.

[0073] Thus, some embodiments may provide a PTG analysis process that may include various models to determine the expression of CaSR and the expression of ionized calcium (Ca or Ca). 2+ ), phosphate (P) and vitamin D (D or 1,25D)-regulated activities to mimic the function and / or calcimimetic activity of PTG. Some embodiments may provide a multi-compartment calcimimetic model based on physiological considerations that capture all major pharmacokinetic parameters of a calcimimetic compound, such as cinacalcet.

[0074] Thus, the PTG analysis process according to some embodiments may provide additional technical advantages and technical features over conventional systems, including improvements in computing technology. A non-limiting example of a technical advantage may include modeling various mechanisms to ensure that elevated PTH levels act on different time scales, thereby allowing predictions to be made for rapid responses (e.g., in the case of induced acute hypocalcemia), as well as reflecting the transformation of a healthy PTG to a Ca-responsive PTG. 2+ and long-term adaptability of hyperplastic glands with reduced 1,25D sensitivity. Another non-limiting example of a technical advantage may include providing a calcimimetic model that is operable to provide intuitive personalized settings for various conditions or dosing regimens and ignore numerical instabilities for easy implementation in other physiological models (e.g., a PTG functional model according to some embodiments). Another non-limiting example of a technical advantage may include providing a PTG analysis process that can use virtual simulations of PTG functionality and / or calcimimetic administration to generate treatment recommendations and / or determine research results without the need for clinical studies with actual patient participants. Other technical advantages are provided in this detailed description. The embodiments are not limited to this context.

[0075] Figure 1 An example of an operating environment 100 that may represent some embodiments is shown. Figure 1As shown, operating environment 100 may include PTG analysis system 105. In various embodiments, PTG analysis system 105 may include computing device 110 communicatively coupled to network 170 via transceiver 160. In some embodiments, computing device 110 may be a server computer or other type of computing device.

[0076] According to some embodiments, computing device 110 may be configured to, among other things, manage operational aspects of the PTG analysis process. Figure 1 Only one computing device 110 is depicted in the figure, but the embodiments are not limited in this regard. In various embodiments, the functions, operations, configurations, data storage functions, applications, logic, etc. described with respect to computing device 110 may be performed by and / or stored in one or more other computing devices (not shown) coupled to computing device 110, for example, via network 150 (e.g., one or more of client or peer devices 170). For illustrative purposes, a single computing device 110 is depicted only for the purpose of simplifying the figure. The embodiments are not limited in this context.

[0077] According to some embodiments, the computing device 110 may include a processor circuit that may include and / or have access to various logics for performing processing. For example, the processor circuit 120 may include and / or have access to PTG analysis logic 122, PTG functional logic 124, and / or calcimimetic logic 126. The processor circuit 120, PTG analysis logic 122, PTG functional logic 124, calcimimetic logic 126, and / or portions thereof may be implemented in hardware, software, or a combination thereof. As used in this application, the terms "logic", "component", "layer", "system", "circuit", "decoder", "encoder", "control loop", and / or "module" are intended to refer to a computer-related entity, which may be hardware, a combination of hardware and software, software, or software in execution, examples of which are provided by the exemplary computing architecture 2100. For example, logic, circuits, or modules may be and / or may include, but are not limited to, a process running on a processor, a processor, a hard drive, multiple storage drives (of optical and / or magnetic storage media), an object, an executable file, an execution thread, a program, a computer, a hardware circuit, an integrated circuit, an application specific integrated circuit (ASIC), a programmable logic device (PLD), a digital signal processor (DSP), a field programmable gate array (FPGA), a system on a chip (SoC), a memory cell, a logic gate, a register, a semiconductor device, a chip, a microchip, a chipset, a software component, a program, an application, firmware, a software module, computer code, a control loop, a computational model or application, an AI model or application, an ML model or application, a proportional integral derivative (PID) controller, variations thereof, combinations of any of the foregoing, and / or the like.

[0078] Although PTG analysis logic 122 Figure 1 140, and the like. For example, PTG analysis logic 122, PTG function logic 124, calcimimetic logic 126, and / or any components thereof may be located within an accelerator, a processor core, an interface, a separate processor die, may be fully implemented as a software application (e.g., PTG analysis application 140), and / or the like.

[0079] The memory unit 130 may include various types of computer-readable storage media and / or systems in the form of one or more high-speed memory units, such as read-only memory (ROM), random access memory (RAM), dynamic RAM (DRAM), double data rate DRAM (DDRAM), synchronous DRAM (SDRAM), static RAM (SRAM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, polymer memory such as ferroelectric polymer memory, Osborn memory, phase change or ferroelectric memory, silicon-oxide-nitride-oxide-silicon (SONOS) memory, magnetic or optical cards, arrays of devices such as redundant array of independent disks (RAID) drives, solid-state storage devices (e.g., USB memory, solid-state drives (SSDs), and any other type of storage medium suitable for storing information. In addition, the memory unit 130 may include various types of computer-readable storage media in the form of one or more low-speed memory units, including internal (or external) hard disk drives (HDDs), magnetic floppy disk drives (FDDs), and optical disk drives that can read or write from removable optical disks (e.g., CD-ROMs or DVDs), solid-state drives (SSDs), and / or the like.

[0080] According to some embodiments, the memory unit 130 may store various types of information and / or applications for the PTG analysis process. For example, the memory unit 130 may store PTG function information 132, calcimimetic information 134, treatment recommendations 136, and / or PTG analysis applications 140. In some embodiments, some or all of the PTG function information 132, calcimimetic information 134, treatment recommendations 136, and / or PTG analysis applications 140 may be stored in one or more data storage areas 152a-n accessible to the computing device 110 via the network 150. For example, one or more of the data storage areas 152a-n may be or may include a HIS, an EMR system, a dialysis information system (DIS), a picture archiving and communication system (PACS), a Centers for Medicare and Medicaid Services (CMS) database, a United States Renal Data System (USRDS), a proprietary database, and the like.

[0081] In some embodiments, PTG analysis logic 122 may operate, for example, via PTG function logic 124 and / or PTG analysis application 140 , to simulate PTG functions via a PTG model. Figure 2A and 2B An illustrative PTG functional model according to some embodiments is depicted. Figure 2A , which shows a PTG functional model 205 that is operable to receive a plurality of inputs or parameters 210a-n associated with the functionality of various aspects of the PTG and generate outputs 220. In various embodiments, the inputs 210a-n may include calcium concentration 210a, vitamin D (1,25D) concentration 210b, phosphorus concentration 210c, calcimimetic concentration 210d (e.g., via a calcimimetic model according to certain embodiments). In some embodiments, the Ca used in the PTH prediction in the PTG functional model 205 is 2+ , 1,25D and P curves can be simulated curves. In various embodiments, the bioinformatics data used as input 210a-n of the PTG functional model 205 can be in the physiologically meaningful range Ca 2+ In certain embodiments, ionized calcium concentration 210a may be correlated to the PTG response via the CaSR. 2+ , 1,25D and P can be considered as the main parameters.

[0082] In an exemplary embodiment, output 220 may be PTG adaptation associated with a primary adaptive mechanism that controls the production and secretion of PTH in a patient with a health abnormality that affects PTH function (e.g., a patient with CKD in HD). In various embodiments, output 220 may be PTH concentration 222 and / or calcium concentration 224, such as ionized calcium (Ca or Ca 2+ ) concentration, for example at one or more specific time intervals (see, for example Fig.10 and 11 ) sensed calcium concentration (e.g., active concentration on the CaSR).

[0083] refer to Figure 2B , which depicts a PTG functional model 205 having a model structure 230. The core of the PTG functional model 205 is CaSR. For the model structure 230, although there is a positive feedback loop between VDR and CaSR, phosphate may inhibit CaSR and VDR expression.

[0084] In some embodiments, the PTG functional model 205 does not model the structure of the CaSR; instead, the PTG functional model 205 may use some physiological principles that control the signaling cascades triggered by the CaSR: (1) If all key parameters (e.g., Ca2+ , 1,25D and phosphate) are all within their optimal ranges, the CaSR signal will ensure that the release rate, production rate and proliferation rate of PTH are downregulated to their basal values ​​and the intracellular degradation rate remains constant; (2) if one or more key parameters are not within their optimal ranges for a critical amount of time, the CaSR signal changes, thereby causing the PTG to adapt the PTH release rate, intracellular PTH degradation rate, PTH production rate and cell proliferation. The critical amount of time varies significantly for different CaSR signaling pathways, being measured in seconds for release rates, minutes for degradation rates, hours for production rates, and days for proliferation rates; (3) because feedback loops act on the CaSR, changes in signaling also change CaSR expression over time, for example, less CaSR expression results in reduced sensitivity of the PTG to blood ionized calcium concentrations; (4) The PTG functional model 205 can use a stimulus function that describes deviations from the optimal range, for example, negative stimuli can correspond to values ​​below the optimal range, while positive stimuli can correspond to values ​​above the optimal range; (5) The stimulus function for all adaptation mechanisms may be the same, for example, the stimulus function can be configured so that small deviations from the optimal value do not trigger a response unless these deviations persist for a long time; (6) Except for proliferation, all other effects are reversible, for example, if a condition such as acute hypocalcemia is resolved, the PTH synthesis rate, intracellular degradation rate, and cell proliferation rate may return to baseline; however, since the apoptosis rate can be assumed to be constant, the size of the PTG may not decrease. However, in some cases, PTG size may be reduced if treated with certain drugs, such as calcimimetics. They act on the rate of apoptosis as well as the rate of proliferation.

[0085] refer to Figure 1 The PTG function information 132 may include information associated with the PTG function logic 124, such as input information, parameters, models, model structures, outputs, thresholds, limits, constants, algorithms, equations, and / or the like. The embodiments are not limited in this context.

[0086] In some embodiments, the PTG analysis logic 122 may operate, for example, via the calcimimetic logic 124 and / or the PTG analysis application 140 , to simulate calcimimetic administration via a calcimimetic model. Figure 3A and 3B Depicted is an illustrative calcimimetic model according to some embodiments. Figure 3A , wherein a calcimimetic model 305 is depicted that is configured to receive an administered calcimimetic concentration 310 as input and generate a virtual patient calcimimetic concentration 315 as output.

[0087] In some embodiments, the calcimimetic model 305 can be a multi-compartment model. Figure 3B, wherein a calcimimetic model 305 having a multi-compartment structure 330 is depicted. For example, in some embodiments, the calcimimetic model 305 may include six compartments, including but not limited to an absorption compartment, a first-pass metabolism compartment, a plasma free drug compartment, a plasma protein binding compartment, a fast tissue compartment, and / or a slow tissue compartment. Although the calcimimetic model 305 may be described as having six compartments, embodiments are not limited thereto, as the calcimimetic model 305 may include more or fewer compartments. For example, in some embodiments, the calcimimetic model 305 may not include a slow tissue compartment.

[0088] The calcimimetic information 134 may include information associated with the calcimimetic logic 126, such as input information, parameters, models, model structures, outputs, thresholds, limits, constants, algorithms, equations, and / or the like. For example, to assess the effect of dosing regimen on total exposure, the calcimimetic model 305 may use the average weekly calcimimetic (e.g., cinacalcet) concentration in the blood for three different dosing regimens: daily dosing, three times weekly dosing, and dosing with an actual patient replenishment rate of 64%. The embodiments are not limited in this context.

[0089] refer to Figure 1 , the PTG analysis logic 122 may be operable to determine the various Ca 2+ , 1,25D and / or P input) and calcimimetic activity (e.g., cinacalcet concentrations at certain time intervals for a particular dosing regimen). In some embodiments, the PTG analysis logic 122, alone or in conjunction with the PTG analysis application, can generate one or more treatment recommendations 136 based at least in part on information generated by a PTG functional model and / or a calcimimetic model according to an exemplary embodiment. For example, a PTG functional model can be developed for certain patient populations (e.g., age, weight, disease state, health abnormalities, and / or the like). In another example, a calcimimetic model can be generated for certain patient populations and / or dosing regimens. The PTG analysis logic 122 can determine treatment recommendations for patients appropriate for the model patient population to generate potential treatment recommendations 136. In some embodiments, the treatment recommendations 136 can include a diagnosis of an abnormal health condition, a potential cause of an abnormal health condition, and / or the like.

[0090] In some embodiments, for a PTG functional model (e.g., model 205), CaSR and VDR expression are determined to assess the overall sensitivity of the receptor to blood ionized calcium concentration and 1,25D concentration. The PTG functional model may include or may use dimensionless CaSR and VDR expression. For both variables, the optimal value may be normalized to 1. Values ​​less than 1 may correspond to a loss of CaSR or VDR expression. Receptor expression may be regulated by a positive feedback loop between CaSR and VDR ( Figure 2B ), and can be inhibited by phosphate. Conventional methods generally involve delay equations. However, these equations are numerically very unstable, and even simulating months with delay equations is challenging (or even impossible). Therefore, some embodiments may use feedback loops or equations described herein to simulate changes in PTG biology, which can be used to enable rapid, accurate, and realistic modeling of PTG biology.

[0091] In some embodiments, dimensionless CaSR expression, CaSR and VDR expression, VDR are governed by the following system of differential equations (1)-(8):

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Among them, Ca opt ,D opt and P opt It is Ca 2+ , 1,25D and phosphate. CS and DS are defined in the following equations (6) and (8), and Ca 2+ The actual blood values ​​of Ca and 1,25D are linked to the receptor density. P is the serum phosphate concentration. The intensity of stimulation and feedback may be controlled by pCa and pD, and the relationship between pCa and nCa and between pD and nD determines the balance of the system. in , D in and P in The time constant τ is the factor that determines the effects of Ca, D, and P stimulation on the CaSR and VDR, respectively. c , τ D and τ P Determine the convergence rate to reach steady state after a step change in calcium, 1,25D and / or phosphate. They are related to the critical time at which the system starts to respond to non-optimal concentrations of ionized calcium, 1,25D or phosphate. The stimulus function can be written according to the following equation (StFx):

[0098] (StFx):

[0099]

[0100] where K and W1 are constants. Under optimal conditions, the stimulation functions of calcium, 1,25D, and phosphate may be zero. Therefore, Ca in , D in , and P in If the deviation from the optimal range is shorter than the critical time associated with the time constant, such as a brief induced hypocalcemia, the CaSR and VDR expressions are unchanged. in The stimulation is too small to significantly change Ca in Therefore, CaSR expression will not be altered. However, in cases of mild but chronic hypocalcemia, due to Ca in The stimulation is small but continuous, and CaSR expression will slowly decrease after a period of time.

[0101] Lower CaSR density may result in less downstream signaling. Thus, the same actual Ca 2+ concentrations can lead to different PTG responses in healthy PTGs. Glands with reduced CaSR expression respond to Ca 2+ Therefore, it is not the level of ionized calcium present that determines the system response, but rather the calcium level associated with the CaSR density, which is called the sensed calcium concentration, CS:

[0102]

[0103]

[0104] (8) sens(x) = A S +(1-A S )·(x / 2),

[0105] Where C is the blood ionized calcium concentration and D is the 1,25D plasma concentration. Under optimal conditions, the dimensionless CaSR and VDR expressions can be equal to 1, and CS and DS are equal to C and D. Therefore, the sensed calcium concentration can be equal to the actual blood Ca 2+ If the dimensionless CaSR expression starts to decrease, the sensed calcium concentration CS will also decrease, but with a slight delay. The maximum rate of decrease is A S This effect is likely reversible. If CaSR expression increases again, for example, due to a low-phosphate diet, 1,25D supplementation, or the long-term effects of calcimimetics, the sensed calcium concentration CS will again approach C.

[0106] CaSR signaling is directly controlled by the sensed ionic calcium concentrations CS and phosphate. In addition, activity is indirectly controlled by the VDR due to a feedback loop between the VDR and the CaSR:

[0107]

[0108]

[0109]

[0110] again, and Determines the stimulus intensity for activity, while the time constant and Determine the critical time for the system to respond to a stimulus. These equations can be used to calculate the cell degradation rate PTH production rate and cell proliferation rate

[0111] Under normal conditions (i.e. C d ≥1), CaSR causes the cellular degradation of PTH k d Maintain basic speed A d If not regulated by CaSR, the rate will drop to the minimum rate B d =0.5·A d :

[0112] (12) k d =B d +(A d -B d )·C d , for C d <1

[0113] PTH is continuously produced by secretory active PTG cells, and its basic rate is A p Similarly, if it is not downregulated by CaSR, the production rate k p Will increase to maximum level B within minutes to hours p =2·A p :

[0114] (13)k p =B p +(A p -B p )·C p , for C p <1

[0115] The cell proliferation rate increases from the basal level to pr Increase to maximum rate B pr =2·A pr , if not downregulated by the CaSR [Refs. 114 and 118]:

[0116] (14)k pr =B pr+(A pr -B pr )·C pr , for C pr <1

[0117] The PTG functional model according to some embodiments can employ two cell populations, active secretory cells S and static cells Q. PTG cells circulate in two states. For example, cells in a static state can proliferate or undergo apoptosis, and if left untreated, enhanced cell proliferation will lead to PTG hyperplasia. This behavior can be simulated in the PTG functional model by a tumor model with a dynamic carrying capacity K. Associating the total number of cells in a static state with the volume by the PTG functional model can be determined according to the following:

[0118]

[0119]

[0120]

[0121] Among them, k SQ and k QS is the constant rate that determines the cell cycle between the secretory active state and the quiescent state, k a is the constant apoptosis rate, constant k k is the rate at which the dynamic growth capacity K adapts to the size of the gland. The size of a healthy gland can be estimated by the initial steady state S0 = S(0), Q0 = Q(0).

[0122] Ca 2+ There is a sigmoid relationship between the storage of PTH and the rate of PTH release. The following submodel can be used to model the storage of PTH in the gland:

[0123]

[0124]

[0125]

[0126] where PTG and PTH are the concentrations of PTH in the gland and serum, respectively. In healthy subjects, with phosphate and 1,25D levels within normal range, PTG will be expressed by Ca 2+ When the concentration of Ca decreases, a large amount of PTH is released or 2+ High concentrations inhibit PTH release and respond rapidly to changes in ionized calcium concentrations. However, if CaSR sensitivity is reduced, i.e., in the setting of chronic hyperphosphatemia or reduced 1,25D plasma levels, the release function automatically shifts, mimicking the set point Sr Migration (see, for example, Figure 4 PTG cannot react with normal Ca 2+ levels or even slightly higher Ca 2+ Respond appropriately to the concentration. Figure 4 PTH release rate and Ca 2+ 405. The reduced expression of CaSR leads to changes in release function. Figure 4 In the example above, CS is equal to 90% of the actual ionized calcium concentration.

[0127] In various embodiments, the only parameters estimated for the simulations were those associated with the strength of the feedback system (Equations (1), (2), (6), and (9)). All basic parameters for PTG, PTH release, and intracellular degradation were based on various conventional values ​​(e.g., see Figure 5 The basic parameters for the stimulation function can be selected (see, for example, Figure 6 Table 605) so that at the critical value (Ca 2+ (arterial blood ionized calcium): 2.8mg / dl, 1,25D: 90ng / ml, P: 6.6mg / dl) near the maximum derivative of the stimulation function, within the reference range (Ca 2+ : 4.4-5.5mg / dl, 1,25D: 20-60ng / dl, P: 3.4-4.5mg / dl) for the average derivative of Ca 2+ and P is less than 0.08 and for 1,25D less than 0.0035. The value of 1,25D is much smaller because it is not as tightly regulated as the other two parameters. Figure 5 Table 505 depicts an illustrative basic parameter set for PTG, PTH release, and intracellular degradation according to some embodiments. In some embodiments, k may be selected QS , so that the fraction of active cells can be at 0.2 in the steady state. Figure 6 A table 605 depicts an illustrative set of basic parameters for a stimulation function, according to some embodiments.

[0128] In some embodiments, the time constant can be selected so that the effect of the stimulation is physiologically plausible (see, e.g., Figure 7 Table 705). Figure 7Depicted is a table 705 of an illustrative basic parameter set for time constants and intensity parameters for stimulation functions according to some embodiments. In various embodiments, changes other than cell proliferation reach a steady state. Therefore, in some embodiments, the only time constant associated with long-term adaptation is the time constant associated with cell proliferation. In some embodiments, the effect of uncertainty in the time constant can be evaluated by multiplying or dividing the basic time constants (equations (10) and (11)) that control the response of the cell proliferation rate to stimulation (equation (14)) one at a time by a factor of 10, while keeping all other parameters unchanged and simulating mild hypocalcemia and hyperphosphatemia. In some embodiments, the PTG functional model according to some embodiments is insensitive to changes in time constants. For example, even after 30 days, the difference in PTH is less than 0.009% for changes in phosphate-related values, and less than 0.003% for changes in calcium-related values.

[0129] The sensitivity of the PTH predictions with respect to the uncertainty in the strength of the stimulation function can be assessed by multiplying or dividing the base values ​​one at a time by a factor of 2, while keeping all other parameters constant. For example, PTH can be simulated for 7 days in the presence of normocalcemia, developed hyperphosphatemia and a decrease in 1,25D levels. Such an analysis may show that for p values ​​associated with the rate of PTH production, Ca and n Ca The changes in (Eqs. (9), (13)) and the p of CaSR Ca and n Ca The highest sensitivity to changes in (Equations (1)-(2)) determines the steady-state of CaSR expression.

[0130] Figure 8 A sensitivity graph or plot 805 according to some embodiments is depicted. For example, the sensitivity graph 805 can be a plot of PTH predictions for changes in various parameters. The graph 805 can depict the maximum deviation from a reference PTH value as a ratio between the calculated PTH and the reference PTH. For example, the smallest circle can correspond to a relative deviation of 0.5 and the largest circle can correspond to a relative deviation of 1.5. Outward arrows indicate that higher parameter values ​​result in higher PTH values; outward arrows indicate that higher parameter values ​​result in smaller PTH values.

[0131] The acute response of PTH to hypocalcemia depends on Ca 2+ For example, a large linear decrease of 1.6 mg / dl Ca in 30 minutes 2+ A linear decrease of the same amount over 120 minutes may not produce a significant PTH peak, but will produce a higher PTH concentration after about 60 minutes.

[0132] Case Study I: PTG Functional Model Simulation

[0133] According to some embodiments, simulations were performed using the PTG functional model, which simulated acute Ca2+ stimulation by starting from a system steady state and changing ionized calcium concentration at different rates. 2+ Since PTH is stored in secretory active cells, rapid induction of hypocalcemia (Ca 2+ A 5% decrease in PTH results in a clinically observed PTH overshoot followed by a sharp decline, whereas a slow induction of hypocalcemia (Ca 2+ 5% reduction) results in a smaller PTH overshoot and then reaches a level similar to that of the fast reduction protocol (see, for example, Fig. 9 905 and 910). Fig. 9 Accordingly, according to some embodiments, the effect of time on Ca during induced hypocalcemia is described. 2+ and predicted PTH concentrations 905 and 910. When the rate of calcium reduction is high (solid line), the PTH response shows a prominent peak, while when the rate of change is low (dashed line), the peak almost disappears.

[0134] In some embodiments, the induced hypocalcemia is followed by a transient return to normocalcemia, and the subsequent hypocalcemia can be used to analyze the PTH hysteresis effect. 2+ After a dramatic increase in PTH during the first peak of 0.8 mg / dl from baseline and a slight decline as the level normalizes, no second transient PTH peak is observed in the PTG functional model (e.g., during induced hypocalcemia, normocalcemia, and subsequent hypocalcemia, see Fig.10 Graph 1005).

[0135] The results of case study I showed that a distinct peak occurred during the first hypocalcemia (due to the rapid release of PTH stored in PTG cells) but no peak during the second hypocalcemia (due to insufficient recovery time in the normocalcemic state to reload PTH stores) (e.g., during induced hypocalcemia, normocalcemia, and subsequent hypocalcemia, see Fig.11 Graph 1105).

[0136] Mild but chronic hypocalcemia may trigger all the mechanisms that lead to elevated PTH levels. 2+ Chronic hypocalcemia is simulated by decreasing the level by 0.25 mg / dl and maintaining it at this low level for 200 days. PTH levels do not reach a steady state but increase slightly but steadily due to a slight decrease in CaSR expression, a decrease in intracellular degradation, an increase in the rate of PTH production, and a slight increase in cell proliferation (see, for example, Fig.12 Graph 1205). Fig.12 Depicts the temporal response of Ca to induced chronic hypocalcemia 2+ and PTH concentrations. The time scale is logarithmic, with black vertical dashed lines representing 1 hour, 1 day, and 1 month.

[0137] If Ca 2+ If maintained at optimal values, a steady increase in PTH may also be observed, but 1,25D may be reduced (e.g., due to impaired synthesis) and phosphate levels may be elevated (e.g., due to impaired clearance, see Fig. 9 ). Although due to Ca 2+ The PTH concentration will continue to increase and will not reach a steady state due to the loss of CaSR expression and sensitivity and the increase in cell proliferation. Previous studies have shown that dietary phosphate and calcitriol supplementation have long-term effects on PTH levels, with the endpoint being nearly ten times higher than normal levels due to a long-term (e.g., two years) steady rise in PTH levels caused by regular phosphate intake. If the reduced phosphate intake coincides with a reduced glomerular filtration rate, the slope of the increase is significantly reduced (e.g., see Fig.13 1305). The PTG functional model predicts the same effect as our model, with a slower ramp observed if phosphate increases only slightly over time (see, e.g., Fig.14 Graphs 1405 and 1410).

[0138] According to some embodiments, predictions generated using the PTG functional model are consistent with those generated in many Ca 2+ The PTH response and PTG adaptation observed in acute and chronic changes in PTH, P and 1,25D are consistent. The PTG functional model accurately describes the adaptive mechanisms, such as reduced intracellular PTH degradation, PTH production rate and increased PTG proliferation rate. More importantly, the PTG functional model can fully capture the different time frames over which these mechanisms act. In some embodiments, the driving force of the PTG functional model is the description of changes in the CaSR, which is a key regulator of PTG. The validity of the PTG functional model can be verified by comparing its predictions with published experimental data under different conditions. The predictions of the model are consistent with the observations in all analyzed cases, such as different rates of induced hypocalcemia, hysteresis, and proliferation in the case of induced chronic mild hypocalcemia, and different rates of secondary hyperparathyroidism in the case of chronically elevated serum phosphate levels and chronically low 1,25DH levels. These features make the PTG functional model useful in patients with secondary hyperparathyroidism, such as those with CKD or receiving dialysis.

[0139] In certain embodiments, the PTG functional model may include all known adaptive mechanisms for regulating CaSR. These predictions are based on the positive feedback system and negative feedback system acting on CaSR. The effect of the therapeutic intervention measures acting on CaSR can be merged by using the operational model of the allosteric effect of CaSR, such as calcimimetic Cinacalcet or Ecalcitide (for example, according to some embodiments, via the calcimimetic model). For example, the calcimimetic model according to some embodiments may include a pharmacokinetic model, which may be easily incorporated into all other models by using the operational model of allosteric effect, and the model is transferred to the actual ion calcium concentration by the amount of free drug in blood plasma. For example, allostery can be achieved as described in Leach et al., "Towards a structural understanding of allosteric drugs at the humancalcium-sensing receptor," Cell Research 26: 574-592, 2016; 35:855–869, 2010; Leach et al., “Allosteric GPCRmodulators: taking advantage of permissive receptor pharmacology,” Trends in Pharmacological Sciences 28:382–389, 2007; and / or Padhi D and Harris R, “ClinicalPharmacokinetic and Pharmacodynamic Profile of Cinacalcet Hydrochloride,” Clinical Pharmacokinetics 48:303-311, 2009.

[0140] Therefore, the PTG functional model can be used to provide an auxiliary tool to study therapeutic strategies, such as the combination of calcimimetics and vitamin D analogs. The only input variables are the key regulators of PTG cells in hemodialysis patients, namely calcium, 1,25D and phosphate. Therefore, the PTG functional model can be used in conjunction with the bone model, allowing the analysis of highly complex systems involving a series of regulatory triggers and feedback loops.

[0141] Although the PTG functional model simulates the situation of patients with complete loss of renal function as a systemic regulator, the model is more generally applicable to other patient groups, such as those with primary hyperparathyroidism. For example, the only parameter directly affected by renal function is the clearance rate k cl Since PTH is cleared by the liver and kidneys, in healthy subjects (e.g., see Figure 5 Table 505) or the clearance rate in CKD patients with residual renal function is higher. For long-term simulations, in some embodiments, it can be assumed that the clearance rate is reduced by a factor of 2.

[0142] Case Study II: Calcimimetic Model Simulation

[0143] The executive summary of the 2017 KDIGO Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD) Guideline Update recommends maintaining PTH between 14 pmol / L and 62 pmol / L. One strategy to achieve this goal is to target the CaSR. Calcimimetics such as cinacalcet or eticlipidide enhance ionized calcium concentration (Ca) through allosteric activation. 2+ ) and CaSR. 2+ The higher sensitivity of cinacalcet results in an inverse relationship between plasma PTH and cinacalcet concentrations. After administration of cinacalcet, PTH concentrations decrease until they reach a minimum value approximately 2-3 hours after administration.

[0144] Cinacalcet hydrochloride is widely used in hemodialysis patients. After oral administration, plasma concentrations reach peak values ​​within 2-6 hours. The absolute bioavailability is only 20-25%, while the absorption rate is close to 100%, indicating a high first-pass metabolism. Since almost 95% of the drug in plasma is bound to proteins, hemodialysis does not change the pharmacokinetics.

[0145] Due to the widespread clinical use of cinacalcet, a realistic model of CKD-MBD may characterize the use and effects of cinacalcet. To be used clinically, the cinacalcet model should be easily adaptable to various situations, such as hepatic impairment enhancing cinacalcet exposure. Moreover, it should be able to reflect different dosing regimens, including the known poor patient compliance due to gastrointestinal side effects and high drug doses.

[0146] Thus, some embodiments may use a multi-compartmental calcimimetic model based on physiological considerations that capture all of the key pharmacokinetic parameters of cinacalcet, for example, at least in part in Figure 2B . Case Study II can use a calcimimetic model with fewer than six compartments, for example, a five-compartment model that does not include a slow tissue compartment can be used. In addition, the calcimimetic model according to some embodiments can provide intuitive personalization for various conditions or dosing regimens and ignore any numerical instabilities for easy implementation in other physiological models.

[0147] Simulated pharmacokinetic profiles of a single oral administration based on the proposed six-compartment model Fig.15 The graph 1505 and Fig.16 is shown in the curve graph 1605. Fig.15 A graph 1505 depicts cinacalcet concentration versus time following a single 75 mg dose. max The average reference value was 26.6 ng / mL (9.4 SD), t max The reference range of CL / F is 314 L / h (148 SD). Fig.16 Depicted is a graph 1505 of cinacalcet concentration versus time following a single 75 mg dose (solid line) and an exponential fit to a logarithmic scale for half-life estimation (dashed line). Reference values ​​for half-life distribution The reference range for the terminal half-life is 6 hours and 30-40 hours. In general, the results are very consistent with established clinical data both qualitatively and quantitatively. Based on known clinical data, simulations of 75 mg cinacalcet taken every 24 hours predict a steady state within 7 days (e.g., see Fig.17 The calcimimetic model can be configured to capture all seven key pharmacokinetic parameters (i.e., C max ,t max 、Bio、CL / F、t 1 / 2 , and VD), while linear mass balance may not be possible.

[0148] To assess the effect of dosing regimen on total exposure, Clinical Study II analyzed the mean weekly blood cinacalcet concentrations (i.e., at each time point) for three different dosing regimens: daily dosing, 3 times weekly dosing, and dosing with an actual patient replenishment rate of 64%. For the actual patient replenishment rate, days without dosing were randomly selected. The results are presented in Fig.18 In the curve graphs 1805, 1810, 1815, 1820, 1825 and 1830.

[0149] Linear multi-compartment calcimimetic models can be used to describe the complex pharmacokinetic behavior of cinacalcet in humans. This approach can allow analysis of the effects of different dosing regimens on drug concentrations in vivo, which otherwise can only be addressed through clinical studies. This analysis can help evaluate dose titration regimens and dosing regimens. A non-limiting technical advantage of the calcimimetic model according to some embodiments is that its linear structure allows long-term numerical stability and rapid predictions. Due to the physiologically effective compartments, adjustments for conditions such as liver damage are intuitive. Combined with models of parathyroid and bone metabolism, the calcimimetic model according to some embodiments can provide a ready-made tool for clinical trial simulations to explore the effects of relevant factors, such as patient compliance, off-label dosing regimens, the effect of dosing with food, etc.

[0150] Low bioavailability of 20-25% suggests high first-pass metabolism. Hepatic impairment results in higher terminal half-life values ​​(40-70% in moderate to severe impairment) and high total exposure (2.4-fold to 4.2-fold higher in patients with moderate to severe impairment). Administration with food results in higher bioavailability, leading to higher peak concentrations and total exposure values. Approximately 95% of the drug is protein bound. Therefore, the effect of HD on pharmacokinetics is negligible. The large amount of distribution at steady state of 1000 L suggests a large amount of distribution outside the systemic circulation. Experiments with radiolabeled cinacalcet showed that the drug peaks at different times in different tissues. In general, tissues can be divided into two groups: one with a shorter time to peak and the other with a longer time to peak, acting like a buffer for cinacalcet.

[0151] exist Figure 3A An exemplary calcimimetic model is depicted in , using six physiologically dynamic compartments, such as compartments for absorption, first-pass metabolism, plasma free drug, and protein binding, and two tissue compartments. A constant rate function is used between the compartments. The amount of drug in each compartment can be calculated by solving the following system of linear ordinary differential equations:

[0152]

[0153] in corresponds to the amount of drug in the absorption compartment, corresponds to the amount of drug in first-pass metabolism, and The amount of drug in the plasma compartment corresponds to free and protein bound. and corresponds to the amount of drug in the fast and slow tissues, respectively. The initial dose is delivered to the absorptive compartment. In patients not receiving cinacalcet, the initial condition is determined by the vector Given. Non-untreated patients at time t a The conditions for drug administration are The coefficient matrix A can be written as:

[0154]

[0155] Removing a compartment from the calcimimetic model of the matrix A can include removing the corresponding columns and / or rows from the matrix. For example, to remove the slow tissue compartment, the last (or bottommost) row and the last (or rightmost) column can be removed to generate the following coefficient matrix A for the five-compartment model:

[0156]

[0157] The linear system has the distinct advantage that it can be solved by solving the corresponding eigenvalue problem, e.g., if λ1, ..., λ6 are unique eigenvalues ​​of A, and is the matrix containing the corresponding eigenvectors, then at time t a The solution to the differential equation for the last dose is:

[0158]

[0159] Therefore, at any given time t, the amount of drug can be calculated by evaluating the amount of drug in all compartments at only the previous dosing time. As a result, simulations over long periods of time are very fast and numerically stable.

[0160] The coefficient matrix A can be estimated using known data. The natural constraint is that all eigenvalues ​​should be unique and negative to ensure convergence to zero in all compartments without further drug administration. The mean plasma volume is assumed to be 3 liters and a single oral dose of 75 mg cinacalcet can be assumed. The target maximum plasma concentration C max It should be close to 26.8 ng / mL until the maximum plasma concentration is reached in about 2.3 hours, with a terminal half-life of t 1 / 2 The half-life of distribution is 30-4 hours. D The apparent oral clearance rate CL / F is defined as:

[0161]

[0162] It is about 314 L / h. The apparent distribution volume V at steady state D Defined as:

[0163]

[0164] It should be approximately 1000 L. Finally, the bioavailability in a fasting patient should be between 20% and 25%. Bioavailability can be determined as:

[0165]

[0166] Among them C iv is the plasma concentration of intravenously administered drug. iv It can be calculated by analyzing a modified model of an IV bolus. The drug can be administered to the "plasma free drug" compartment, thereby eliminating the absorption and first-pass metabolism compartments. oral It is the plasma concentration of an orally administered drug.

[0167] Typical model parameters are Fig.19 In some embodiments, k f Set to 0.0526k b to ensure that 95% of the drug is bound to the protein at steady state. For simulations involving food intake, the absorption rate can be slightly increased to k a =0.6h -1 , to accommodate a slightly lower t max , and the first-pass metabolic rate k e Can be reduced to 0.13h -1 .

[0168] A sensitivity analysis was performed to investigate the impact of uncertainty on all parameters in the coefficient matrix A. The base values ​​for each of these parameters were divided or multiplied by a factor of 2. The corresponding pharmacokinetic parameters were calculated assuming a single dose of 60 mg cinacalcet. These values ​​were compared to the corresponding base values, generating the following results: Fig. 20 The analysis showed, among other things, that C max K e , k lp and k PTf Bioavailability is most sensitive to changes in k e and k lp The terminal half-life is most sensitive to changes in k. PTf , k PTs and k PTs The distribution half-life and t max K b and k e By definition, the apparent oral clearance rate CL / F is sensitive to changes in je and k lp sensitive to changes.

[0169] Fig.21 An embodiment of an exemplary computing architecture 2100 suitable for implementing various embodiments as described above is shown. In various embodiments, the computing architecture 2100 may include an electronic device or be implemented as part of an electronic device. In some embodiments, the computing architecture 2100 may represent, for example, the computing device 110. The embodiments are not limited in this context.

[0170] As used in this application, the terms "system" and "component" and "module" mean a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution, examples of which are provided by the exemplary computing architecture 2100. For example, a component can be, but is not limited to, a process running on a processor, a processor, a hard drive, multiple storage drives (optical and / or magnetic storage media), an object, an executable file, an execution thread, a program, and / or a computer. As an illustration, both an application running on a server and a server can be a component. One or more components can reside within a process and / or execution thread, and a component can be located on one computer and / or distributed between two or more computers.

[0171] In addition, components can be communicatively coupled to each other through various types of communication media to coordinate operations. Coordination can involve a one-way or two-way exchange of information. For example, components can communicate information in the form of signals communicated on a communication medium. The information can be implemented as signals assigned to various signal lines. In such an assignment, each message is a signal. However, other embodiments may alternatively use data messages. Such data messages can be sent through various connections. Exemplary connections include parallel interfaces, serial interfaces, and bus interfaces.

[0172] The computing architecture 2100 includes various common computing elements such as one or more processors, multi-core processors, coprocessors, memory units, chipsets, controllers, peripherals, interfaces, oscillators, timing devices, video cards, audio cards, multimedia input / output (I / O) components, power supplies, etc. However, the embodiments are not limited to being implemented by the computing architecture 2100.

[0173] like Fig.21 As shown, computing architecture 2100 includes a processing unit 2104, a system memory 2106, and a system bus 2108. Processing unit 2104 may be a commercially available processor and may include dual microprocessors, multi-core processors, and other multi-processor architectures.

[0174] The system bus 2108 provides an interface to the processing unit 2104 for system components including, but not limited to, the system memory 2106. The system bus 2108 may be any of a variety of types of bus structures that may be further interconnected to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. Interface adapters may be connected to the system bus 2108 via a slot architecture. Example slot architectures may include, but are not limited to, Accelerated Graphics Port (AGP), Card Bus, (Extended) Industry Standard Architecture ((E)ISA), Micro Channel Architecture (MCA), NuBus, Peripheral Component Interconnect (Extended) (PCI(X)), PCI Express, Personal Computer Memory Card International Association (PCMCIA), and the like.

[0175] The system memory 2106 may include various types of computer-readable storage media in the form of one or more higher speed memory cells, such as read-only memory (ROM), random access memory (RAM), dynamic RAM (DRAM), double data rate DRAM (DDRAM), synchronous DRAM (SDRAM), static RAM (SRAM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, polymer memory such as ferroelectric polymer memory, austenite memory, phase change or ferroelectric memory, silicon oxide-nitride-oxide-silicon (SONOS) memory, magnetic or optical cards, array memory of devices such as redundant array of independent disks (RAID) drives, solid-state memory devices (e.g., USB memory, solid-state drive (SSD), and any other type of storage medium suitable for storing information. Fig.21 In the illustrative embodiment shown, the system memory 2106 may include non-volatile memory 2110 and / or volatile memory 2112. A basic input / output system (BIOS) may be stored in the non-volatile memory 2110. The computer 2102 may include various types of computer-readable storage media in the form of one or more lower speed memory units, including an internal (or external) hard disk drive (HDD) 2114, a magnetic floppy disk drive (FDD) 2116 that reads or writes from a removable disk 2111, and an optical drive 2120 that reads or writes from a removable disk 2122 (e.g., a CD-ROM or DVD). The HDD 2114, FDD 2116, and optical drive 2120 may be connected to the system bus 2108 by a HDD interface 2124, an FDD interface 2126, and an optical drive interface 2128, respectively. The HDD interface 2124 for external drive implementations may include at least one or both of a universal serial bus (USB) and IEEE 1114 interface technologies.

[0176] The drives and associated computer-readable media provide volatile and / or nonvolatile storage of data, data structures, computer-executable instructions, etc. For example, a number of program modules may be stored in the drives and memory units 2110, 2112, including an operating system 2130, one or more application programs 2132, other program modules 2134, and program data 2136. In one embodiment, the one or more application programs 2132, other program modules 2134, and program data 2136 may include, for example, various applications and / or components of the computing device 110.

[0177] A user can enter commands and information into the computer 2102 through one or more wired / wireless input devices, such as a keyboard 2138 and a pointing device such as a mouse 2140. These and other input devices are typically connected to the processing unit 2104 through an input device interface 2142 coupled to the system bus 2108, but may be connected by other interfaces.

[0178] A monitor 2144 or other type of display device is also connected to the system bus 2108 via an interface, such as a video adapter 2146. The monitor 2144 may be internal or external to the computer 2102. In addition to the monitor 2144, computers typically include other peripheral output devices, such as speakers, printers, and the like.

[0179] The computer 2102 can operate in a network environment using logical connections via wired and / or wireless communications to one or more remote computers, such as remote computer 2148. The remote computer 2148 can be a workstation, server computer, router, personal computer, portable computer, microprocessor-based entertainment device, peer device or other public network node, and typically includes many or all of the elements described with respect to the computer 2102, but only a memory / storage device 2150 is shown for simplicity. The depicted logical connections include wired / wireless connections to a local area network (LAN) 2152 and / or a larger network, such as a wide area network (WAN) 2154. Such LAN and WAN networking environments are commonplace in offices and companies, and facilitate enterprise-wide computer networks, such as intranets, all of which can be connected to a global communication network, such as the Internet.

[0180] The computer 2102 may be configured to communicate with wired and wireless devices or entities using the IEEE 802 family of standards, such as wireless devices operatively configured for wireless communications (e.g., IEEE 802.16 over-the-air modulation techniques). This includes at least Wi-Fi (or Wireless Fidelity), WiMax, and Bluetooth. TMWireless technology. Therefore, the communication can be a predefined structure like a conventional network, or just a simple and self-organizing communication between at least two devices. Wi-Fi networks use radio technology called IEEE802.11x (a, b, g, n, etc.) to provide secure, reliable, and fast wireless connections. Wi-Fi networks can be used to connect computers to each other, to the Internet, and to wired networks (which use the media and functions associated with IEEE 802.3).

[0181] Many specific details have been set forth herein to provide a thorough understanding of the embodiments. However, those skilled in the art will appreciate that the embodiments may be practiced without these specific details. In other cases, well-known operations, components, and circuits are not described in detail to avoid confusing the embodiments. It is understood that the specific structural and functional details disclosed herein may be representative and do not necessarily limit the scope of the embodiments.

[0182] Some embodiments may be described using the expressions "coupled" and "connected" and their derivatives. These terms are not intended to be synonymous with each other. For example, some embodiments may be described using the terms "connected" and / or "coupled" to indicate that two or more elements are in direct physical or electrical contact with each other. However, the term "coupled" may also mean that two or more elements are not in direct contact with each other, but still cooperate or interact with each other.

[0183] Unless expressly stated otherwise, it is understood that terms such as "processing", "computing", "calculating", "determining", etc. refer to the actions and / or processes of a computer or computing system or similar electronic computing device that manipulate and / or transform data represented as physical quantities (e.g., electronic) in registers and / or memories of the computing system into other data similarly represented as physical quantities within the memory, registers, or other such information storage, transmission, or display devices of the computing system. The embodiments are not limited in this context.

[0184] It should be noted that the methods described herein do not have to be executed in the order described or in any particular order. In addition, various activities described with respect to the methods identified herein can be executed in serial or parallel manner.

[0185] Although specific embodiments have been shown and described herein, it should be understood that any arrangement calculated to achieve the same purpose can replace the specific embodiments shown. The present disclosure is intended to cover any and all modifications or variations of the various embodiments. It should be understood that the above description is made in an illustrative manner and not restrictive. Upon reviewing the above description, the above embodiments and other embodiments not specifically described herein will be apparent to those skilled in the art. Therefore, the scope of the various embodiments includes any other application in which the above-mentioned compositions, structures and methods are used.

[0186] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

[0187] As used herein, an element or operation recited in the singular and followed by the word "a" or "an" should be understood as not excluding plural elements or operations, unless such exclusion is explicitly stated. In addition, reference to "one embodiment" of the present disclosure is not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the described features.

[0188] The present disclosure is not limited to the scope of the specific embodiments described herein. In fact, in addition to those embodiments and modifications described herein, various other embodiments and modifications of the present disclosure will be apparent to those of ordinary skill in the art from the foregoing description and the accompanying drawings. Therefore, these other embodiments and modifications are intended to fall within the scope of the present disclosure. In addition, although the present disclosure has been described herein in the context of a specific implementation in a specific environment for a specific purpose, it will be appreciated by those of ordinary skill in the art that its usefulness is not limited thereto and that the present disclosure can be used in any number of environments for any purpose that is beneficial. Therefore, in view of the full scope and spirit of the present disclosure as described herein, the claims set forth below should be interpreted.

Claims

1. A computer-implemented method for virtual parathyroid gland (PTG) function analysis, the computer-implemented method comprising: via a processor of a computing device, A calcimimetic model is provided, the calcimimetic model being configured for simulating administration of a calcimimetic compound to a patient having at least one health abnormality affecting PTG function, the calcimimetic model being operable to: receiving calcimimetic doses, determining the concentration of the calcimimetic compound in a plurality of physiological compartments, each of the plurality of physiological compartments being configured to model pharmacokinetic parameters of the calcimimetic compound in a different physiological compartment, and the plurality of physiological compartments comprising at least two of an absorption compartment, a first-pass metabolism compartment, a plasma free drug compartment, a plasma protein binding compartment, a fast tissue compartment, and a slow tissue compartment, and each of the plurality of physiological compartments is respectively related to an adjacent physiological compartment via at least one constant rate function, and determining an output of a total calcimimetic concentration for at least one time period by evaluating the concentration of the calcimimetic compound in all of the plurality of physiological compartments for at least one time period, wherein the total calcimimetic concentration is determined based on the sum of the amounts of the calcimimetic compound in each of the plurality of physiological compartments.

2. The computer-implemented method of claim 1, wherein the calcimimetic compound comprises cinacalcet.

3. The computer-implemented method of claim 1, wherein the plurality of physiological compartments comprises an absorption compartment, a first-pass metabolism compartment, a plasma free drug compartment, a plasma protein-bound compartment, a fast tissue compartment, and a slow tissue compartment.

4. The computer-implemented method of claim 3, wherein the absorption compartment is disposed adjacent to the first-pass metabolism compartment and is related via a constant rate function.

5. The computer-implemented method of claim 1, wherein the output is provided as a calcium concentration input to a PTG functional model.

6. The computer-implemented method of claim 1, the output being provided as a calcium concentration input to a PTG functional model via an allosteric operational model configured to shift calcium concentration based on the amount of free drug in plasma.

7. The computer-implemented method of claim 1, the calcimimetic model being operable to determine the amount of the calcimimetic compound in each of the plurality of physiological compartments by performing the following calculations for each of the plurality of physiological compartments: in, Corresponding to the amount of the calcimimetic compound in one of the plurality of physiological compartments, A is a coefficient matrix for the plurality of physiological compartments.

8. The computer-implemented method of claim 7, wherein: for determining a calcimimetic compound in each of the plurality of physiological compartments, wherein: corresponds to the amount of calcimimetic compound in the absorptive compartment, corresponds to the amount of calcimimetic compound in the first-pass metabolic compartment, corresponds to the amount of calcimimetic compound in the plasma free drug compartment, corresponds to the amount of calcimimetic compound in the plasma protein binding compartment, Corresponds to the amount of calcimimetic compound in the fast tissue compartment.

9. The computer-implemented method of claim 7, wherein: The coefficient matrix A is constructed as follows:

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