Monitoring cardiac contractility during cardiac treatments

Abstract

A computer-implemented method may be provided. The method may include receiving, by a computing system, a pulmonary7 capillary7 wedge pressure and cardiac output for a human heart. The method may also include determining, by the computing system, a cardiac contractility for the human heart based on a left ventricular end-systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary7 capillary^ wedge pressure and the cardiac output, while avoiding singularities in the inverse function. The method may further include generating, by the computing system, an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility.

Description

Attorney Docket No.390351-100201 MONITORING CARDIAC CONTRACTILITY DURING CARDIAC TREATMENTS CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No.63 / 493,619, filed March 31, 2023, and entitled “Monitoring Cardiac Contractility During Cardiac Treatments,” which has been incorporated by reference in its entirety.

[0002] This disclosure is related to U.S. Provisional Application No.63 / 346,143, filed May 26, 2022, and entitled “Optimizing Drug Combinations for Treating Acute Heart Failure,” which has been incorporated by reference in its entirety. FIELD

[0003] This disclosure relates to systems, methods, and devices for continuously or near-continuously monitoring cardiac contractility during cardiac treatment such as drug therapies. BACKGROUND

[0004] The human heart is a pumping organ that actively circulates blood throughout the body. The pumping action is generated by the contraction of the cardiac muscles to decrease the size of a section of the heart, for example, an auricle or ventricle, and exert a mechanical force on the blood contained therein. These contractions, repeated in cycles, create the human heartbeat. Cardiac contractility, which represents an ability of the heart muscle to contract for the pumping action, is an important cardiovascular parameter that has to be monitored for patients undergoing cardiac treatments.

[0005] One way of determining cardiac contractility is through a measurement or an estimation of left ventricular end-systolic elastance (Ees). Elastances, including Ees, are generally measured by pressure to volume ratio within a corresponding heart chamber. Both pressure and the volume in the chamber are determined by the state of contraction of the chamber. For instance, during systole in which the heart contracts, pressure increases to decrease the volume by squeezing the blood out of the corresponding chamber. The end- systolic elastance is therefore the pressure to volume ratio when a systole has just ended. In a pressure-volume (PV) diagram, the end-systolic elastance is the slope of the end-systolic pressure-volume relationship (ESPVR) curve. Therefore, Ees is the slope of the ESPVR curve for the left ventricle. The conventional techniques for measuring Eesdepend on this 1 1608025632.3Attorney Docket No.390351-100201 definition—to estimate / measure Eesthey will have to necessarily determine the left ventricular pressure (PLV) and left ventricular volume (VLV) at multiple points to generate a ESPVR curve.

[0006] These conventional methods of measuring or estimating Ees pose significant technical challenges. For example, the conventional VLVestimation methods are inaccurate: it has been experimentally known that the relationship between the true and estimated VLV varies with changes in conditions. Additionally, PLVis not measured for the purposes of monitoring hemodynamics in clinical practice because inserting a catheter to continuously measure PLV outweighs its benefits due to the complications such as the risk of arrhythmia. In the absence of accurate VLV and PLV measurements, machine learning techniques have been used for Ees estimation, but these techniques have also struggled to achieve a desired level of versatility because of the dearth of training data.

[0007] Because of these technical difficulties, cardiac therapies, particularly in Intensive Care Unit (ICU) / Critical Care Unit (CCU) settings, are conducted without the adequate knowledge of Ees. For instance, a clinician does not have a way of knowing how Ees is impacted by a particular drug or a combination of drugs. The clinician therefore will have to rely on experience and guesswork to make a mental estimate of the effect of the drug on Ees. Additionally, this lack of knowledge does not allow for a closed-loop hemodynamic control system, where an optimized combination of drugs could be automatically infused. In these situations where the organ as important as a human heart is involved, this lack of knowledge— notwithstanding the clinical expertise and experience—can be fatal for the patient.

[0008] As such, a significant improvement in systems, methods, and devices to measure or Ees (and cardiac contractility in general) is therefore desired. SUMMARY

[0009] In some embodiments, a computer-implemented method may be provided. The method may include receiving, by a computing system, a pulmonary capillary wedge pressure and cardiac output for a human heart. The method may also include determining, by the computing system, a cardiac contractility for the human heart based on a left ventricular end- systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function. The method may further include generating, by the computing system, an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility. 2 1608025632.3Attorney Docket No.390351-100201

[0010] In some embodiments, a system may be provided. The system may include a non-transitory storage medium storing computer program instructions and a processor configured to execute the computer program instructions to cause operations. The operations may include receiving a pulmonary capillary wedge pressure and cardiac output for a human heart. The operations may further include determining a cardiac contractility for the human heart based on a left ventricular end-systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function. The operations may also include generating an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility.

[0011] In some embodiments, a non-transitory storage medium storing computer program instructions may be provided. The computer program instructions that when executed may cause a computing system to perform operations. The operations may include receiving a pulmonary capillary wedge pressure and cardiac output for a human heart. The operations may further include determining a cardiac contractility for the human heart based on a left ventricular end-systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function. The operations may also include generating an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility. BRIEF DESCRIPTION OF DRAWINGS

[0012] FIG. 1 depicts an example computing environment for monitoring cardiac contractility during cardiac treatments, according to example embodiments of this disclosure.

[0013] FIG.2 depicts an example analytical model, according to example embodiments of this disclosure.

[0014] FIG. 3 depicts a flow diagram of an example method, based on the example embodiments of this disclosure.

[0015] FIG 4 depicts example charts visualizing comparison between the different methods, according to example embodiments of this disclosure.

[0016] FIG.5 depicts example charts showing modulation of hemodynamics, based on the example embodiments of this disclosure. 3 1608025632.3Attorney Docket No.390351-100201

[0017] FIG.6 depicts example charts showing modulation of hemodynamics, based on the example embodiments of this disclosure.

[0018] FIG.7 shows a block diagram of an example computing device that implements various features and processes, according to example embodiments of this disclosure. DESCRIPTION

[0019] Embodiments disclosed herein generally related to a system and method of estimating cardiac contractility using readily available clinical data. As discussed above, conventional methods for estimating cardiac contractility typically require continuous measurement of left ventricular pressure and volume, which is difficult to achieve in a clinical setting. The one or more techniques disclosed herein improve upon conventional methods by utilizing pulmonary capillary wedge pressure and cardiac output, which are regularly measured metrics in clinical settings using pulmonary artery catheterization. In some embodiments, such an approach may utilize only a single point of left ventricular end-diastolic pressure and volume—non-invasively estimated using echocardiography—to extrapolate a left ventricular end-diastolic pressure-volume relationship curve. This curve may be augmented by physiological constraints and optimized parameters for singularity avoidance, and used with the pulmonary capillary wedge pressure and cardiac output to estimate left ventricular end- systolic elastance (Ees), which is an index of cardiac contractility. Therefore, the clinical feasibility and accuracy of cardiac monitoring and therapy that use the disclosed embodiments is significantly improved in comparison to the conventional systems. This improved clinical feasibility can support not only clinical decision making, for example, adjusting drug dosages in a current clinician cardiac therapy, but also closed-loop hemodynamic control system that requires accurate and continuous estimates of Ees.

[0020] FIG. 1 depicts an example computing environment 100 for monitoring cardiac contractility during cardiac treatments, according to example embodiments of this disclosure. In some embodiments, the example computing environment 100 may be configured to estimate Ees as an index of cardiac contractility. As shown, the computing environment 100 may be based on a client-server model, with a server 102 connected to multiple clients 106a-106d (commonly referred to as a client 106 or collectively referred to as clients 106) and a cardiac monitoring system 122 (which too may be considered a client to the server 102) via a network 104. It should, however, be understood that the client-server model is just for illustration and 4 1608025632.3Attorney Docket No.390351-100201 ease of explanation and should not be considered limiting. Therefore, any type of computing environment performing the functionality disclosed herein should be considered within the scope of this disclosure. Furthermore, the individual components of the computing environment 100 are just illustrative and computing environments with alternative, additional, or fewer number of components should be considered within the scope of this disclosure.

[0021] The computing environment 100 may be generally in a clinical setting to monitor cardiac contractility—particularly Ees—for cardiac patients such as patients with acute heart failure. In some example use cases, the server 102 may store different software modules 108 that may be accessed by the clients 106 and cardiac monitoring system 122 using the network 104. The clients 106 themselves may have standalone applications (not shown) to access the software modules 108. Alternatively, the clients 106 may access the software modules 108 through a browser application, for example. Similarly, the cardiac monitoring system 122 may access the software modules 108 through any type of firmware and / or software installed in the cardiac monitoring system 122. In some embodiments, the cardiac monitoring system 122 may communicate with the server 102 using one or more of the clients 106.

[0022] The hardware of the server 102 storing the software modules 108 may include any kind of computing device. For example, the server 102 may include any kind of computing device, including but not limited to a server computer, a desktop computer, a laptop computer, a tablet computer, a smartphone. The server 102 may not necessarily be at a single location and may be realized by a network of computers. Furthermore, the server 102 may not necessarily be co-located within the clinical setting itself, and may be hosted by a third party cloud computing provider. Therefore, any kind of server 102 should be considered within the scope of this disclosure.

[0023] As described above, the clients 106 and the cardiac monitoring system 122 may access the server 102 through the network 104. The network 104 may include any combination of one or more packet switching networks (e.g., an IP based network) and one or more circuit switching networks (e.g., a cellular telephony network). Some non-limiting examples of the network 104 include a local area network, a metropolitan area network, a wide area network such as the Internet, etc. Similarly, non-limiting examples of the clients 106 may include a desktop terminal (e.g., desktop terminal 106a), a laptop computer (e.g., a laptop computer 106b), a tablet computer (e.g., a tablet computer 106c), a smartphone (e.g., a smartphone 106d), etc. Any type of computing device that allows an access to the server 102 through the network 104 should be considered within the scope of this disclosure. Furthermore, the functionality 5 1608025632.3Attorney Docket No.390351-100201 described within this disclosure can be distributed in any fashion, i.e., functionality of the server 102 may be performed by one or more clients 106 and vice versa.

[0024] The cardiac monitoring system 122 may include any combination of diagnostic and therapeutical devices used for cardiac patients. For instance, the cardiac monitoring system 122 may include cardiac monitors, Holter ECG monitors, cardiac echo devices, cardiac nuclear stress test devices, cardiac catheters, cardiac drug infusing devices, external pacemakers, and / or any other type of cardiac diagnostic and therapeutic devices. Although a single cardiac monitoring system 122 is shown, any number of monitoring systems is to be considered within the scope of this disclosure. Furthermore, one monitoring system 122 may not necessarily localized within a single device and may include a combination of devices (and constituent software / firmware) distributed throughout the clinical setting. Additionally, the functionality between the monitoring system 122 and the server 102 may be interchangeable, for example, some of the software modules 108 implemented in the server 102 may be implemented by the monitoring system 122. In some embodiments, the cardiac monitoring system 122 may implement a closed-loop hemodynamic control system that controls the amount of drug infused in response to monitored cardiac contractility (e.g., Ees).

[0025] As described above, the server 102 may include multiple software modules. FIG.1 shows some non-limiting example software modules: a cardiac data input module 110, a cardiac contractility calculation module 112, a closed-loop hemodynamic control module 114, an optimal dosage calculation module 116, a model development and simulation module 118, and an experimental data ingestion module 120. It should be understood that this described modularization of the server 102 functionality is just for the ease of explanation and should not be considered limiting. Therefore, any kind of alternative modularization should be considered within the scope of this disclosure.

[0026] The cardiac data input module 110 may receive cardiac data from the clients 106 and the cardiac monitoring system 122. The received cardiac data may include any kind of cardiac data measured or estimated in the clinical setting. For instance, the cardiac data may include left ventricular end-diastolic pressure and volume that may be generated by echocardiography. The cardiac data may further include pulmonary capillary wedge pressure and cardiac output measured through pulmonary artery catheterization. Additionally, the received cardiac data may include current cardiovascular metrics for a patient and target cardiovascular metrics. For instance, as the current cardiovascular metrics, cardiac data input module 110 may receive one or more of the current measurements of left atrial pressure, cardiac output, mean atrial pressure, or myocardial oxygen consumption. Similarly, as the target 6 1608025632.3Attorney Docket No.390351-100201 cardiovascular metrics, the cardiac data input module 110 may receive one or more of the desired measurements of left atrial pressure, cardiac output, mean atrial pressure, or myocardial oxygen consumption. The cardiovascular metrics data, in addition to other data, may be used for enabling a closed-loop hemodynamic control module. In some embodiments, the cardiac data input module 110 may support real-time data input (e.g., for closed-loop hemodynamic control), where the server 102 processes the received cardiac data in real-time. In other embodiments, the cardiac data input module 110 may support batch processing, where individual cardiac data are batched (e.g., buffered or stored), and the processing may be performed together for the batched data (e.g., during off-peak hours for the server 102). Therefore, the cardiac data input module 110 may manage the receipt of cardiac data from the clients 106 and the cardiac monitoring system 122 for any type of processing.

[0027] The cardiac contractility calculation module 112 may calculate cardiac contractility using the analytical models disclosed throughout this disclosure. In some embodiments, the cardiac contractility module may calculate Ees as an index of cardiac contractility. Such Ees calculation may be based on left ventricular end-diastolic pressure and volume measured non-invasively through echocardiography. Additionally, the Ees calculation may be based on pulmonary capillary wedge pressure and cardiac output. These measurements may be passed on to the cardiac contractility calculation module 112 by the cardiac data input module 110.

[0028] The closed-loop hemodynamic control module 114 may implement an automatic infusion of optimal combination of drugs (e.g., calculated by the optimal dosage calculation module 116). That is, the closed-loop hemodynamic control module 114 may regularly monitor Eescalculated by the cardiac contractility module, and based on this monitoring, transmit instructions to the cardiac monitoring system 122 to infuse the optimal combination of drugs. This automatic infusion may not necessarily require clinician intervention to keep a patient within a desired range of cardiac contractility.

[0029] The optimal dosage calculation module 116 may calculate optimal dosage based on the Eescalculated by the cardiac contractility calculation module 112. For example, the optimal dosage calculation module 116 may use the calculated Ees to compare it against a target baseline and / or received desired Ees, and invoke one or more analytical models disclosed herein to calculate the optimal dosage of drugs. The optimal dosage calculation module 116 may consider the different effects (e.g., a first drug may cause a change in one direction for Eesand a second drug may cause a change in an opposite direction) to generate an optimal combination. 7 1608025632.3Attorney Docket No.390351-100201

[0030] The model development and simulation module 118 may allow a model developer to develop and simulate one or more analytical modules. For instance, the model development and simulation module 118 may provide an interface, e.g., a graphical user interface, for the model developer to define one or more analytical models. Furthermore, the model development and simulation module 118 may allow the model developer to upload and / or port a pre-defined analytical module to the server 102. The model development and simulation module 118 may therefore generally provide any kind of computing environment support to develop the analytical models described throughout this disclosure.

[0031] The model development and simulation module 118 may further allow the model developer to simulate the analytical models. The simulations may include, for example, numerical simulation, where collected numerical data may be used on the analytical models to observe the outputs. The simulations may produce, for example, numerical data, graphical data, and / or any other type of output data. The model development and simulation module 118 may generally allow for validations of the analytical models based on these simulations (e.g., to determine whether the analytical models perform as desired with simulated scenarios).

[0032] The experimental data ingestion module 120 may ingest experimental data used for model development. For instance, the experimental data may include measured cardiovascular parameters and / or metrics of animals. Such experimental data may be used by the model development and simulation module 118 to simulate the analytical models. Other experimental data may include a detailed experimental data containing both inputs and outputs, and can be used to compare the real-world results with the simulated results. In yet another example, the experimental data may include a continuous stream of data as the patients are being treated in clinical settings, which may be used to continuously modify and / or refine the analytical models. Therefore, the experimental data ingestion module 120 may receive any kind of real-world numerical data that may be used to develop, refine, and / or modify the analytical modules disclosed throughout this disclosure.

[0033] After one or more analytical models have been developed and validated, clinicians may use the software modules 108 within the server 102 in the therapy of patients such as acute heart failure patients. In an example operation, a clinician may use the cardiac monitoring system 122 to non-invasively measure a single point of left ventricular end-diastolic volume and pressure using echocardiography techniques. This measurement may either be entered by the clinician to a client 106 to be transmitted to the server 102 and / or directly transmitted by the cardiac monitoring system 122 to the server 102. The clinician may further measure pulmonary capillary wedge pressure and cardiac output using a pulmonary artery 8 1608025632.3Attorney Docket No.390351-100201 catheterization (which may be functionality supported by the cardiac monitoring system 122). This measurement too may be transmitted to the server 102 through a client 106 and / or the cardiac monitoring system 122. The cardiac data input module 110 may receive these measurements, perform pre-processing as needed, and provide them to the cardiac contractility calculation module 112. The cardiac contractility calculation module 112 may use these measurements to estimate the cardiac contractility (e.g., Ees). This estimated cardiac contractility may be used by the optimal dosage calculation module 116 to provide a recommended dosage to the clinician (e.g., on a client 106 and / or on the cardiac monitoring system 122). Alternatively, the estimated cardiac contractility may be used by the closed-loop hemodynamic control module 114 to provide signals to the cardiac monitoring system 122 for an infusion based on the optimal dosage.

[0034] FIG. 2 depicts an example analytical model 200, according to example embodiments of this disclosure. The example analytical model 200 may be used by the software modules 108 described in FIG.1. For instance, the model development and simulation module 118 may be used to define (and / or port) and simulate the analytical model 200, the experimental data ingestion module 120 may be used to receive experimental data to validate, modify, and / or refine the analytical model 200. Furthermore, the cardiac data input module 110 may receive data to be used by the analytical model 200, the cardiac contractility calculation may calculate cardiac contractility (e.g., Ees) based on the received cardiac data, the optimal dosage calculation module 116 may use the analytical model 200 to calculate an optimal dosage, and the closed-loop hemodynamic control module 114 may provide instructions to the cardiac monitoring system 122 to automatically infuse the calculated dosage. It should further be understood that the analytical model 200 is just an example and should not be considered limiting: analytical models with additional, alternative, or fewer number of steps, and / or components should be considered within the scope of this disclosure.

[0035] As shown, the analytical model 200 is based on a first chart 202 that shows a pressure volume (PLV - VLV) relationship in the left ventricle and a second chart 204 that shows a relationship between cardiac output (CO) and pressure in the left auricle (PLA).

[0036] Particularly, the first chart 202 shows multiple pressure volume loops 206a- 206d (commonly referred to as a pressure volume loop 206 and collectively referred to as pressure volume loops 206). In a pressure volume loop 206, an end-systolic pressure-volume relationship (ESPVR) of the left ventricle can be mathematically represented as: ^^^^ ^^= ^^^^ ^^( ^^^^ ^^− ^^ ^^ − ^^0) (1) 9 1608025632.3Attorney Docket No.390351-100201 where Pes(measured in mmHg) is end-systolic pressure, Ved(measured in ml) is end-diastolic volume, Ees(measured in mmHg / ml) is end-systolic elastance indicating heart contractility, SV (measured in ml / beat) is the stroke volume per beat, and V0 (measured in ml) is a constant parameter that indicates the volume intercept of ESPVR when Pes=0.

[0037] Pescan be approximated using mean arterial pressure (MAP): ^^^^ ^^≈ ^^ ^^ ^^ = ^^^^^^ ^^ = ^^^^^^ ^^60^^ ^^ = ^^^^^^ ^^ (2) where COis systemic vascular resistance, HR (beat / min) is heart rate. It follows from equations (1) and (2) that: ^^ ^^ = ^^ ^^ ^^ ^^ =^^ ^^ ^^ ^^ ^^^^^^ ^^+ ^^^^(^^^^ ^^− ^^0). (3)

[0038] Theof the left ventricle can be represented using the following three-parameter model: ^^^^ ^^= ^^^^ ^^( ^^ ^^ ^^{ ^^^^ ^^( ^^^^ ^^− ^^^^)} − 1) (4) ^ ^^^^ ^^=1 ^^ ^^ ^^+ ^^ ^^ ^^^^ ^^ ^^{log (^^ ^^ ^^) + ^^^^ ^^ ^^ ^^} (5)where Ped (measured pressure ventricle, Ved (measured in ml) is the end-diastolic volume in the left ventricle, and ^^^^ ^^> 0 (measured in mmHg), ^^^^ ^^> 0 (measured in per ml), and Vd (measured in ml) are constant parameters. It should be understood that Vd (at point 208) indicates the volume intercept of EDPVR when Ped = 0.

[0039] Replacing Vedin equation (3) by its expression in equation (5) yields an analytical representation of the Frank-Starling curve as follows: ^^^^ ^^^^ ^^ ^^ ^^ =1^^^^ ^^^^^^ ^^+ ^^^^{log (^^ ^^ ^^^^^^ ^^+ 1) + ^^^^ ^^( ^^^^− ^^0)}. (6)

[0040] Let the gradient of the Frank-Starling curve sL (measured in ml / min) be defined as ^^^^=1 ^^ ^^ ^^ ^^ ^^^^ ^^ ^^ ^^ ^^ ^^+ ^^ ^^. (7) 10 1608025632.3Attorney Docket No.390351-100201 Now, given that Pedis equivalent to left atrial pressure PLA(measured in mmHg) in diastole, ^^^^can be numerically computed by the following expression: ^^^^=^^ ^^log( ^^ ^^ ^^+ ^^ ^^ ^^)−log ^^ ^^ ^^+ ^^ ^^ ^^( ^^ ^^− ^^0)(8) provided that CO and PLAare measurable (e.g., as shown in chart 204) and the constant parameters for the ESPVR model represented by equation (1) and the EDPVR model represented by equation (4) are given.

[0041] Solving Ees as an inverse function of ^^^^yields ^^^^ ^^=^^ ^^ ^^ ^^ ^^ ^^^^ ^^− ^^ ^^ ^^ ^^ ^^^^^^^^60. (9) where Rs can also be^^ − ^^^^ ^^) / ^^ ^^ in which PRA is right atrial pressure.

[0042] The inverse ESPVR estimation method described above works most of the time. Occasionally, however, divergent results are obtained due to singularities caused by zero division in equations (8) and (9). The description below further analyzes these singularities.

[0043] The first singularity is from equation (8) corresponding to the denominator of ^^^^. That is, the first singularity condition is encountered when the denominator of equation (8) equals 0. This singularity condition yields: ^^^^ ^^( ^^) = ^^^^(exp{ ^^^^( ^^0− ^^^^)} − 1) (10)where the LHS is a a constant based on the ESPVR and EDPVR model parameters.

[0044] Let the singular point (e.g., against PLA(t) be defined as: ^^(^^)∶= ^^^^(exp{^^^^(^^0− ^^^^)}− 1)(11) where ^^ = [ ^^0, ^^0, ^^^^, ^^0] is the vector of constant parameters of both EDPVR and ESPVRbe understood that ^^( ^^) can be determined by using only the ESPVR and EDPVR parameters and that ^^( ^^) corresponds to the PLAintercept of the Frank-Starling curve of equation (6). 11 1608025632.3Attorney Docket No.390351-100201

[0045] In addition, let ^^^^ ^^be the lower bound of the measure signal PLA(t), thereby satisfying ^^^^ ^^≤ PLA(t). Therefore, the singularity condition in equation (10) can be avoided if ^^( ^^) < ^^^^ ^^is guaranteed (as shown by curve 210).

[0046] The other findings from analyzing ^^(^^)further are: ^^0≤ ^^^^^ ^^( ^^) ≤ 0 (12) ^^^^< ^^0^ ^^( ^^) > 0. (13)

[0047] In the case of a realistic physiological range where PLA(t) > 0 mmHg, ^^( ^^) ≤0 may need to be satisfied, according to equation (12). In the case that Vd < V0 relationship isfixed, 0 < ^^( ^^) cannot be avoided. The singularity condition, however, can be avoided by minimizing ^^( ^^) by optimizing ^^^^ ^^and ^^^^ ^^, given the acceptable values of ^^^^ ^^> 0, as shown by the singularity avoidance condition 212.

[0048] The second singularity is from equation (9) for Ees and occurs when the denominator is equal to zero. The singularity condition yields: ^^ ^^( ^^) ^^ ^^( ^^)= ^^^^ ^^(14) where the LHS is aor and where the RHS is a constant parameter. Let the physiological ranges of these measured values be given by ^^ ^^ ≤ ^^ ^^( ^^) ≤ ^^ ^^ and ^^^^≤ ^^^^( ^^) ≤ ^^^^, then the constraint to avoid this second singularity condition 214 can be derived as: 0 < ^^^^ ^^<̅^^̅ ̅^^̅^̅^=^^ ^^^^ ^^. (15)

[0049] As an alternates or additions to the above singularity avoidances, the above- described parameters can be optimized to avoid the singularities. For instance, to estimate the parameters λ that facilitate singularity avoidance, the optimization problem can be formulated as a constrained nonlinear least squares problem as follows: minimize (16) ^^^^ ^^ ^^ ^^ ^^−^^ ^^ ^^ ^^ ^^( ^^^^ ^^; ^^)2+ ^^^^ ^^− ^^( ^^)‖21608025632.3Attorney Docket No.390351-100201 0 ≤ ^^^^ ^^≤ + ^^ ^^ƒ ^^ ^^ 0 ≤ ^^^^ ^^≤ ^^^^^^ ≤ ^^^^≤ ^^^^^^0≤ ^^0≤ ^^ where yedpvr is the dataset of end-diastolic points (VLV, PLV), fedpvr (Ved; λ) is the EDPVR model shown in equation (4), μ is the weight parameter for tuning, and ^^^^ ^^, ^^ ^^, ^^^̅^,̅^^̅^̅^, ^^0are parameters based on the physiological knowledge.

[0050] The parameter k is set to impose the inequality ^^0≤ ^^^^as shown in curve 216, which guarantees no singularities in equation (8) when PLA(t) > 0 mmHg is considered. By iterating the parameter k, the optimal parameters λ can be identified when the objective function shown in equation (16) gives the least error.

[0051] FIG.3 depicts a flow diagram of an example method 300, based on the example embodiments of this disclosure. The example method 300 may be performed by any combination of components of the computing environment 100 shown in FIG. 1, using any portion of the analytical model 200 shown in FIG. 2. It should be understood that the steps of the method 300 are just examples and should not be considered limiting. Methods with additional, alternative, or fewer number of steps should be considered within the scope of this disclosure.

[0052] The method 300 may begin at step 302. At step 302, server 102 may receive an input of cardiac data. For example, a desktop terminal in a hospital terminal may be used by a clinician to enter the cardiac data. In some embodiments, the clinician may enter the cardiac data on a smartphone or a tablet computer. In some embodiments, the cardiac data may be sent by a cardiac monitoring system. The cardiac data may include, for example, single point of left ventricular end-diastolic volume and pressure (non-invasively measured through echocardiography), pulmonary capillary wedge pressure, and cardiac output.

[0053] At step 304, the server 102 may calculate cardiac contractility based on the received input cardiac data. For example, the server 102 may use the single point of left ventricular end-diastolic volume to extrapolate an EDPVR curve to generate more samples from the single point (e.g., by using equation 16 associated with the analytical model 200). The server 102 may then impose physiological constraints and singularity avoidance (as per the analytical model 200) to update the EDPVR parameters. The server 102 may then estimate Ees (as an index of cardiac contractility) based on the received pulmonary capillary wedge pressure 13 1608025632.3Attorney Docket No.390351-100201 and cardiac output. For the estimation, the server 102 may consider the pulmonary capillary wedge pressure as left atrial pressure, and also by using the pulmonary artery catheter to estimate cardiac output.

[0054] At step 306, the server 102 may calculate an optimal drug combination based on the cardiac contractility. For example, the optimal drug combination calculation may be based on a desired cardiac contractility vis-à-vis the calculated cardiac contractility.

[0055] In some embodiments, method 300 may include step 308a. At step 308a, the server 102 may output the optimal drug combination (e.g., at the requesting device) to assist clinical decision making. That is, the clinician can rely on the tested and simulated models to aid the decision making and rely less on guesswork.

[0056] In some embodiments, method 300 may include step 308b. At step 308b, the server 102 may use the optimal drug combination for closed-loop hemodynamic system. That is, the server 102 may send instructions to the cardiac monitoring system 122 to automatically infuse the optimal drug combination.

[0057] In some embodiments, server 102 may perform both of the steps 308a, 308b.

[0058] The disclosed analytical model 200 have been evaluated experimentally and through simulation. In an animal experiment, a dog was anesthetized and its bilateral carotid bioreceptors and vagal trunk were denervated. A thoracotomy was conducted, after which the dog was connected to a system that measures arterial pressure (AP) from right femoral artery, cardiac output (CO) via ultrasonic flow meter around ascending aorta, left atrial pressure (PLA) and right atrial pressure (PRA) from fluid filled catheters, left ventricular pressure (PLV) from micromanometer, and hear rate (HR) from an electrocardiogram (ECG) sensor. Two pairs of sono-micrometry crystals were placed in the left ventricle to estimate left ventricular volume (VLV) using a method based on modified ellipsoid formula.

[0059] In a drug infusion experiment, an inferior vena cava occlusion (IVCO) was conducted to record the end-systolic and end-diastolic points in (PLV, VLV) space. Next, a baseline was measured for 1 minute. A single drug was then administered for 10 minutes to measure the pharmacological effect until a steady state. Finally, IVCO was conducted again to measure the drug impacts on Ees before stopping the drug administration. A washout time was given until mean atrial pressure (MAP) stabilized at the pre-drug value. Ees, both before and after the drug administration, was then calculated by applying linear regression to the end- systolic points. Additionally, a nonlinear least squares method was applied to the end-diastolic points to fit the EDPVR function in equation (4) above before the drug administration. Both of these fitting algorithms (i.e., linear regression to the end-systolic points and nonlinear least 14 1608025632.3Attorney Docket No.390351-100201 squares method to the end-diastolic points) were conducted independently and used for a comparison study to evaluate the disclosed analytical models. The same procedures were repeated for each of the four key drugs used in the treatment of acute heart failure: Dobutamine (DOB) at dosage 5.0 μg / kg / min as a positive inotrope, Norepinephrine (NE) at dosage 0.15 μg / kg / min as a vasopressor, Sodium Nitroprusside (SNP) at dosage 5.0 μg / kg / min as a vasodilator, and Dextran (DEX) at dosage 5.0 ml / kg as a fluid. It should be noted that this animal experiment was approved by the animal subjects committee of the National Cerebral and Cardiovascular Center (NCVC), Japan.

[0060] The animal experimentation was further used for a drug library development. A drug library, as detailed here, represents an effect of a combination of drugs on cardiovascularparameters. For this experimentation, let x be cardiovascular parameters such that ^^ =[ ^^ ^^, ^^ ^^ ^^, ^^ ^^, ^^ ^^ ^^] ^^ ^^ ℝ4, where Rs (systemic vascular resistance) is computed by 60 (MAP-PRA) / CO, Ees is measurable either via the analytical models disclosed herein or by a linear regression of end-systolic points of (PLV, VLV) obtained by IVCO, HR is measurable by simple techniques known in the art, and SBV is stressed blood volume estimated through a circulatoryequilibrium format known in the art. Let input u be a drug infusion such that ^^ =[ ^^1, ^^2, ^^3, ^^4] ^^ ^^ ℝ4, which includes the above-described drugs in the treatment of acute heartfailure: DOB, NE, SNP, and DEX. The drug infusion u directly affects the cardiovascular parameters x based on drug pharmacology.

[0061] This drug infusion system can be represented as ^^ƒ= ^^^^+ ^^0(17)In the above equation (17), a that represents multi-dependency effect from each drug (e.g., described above) to cardiovascular parameters in a steady state. As a result of the change in cardiovascular parameter x—for example Ees—multiple cardiovascular metrics such as MAP(t), CO(t), PLA(t) are modulated. To develop the drug library B (i.e., the input matrix), the gains from each drug input ui to each cardiovascular parameter xi were identified by fitting a first order single-input single-output process model. Aggregating the identified gains, a first drug library Bavia the embodiments of ESPVR estimated method and a second drug library Bb may be developed as 15 1608025632.3Attorney Docket No.390351-100201 −0.0335 3.33 −0.419 −0.00725^^ ^^ = [ 3.88 26.1 −1.14 −0.01358.10 24.9 0.164 −0.450] (18) It can be notedlibraries Baand Bb, which indicates a difference in the estimated Ees

[0062] Furthermore, hemodynamic changes (i.e., change in the cardiovascular metrics) may be simulated. For example, a mechanistic, lumped parameter model of the cardiovascular system was utilized to simulate hemodynamic changes introduced by the drug administration. The simulator modeled blood flow through the cardiovascular system by using establishing electrical analogs for fluid dynamics, representing vascular resistance as electrical resistors and compliance as electrical capacitors. The model further used a time-time varying elastance function for each heart chamber, with the valves at the exit of each chamber modeled with electrical diodes and electrical resistors. Each time-varying elastance function therefor depended upon the chamber specific parameters of the ESPVR and EDPVR; and on each cardiac cycle the function simulated contraction as a sinusoidal increase in elastance to a peak of that chamber’s Ees, flowed by a combined sinusoidal and exponential relaxation (indicating a decrease in elastance). Modified Windkessel vascular components may be used to represent systemic and pulmonary circulations, with each including a characteristic impedance along with resistance and capacitance distributed between the arterial, capillary, and venous portions of the circulation. Taken together, these cardiac and vascular components may allow the simulation of time-varying pressures and flows throughout the cardiovascular system, similar to the lumped parameter model. This model was simulated using MATLAB and Simulink computing software (version R2021b, The MathWorks, Inc.), which outputs PLA, PRA, CO, and MAP being simulated for different parameter values. The identified drug library may be used to modulate the cardiovascular parameters within this model and obtain hemodynamic simulation results under the relevant drug infusion scenarios.

[0063] The embodiments for singularity avoidance may also be validated experimentally. For comparison, the following experimental / analytical methods may be implemented: (i) Ees by inverse estimation with singularity avoidance; (ii) Ees by the inverse 16 1608025632.3Attorney Docket No.390351-100201 estimation with ESPVR an EDPVR parameters identified via independent fittings; and (iii) Eesby linear regression to end-systolic points. The analyzed dataset in this experiment is the resulting cardiovascular parameters x and cardiovascular metrics data with the four different drug administration in the animal experimentation described above. Table I shows the parameter settings that may be used in these methods. An optimization library in SciPy software may be used as a solver. TABLE I: Parameters for the proposed optimization problem Const. Value Unit Description µ 10 unitless tuning parameter for optimization ^^ ^^ ^^0.0 [mmHg] singularity 1 Constraint ^^0-10.0 [ml]lower limit of ^^^^ ^^intercept of ESPVR ^^ ^^20.0 [ml] upper limit of ^^^^ ^^intercept of EDPVR ^^ ^^^^ ^^( ^^ = 0) − 20 [ml] lower limit of ^^ ^^100*BW [ml / min] upper limit of ^^^^^^ ^^ 9.7 [kg] weight of the subject

[0064] FIG. 4 depicts example charts 402-408 visualizing comparison between the different methods, according to example embodiments of this disclosure. As can be seen in the charts 402-408, singularity avoidance results in a much smoother Ees curve, particularly for Dobutamine and Dextran infusions. As demonstrated using the embodiments disclosed herein, Norepinephrine is clinically expected to increase Ees (chart 404). As further expected clinically, Dextran infusion (chart 408), based on the embodiments disclosed herein, causes minimal changes. In contrast, the linear fit indicates a decrease, possibly caused by the non-linearity of ESPVR: if VLVincreases, the linear fitting may identify decreased Ees. When the embodiments of the inverse method are used, no such nonlinearity is generated.

[0065] The Eesmay further be validated by simulating hemodynamic changes (i.e., changes in the cardiovascular metrics). In a clinical practice, it may be important to accurately reproduce hemodynamics behavior (i.e., changes in cardiovascular metrics) caused by the change in Ees following drug administration. As described throughout the disclosure, a drug library (e.g., matrix B) may model changes of cardiovascular parameters x induced by drug administration. By using an identified drug library, the simulation may reproduce pharmacological effects to cardiovascular parameters x, which in turn modulate cardiovascular metrics. To that end, this simulation may consider two Eesestimation methods: (i) Eesby the inverse estimation with singularity avoidance and (ii) Ees by linear regression to the end- systolic points. For evaluation, a resulting modulation of the three-dimensional hemodynamics 17 1608025632.3Attorney Docket No.390351-100201 (∆ ^^^^ ^^, ∆ ^^ ^^, ∆ ^^ ^^ ^^) may be used to visualize the performance comparison of the two Eesestimation methods with respect to the animal data. Particularly for the heart failure treatment scenario, a common metric space (∆ ^^^^ ^^, ∆ ^^ ^^), where cardiac CI measured in L / min / m2is calculated as CO normalized by body surface area, may be used based on Forrester classification.

[0066] FIG.5 depicts example charts 502-508 showing modulation of hemodynamics, based on the example embodiments of this disclosure. Particularly, chart 502 shows metrics space (∆ ^^^^ ^^, ∆ ^^ ^^) simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Dobutamine. Chart 504 shows metrics space (∆ ^^^^ ^^, ∆ ^^ ^^) simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Norepinephrine. Chart 506 shows metrics space (∆ ^^^^ ^^, ∆ ^^ ^^) simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Sodium Nitroprusside. Chart 508 shows metrics space (∆ ^^^^ ^^, ∆ ^^ ^^) simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Dextran. As seen in the charts 502-508, the simulations based on the analytical models disclosed herein reproduced the real-world data for ∆ ^^^^ ^^, ∆ ^^ ^^ more accurately compared to the linear fit method.

[0067] FIG.6 depicts example charts 602-608 showing modulation of hemodynamics, based on the example embodiments of this disclosure. Particularly, chart 602 shows metric space ∆ ^^ ^^ ^^ simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Dobutamine. Chart 604 shows metric space ∆ ^^ ^^ ^^ simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Norepinephrine. Chart 606 shows metric space ∆ ^^ ^^ ^^ simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Sodium Nitroprusside. Chart 608 shows metric space ∆ ^^ ^^ ^^ simulated based on the analytical models of ESPVR disclosed herein and ESPVR derived by linear fitting, both compared to real-world animal experimental data for infusion of the drug Dextran. As 18 1608025632.3Attorney Docket No.390351-100201 seen in the charts 602-608, the simulations based on the analytical models disclosed herein reproduced the real-world data for ∆ ^^ ^^ ^^ more accurately compared to the linear fit method.

[0068] Embodiments disclosed herein may therefore improve the robustness of Eesestimation via decreased sensitivity to the nonlinearity of ESPVR. For example, in the Dextran infusion shown in chart 408 of FIG.5, Eesestimated by the analytical models disclosed herein may not substantially change after the drug administration, which Ees estimated by linear fitting may be affected by the nonlinearity of ESPVR. As further shown in chart 508 in FIG. 5 and chart 608 in FIG.6, the analytical models disclosed herein reproduced the response of Dextran with higher accuracy than linear fitting. In addition, when Dobutamine, Norepinephrine, and Sodium Nitroprusside infusion affects both preload and afterload due to the simultaneous change of the cardiovascular parameters x (i.e., Rs, Ees, HR, SBV), the results described above indicate that the analytical models may accurately estimate Eeswithout being affected by such changes.

[0069] It should further be noted that a drop in Eesduring Sodium Nitroprusside infusion may be observed, as shown by chart 406 in FIG. 4. This may likely be caused by hyperfusion of coronary circulation due to excessive lowering of blood pressure, resulting in an actual reduction in cardiac contractility. The simulations—as shown by chart 506 in FIG.5 and chart 606 in FIG.6—indicate that Eesestimations using the embodiments disclosed herein are advantageous for accurately identifying pharmacological effects.

[0070] FIG. 7 shows a block diagram of an example computing device 700 that implements various features and processes, according to example embodiments of this disclosure. For example, computing device 700 may function as the server 102, the clients 106, the cardiac monitoring system 122, or a portion or combination thereof in some embodiments. Additionally, the computing device 700 may partially or wholly host and deploy analytical model 200. The computing device 700 may also perform one or more steps of the method 300. The computing device 700 is implemented on any electronic device that runs software applications derived from compiled instructions, including without limitation personal computers, servers, smart phones, media players, electronic tablets, game consoles, email devices, etc. In some implementations, the computing device 700 includes one or more processors 702, one or more input devices 704, one or more display devices 706, one or more network interfaces 708, and one or more computer-readable media 712. Each of these components is be coupled by a bus 710.

[0071] Display device 706 includes any display technology, including but not limited to display devices using Liquid Crystal Display (LCD) or Light Emitting Diode (LED) 19 1608025632.3Attorney Docket No.390351-100201 technology. Processor(s) 702 uses any processor technology, including but not limited to graphics processors and multi-core processors. Input device 704 includes any known input device technology, including but not limited to a keyboard (including a virtual keyboard), mouse, track ball, and touch-sensitive pad or display. Bus 710 includes any internal or external bus technology, including but not limited to ISA, EISA, PCI, PCI Express, USB, Serial ATA or FireWire. Computer-readable medium 712 includes any non-transitory computer readable medium that provides instructions to processor(s) 702 for execution, including without limitation, non-volatile storage media (e.g., optical disks, magnetic disks, flash drives, etc.), or volatile media (e.g., SDRAM, ROM, etc.).

[0072] Computer-readable medium 712 includes various instructions 714 for implementing an operating system (e.g., Mac OS®, Windows®, Linux). The operating system may be multi-user, multiprocessing, multitasking, multithreading, real-time, and the like. The operating system performs basic tasks, including but not limited to: recognizing input from input device 704; sending output to display device 706; keeping track of files and directories on computer-readable medium 712; controlling peripheral devices (e.g., disk drives, printers, etc.) which can be controlled directly or through an I / O controller; and managing traffic on bus 710. Network communications instructions 716 establish and maintain network connections (e.g., software for implementing communication protocols, such as TCP / IP, HTTP, Ethernet, telephony, etc.).

[0073] Cardiac contractility calculation instructions 718 includes instructions that implement the disclosed process for calculating cardiac contractility for clinical decision making and / or closed-loop hemodynamic control system, as described throughout this disclosure. Application(s) 720 may comprise an application that uses or implements the processes described herein and / or other processes. The processes may also be implemented in the operating system.

[0074] The described features may be implemented in one or more computer programs that may be executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program may be written in any form of programming language (e.g., Objective-C, Java), including compiled or interpreted languages, and it may be deployed in any form, including as a stand-alone program or as a 20 1608025632.3Attorney Docket No.390351-100201 module, component, subroutine, or other unit suitable for use in a computing environment. In one embodiment, this may include Python. The computer programs therefore are polyglots.

[0075] Suitable processors for the execution of a program of instructions may include, by way of example, both general and special purpose microprocessors, and the sole processor or one of multiple processors or cores, of any kind of computer. Generally, a processor may receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer may include a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer may also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data may include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory may be supplemented by, or incorporated in, ASICs (application-specific integrated circuits).

[0076] To provide for interaction with a user, the features may be implemented on a computer having a display device such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user and a keyboard and a pointing device such as a mouse or a trackball by which the user can provide input to the computer.

[0077] The features may be implemented in a computer system that includes a back- end component, such as a data server, or that includes a middleware component, such as an application server or an Internet server, or that includes a front-end component, such as a client computer having a graphical user interface or an Internet browser, or any combination thereof. The components of the system may be connected by any form or medium of digital data communication such as a communication network. Examples of communication networks include, e.g., a telephone network, a LAN, a WAN, and the computers and networks forming the Internet.

[0078] The computer system may include clients and servers. A client and server may generally be remote from each other and may typically interact through a network. The relationship of client and server may arise by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 21 1608025632.3Attorney Docket No.390351-100201

[0079] One or more features or steps of the disclosed embodiments may be implemented using an API. An API may define one or more parameters that are passed between a calling application and other software code (e.g., an operating system, library routine, function) that provides a service, that provides data, or that performs an operation or a computation.

[0080] The API may be implemented as one or more calls in program code that send or receive one or more parameters through a parameter list or other structure based on a call convention defined in an API specification document. A parameter may be a constant, a key, a data structure, an object, an object class, a variable, a data type, a pointer, an array, a list, or another call. API calls and parameters may be implemented in any programming language. The programming language may define the vocabulary and calling convention that a programmer will employ to access functions supporting the API.

[0081] In some implementations, an API call may report to an application the capabilities of a device running the application, such as input capability, output capability, processing capability, power capability, communications capability, etc.

[0082] Additional examples of the presently described method and device embodiments are suggested according to the structures and techniques described herein. Other non-limiting examples may be configured to operate separately or can be combined in any permutation or combination with any one or more of the other examples provided above or throughout the present disclosure.

[0083] It will be appreciated by those skilled in the art that the present disclosure can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restricted. The scope of the disclosure is indicated by the appended claims rather than the foregoing description and all changes that come within the meaning and range and equivalence thereof are intended to be embraced therein.

[0084] It should be noted that the terms “including” and “comprising” should be interpreted as meaning “including, but not limited to”. If not already set forth explicitly in the claims, the term “a” should be interpreted as “at least one” and “the”, “said”, etc. should be interpreted as “the at least one”, “said at least one”, etc. Furthermore, it is the Applicant's intent that only claims that include the express language "means for" or "step for" be interpreted under 35 U.S.C.112(f). Claims that do not expressly include the phrase "means for" or "step for" are not to be interpreted under 35 U.S.C.112(f). 22 1608025632.3

Claims

Attorney Docket No.390351-100201 CLAIMS What is claimed is:

1. A computer-implemented method comprising: receiving, by a computing system, a pulmonary capillary wedge pressure and cardiac output for a human heart; determining, by the computing system, a cardiac contractility for the human heart based on a left ventricular end-systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function; and generating, by the computing system, an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility.

2. The computer-implemented method of claim 1, further comprising: outputting, by the computing system, the optimal combination of drugs to a client device.

3. The computer-implemented method of claim 1, further comprising: controlling, by the computing system, a closed-loop hemodynamic control system based on the optimal combination of drugs to automatically infuse the optimal combination of drugs.

4. The computer-implemented method of claim 1, further comprising: transmitting, by the computing system, the optimal combination of drugs to a closed loop hemodynamic control system that automatically infuses the optimal combination of drugs.

5. The computer-implemented method of claim 1, further comprising: receiving, by the computing system, a single point of left ventricular end-diastolic pressure and volume; extrapolating, by the computing system, a left ventricular end-diastolic pressure and volume relationship curve from the single point; 23 1608025632.3Attorney Docket No.390351-100201 applying, by the computing system, physiological constrained to the extrapolated left ventricular end-diastolic pressure and volume relationship curve to generate updated left ventricular pressure and volume relationship parameters; and generating, by the computing system, the optimal combination of drugs based on the updated left ventricular pressure and volume relationship parameters.

6. The computer-implemented method of claim 5, wherein the single point of left ventricular end-diastolic pressure and volume is non-invasively measured using echocardiography.

7. The computer-implemented method of claim 1, wherein the pulmonary capillary wedge pressure is measured using pulmonary artery catheterization.

8. The computer-implemented method of claim 1, wherein the cardiac output is measured using pulmonary artery catheterization.

9. The computer-implemented method of claim 1, wherein the computing system avoids singularities by parameter optimization.

10. A system comprising: a non-transitory storage medium storing computer program instructions; and a processor configured to execute the computer program instructions to cause operations comprising: receiving a pulmonary capillary wedge pressure and cardiac output for a human heart; determining a cardiac contractility for the human heart based on a left ventricular end-systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function; and generating an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility.

11. The system of claim 10, the operations further comprising: outputting the optimal combination of drugs to a client device. 24 1608025632.3Attorney Docket No.390351-100201 12. The system of claim 10, the operations further comprising: controlling a closed-loop hemodynamic control system based on the optimal combination of drugs to automatically infuse the optimal combination of drugs.

13. The system of claim 10, the operations further comprising: transmitting the optimal combination of drugs to a closed loop hemodynamic control system that automatically infuses the optimal combination of drugs.

14. The system of claim 10, the operations further comprising: receiving a single point of left ventricular end-diastolic pressure and volume; extrapolating a left ventricular end-diastolic pressure and volume relationship curve from the single point; applying physiological constrained to the extrapolated left ventricular end-diastolic pressure and volume relationship curve to generate updated left ventricular pressure and volume relationship parameters; and generating the optimal combination of drugs based on the updated left ventricular pressure and volume relationship parameters.

15. The system of claim 14, wherein the single point of left ventricular end-diastolic pressure and volume is non-invasively measured using echocardiography.

16. The system of claim 10, wherein the pulmonary capillary wedge pressure and cardiac output data is measured using pulmonary artery catheterization.

17. The system of claim 10, wherein the processor avoids the singularities by parameter optimization.

18. The system of claim 10, wherein the cardiac contractility comprises left ventricular end- systolic resistance.

19. A non-transitory storage medium storing computer program instructions that when executed causes a computing system to perform operations comprising: receiving a pulmonary capillary wedge pressure and cardiac output for a human heart; 25 1608025632.3Attorney Docket No.390351-100201 determining a cardiac contractility for the human heart based on a left ventricular end- systolic elastance generated as an inverse function of a gradient of a relationship between the pulmonary capillary wedge pressure and the cardiac output, while avoiding singularities in the inverse function; and generating an optimal combination of drugs to reach a target cardiac contractility from the determined cardiac contractility.

20. The non-transitory storage medium of claim 19, the operations further comprising: controlling a closed-loop hemodynamic control system based on the optimal combination of drugs to automatically infuse the optimal combination of drugs. 26 1608025632.3

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