Invertible models of cardiac function

Abstract

Systems and methods are described herein for predicting change in cardiac function based on in silico modeling. In various aspects, the systems and methods are configured for inverse mechanistic modelling of cardiac function which allows effective and efficient predictions of cardiac function to be made thereby opening the possibility of such approaches to be used in many drug discovery and drug development applications. In one example, in vitro responses of first and second cardiac cell cultures are obtained under a reference condition and a perturbed condition, respectively. A mechanistic model is then obtained or generated to determine estimated value(s) of a functional response. First and second distributions values are obtained from the mechanistic model upon inputting an input parameter vector, and a first relative distribution shift can be determined therefrom, which is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

Description

[0001] INVERTIBLE MODELS OF CARDIAC FUNCTION

[0002] BACKGROUND

[0003] Mechanistic models provide a powerful approach for modelling the dynamical behavior of biological systems such as cardiac cell cultures. Such models typically require that model parameters be estimated from empirical data. However, obtaining adequate data to fit parameters for these models is often a challenging and time consuming tasks. Moreover, it is often difficult to incorporate these mechanistic models into downstream tasks such as drug development and discovery. The successful incorporation of such models into the drug development and discovery process could give rise to numerous benefits such as personalized computational models using patient specific cells (i.e., cells derived from patients), prediction of a patient's responses to treatments, understanding mechanisms underlying non-fully understood cardiac diseases, disease model development, treatment optimization, drug safety and off-target / side effects, and exercise or heavy cardiac load simulation.

[0004] Therefore, there is a need for new approaches to modelling the dynamical behavior of cardiac cell cultures which can be used as the basis for downstream drug development and discovery tasks.

[0005] SUMMARY OF DISCLOSURE

[0006] According to one aspect of the present disclosure, there is provided a method for predicting change in cardiac function. The method comprises obtaining, by one or more processors, a first plurality of in vitro responses comprising measurements of a first functional response of a first cardiac cell culture under reference conditions, and obtaining, by the one or more processors, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture. The method further comprises obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector. The method further comprises determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses, and determining, by the one or more processors, a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses. The method further comprises determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

[0007] According to another aspect of the present disclosure, there is provided a method for inverse mechanistic modelling of cardiac function. The method comprises obtaining, by one or more processors, a first plurality of in vitro responses comprising measurements of at least one functional response of a first cardiac cell culture under a first set of conditions, and obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model predicts one or more values of the at least one functional response based on an input parameter vector. The method further comprises determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses, and determining, by the one or more processors, a shifted first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the shifted first distribution of values meet a predetermined functional response criterion. The method further comprises determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the shifted first distribution of values, wherein the first relative distribution shift is indicative of a predicted change in cardiac function from the first set of conditions to a set of conditions associated with the predetermined functional response criterion.

[0008] According to a still further aspect of the disclosure, systems and methods are disclosed for predicting change in cardiac function. The systems and methods may comprise obtaining, by one or more processors from a bioreactor containing a first cardiac cell culture (e.g., of an engineered cardiac tissue), a first plurality of in vitro responses comprising measurements of a first functional response of the first cardiac cell culture under reference conditions. The systems and methods may further comprise obtaining, by the one or more processors from the bioreactor, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture. The systems and methods may further comprise obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector. The systems and methods may further comprise determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses. The systems and methods may further comprise determining, by the one or more processors, a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses. The systems and methods may further comprise determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition. The systems and methods may further comprise generating, based the change in function of the first cardiac cell culture due to the perturbed condition, one or more outputs identifying or indicative of one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds.

[0009] In accordance with the above, and with the disclosure herein, the present disclosure includes applying certain features or aspects with or by use of, a particular machine, e.g., a bioreactor. In various aspects, the bioreactor may comprise a device configured for growing or manipulating human tissue (e.g., human body tissue such as cardiac tissue). Additionally, or alternatively, bioreactor may comprise a sensor assembly configured to detect one or more functional responses of the tissue within the device.

[0010] Further, the present disclosure includes effecting a transformation or reduction of a particular article to a different state or thing, e.g., the transformation or reduction of functional responses of human tissue, such as cardiac tissue, e.g., within a bioreactor as sensed by a sensor assembly as waveforms, to a different state or thing, e.g., the encoding or transformation of shifts in distribution values of a cardiac cell culture across different conditions (e.g., reference state and perturbed state), which can be directly compared to link and classify functional changes for encoding functional change in a cardiac cell culture. Such different shifts and transformations can be utilized in applications such as predicting effects of unknown compounds and constructing a database of relative shifts for use in drug discovery and development.

[0011] Still further, the present disclosure includes improvements in computer functionality or in improvements to other technologies at least because the disclosure herein discloses systems and methods for implementing in silico (simulated) prediction of effects (e.g., mechanism of action, toxicity, etc.) of an unknown real-world compounds. When implemented on an underlying device, the systems and methods herein allow for generation of data (e.g., features) that define change(s) in dynamical behavior of cardiac tissue or its related function between different states (e.g., a reference state and perturbed state). Such data can be used in drug discovery and development, reducing or eliminating the need for empirical testing, and related processor and data usage therefrom. For example, when deployed on the underlying system, allows the systems and methods of the present disclosure to execute with fewer iterations, and use fewer computing resources, than prior art related systems and methods. That is, the present disclosure describes improvements in the functioning of the computer itself or "any other technology or technical field" because the data generated provided by the in silico algorithms described herein allows the underlying computer system to utilize less processing and memory resources compared to prior art systems and methods. This at least because the in silico data algorithms can generate or determine data of a predictive function of cardiac tissue (e.g., for various control and test conditions), without the need for various tests and / or empirical computer simulation across a wide range of tests using multiple compute cycles and data. Therefore use of the in silico algorithm results in fewer compute cycles, or otherwise iterations, that has less of an impact on the underlying computing device compared to previous prior art systems and methods. Said another way, the systems and methods of the present disclosure improve over the prior art at least because prior art systems and methods require an empirical or trial-and-error approach that can involve real-world trials on human tissue (e.g., cardiac tissue) that can result in, and require, large database and memory utilization and processor usage to arrive at a similar real-world or simulated results that has a same or similar result. On the other hand, the disclosed systems and methods describe generation and / or use of a bioreactor for growing and testing tissue for defining a limited set of data specific to the tissue (e.g., engineered cardiac tissue), which requires less memory usage and / or processing utilization compared to a conventional approach where large sets of unknown, potentially irrelevant data is used or required. Moreover, the disclosure herein allows for prediction of potential treatments to obtain a required change in functional response. For example, in some aspects, this may include generating output(s), based on a change in function or condition i of a cardiac cell culture, for example, from a first condition (e.g., reference condition) to a second condition (e.g., a perturbed condition), which may be used to more accurately identify, or indicate, one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds, for use in drug discovery or development, thus resulting in an improvement to an underlying machine or device upon which the in silico algorithm is deployed.

[0012] In addition, the present disclosure relates to improvement to other technologies or technical fields at least because the systems and methods of the present disclosure provide a robust, efficient, and comparable encoding of cardiac tissue behavior that can be used to improve the efficiency and performance of several downstream drug discovery and development tasks. This may be performed, for example, by a mechanistic model that is determined or otherwise generated with based on in vitro responses comprising measurements of a functional response(s) of a cardiac cell culture. The mechanistic model may be deployed on an underlying computing device or system, thereby, improving its accuracy and prediction in performing drug discovery and development tasks as described herein.

[0013] Still further, the present disclosure includes specific features other than what is well- understood, routine, conventional activity in the field, and / or otherwise adds unconventional steps that confine the disclosure to a particular useful application, e.g., systems and methods for predicting change in cardiac function based on in silico modeling, which can be used, for example, for the effective and efficient output of predictions of cardiac function, which may be used or applied for drug discovery and drug development applications.

[0014] Advantages will become more apparent to those of ordinary skill in the art from the following description of the preferred embodiments which have been shown and described by way of illustration. As will be realized, the present embodiments may be capable of other and different embodiments, and their details are capable of modification in various respects. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive.

[0015] BRIEF DESCRIPTION OF DRAWINGS

[0016] Embodiments of the invention will now be described, by way of example only, and with reference to the accompanying drawings, in which: Figure 1 shows a general architecture for the generation of invertible models of cardiac function according to an aspect of the present disclosure;

[0017] Figure 2 shows a mechanistic model of cardiac function according to an embodiment of the present disclosure;

[0018] Figure 3 illustrates a Markov chain Monte Carlo (MCMC) parameter fitting algorithm according to embodiments of the present disclosure;

[0019] Figure 4 illustrates a hierarchical Bayesian parameter fitting algorithm according to embodiments of the present disclosure;

[0020] Figure 5 illustrates a generative adversarial network (GAN) parameter fitting algorithm according to embodiments of the present disclosure;

[0021] Figure 6 illustrates inverse mechanistic modelling according to an aspect of the present disclosure;

[0022] Figure 7 shows a method for determining a change in cardiac function according to an aspect of the present disclosure;

[0023] Figure 8 shows a set of steps performed in conjunction with the method of Figure 6 according to embodiments of the present disclosure;

[0024] Figure 9 shows a set of steps performed in conjunction with the method of Figure 6 according to embodiments of the present disclosure;

[0025] Figure 10 shows a method for inverse mechanistic modelling of cardiac function according to an aspect of the present disclosure;

[0026] Figure 11 shows a set of steps performed in conjunction with the method of Figure 9 according to embodiments of the present disclosure;

[0027] Figure 12 shows a system for obtaining cardiac cell culture functional response data according to an aspect of the present disclosure;

[0028] Figure 13 shows a waveform comprising a functional response of a tissue over a predetermined time period according to embodiments of the present disclosure; and

[0029] Figure 14 shows an example computing system according to embodiments of the present disclosure. i TECHNICAL FIELD

[0030] The present disclosure relates to the generation of invertible in silico models of cardiac function. Particularly, but not exclusively, the present disclosure relates to the use of functional response data to generate invertible in silico models of cardiac function. Particularly, but not exclusively, the functional response data comprises in vitro functional responses of an engineered cardiac tissue.

[0031] DETAILED DESCRIPTION

[0032] The ability to make accurate, biologically plausible, predictions of cardiac function from an in silico model of a cardiac cell culture is an important step in when identifying target molecules as potential drug candidates and identifying potential effects (e.g., mechanism of action, toxicity, etc.) of unknown compounds. The present disclosure describes systems and methods for inverse mechanistic modelling of cardiac function which allows effective and efficient predictions of cardiac function to be made thereby opening the possibility of such approaches to be used in many drug discovery and drug development applications.

[0033] Figure 1 shows a general architecture for the generation of invertible models of cardiac function.

[0034] The general architecture comprises a non-invertible phase 102 and an invertible phase 104. The non-invertible phase 102 involves a plurality of in vitro responses 106 of a cardiac cell culture 108 under one or more conditions, a mechanistic model 110 of cardiac function, a parameter fitting algorithm 112, and a distribution of values 114. The mechanistic model 110 takes an input parameter vector 116 as input and determines estimated functional response values (e.g., a set of first estimated functional response values 118-1) as output. In an embodiment, a database 120 is used to store the distribution of values 114 and other such information. The invertible phase 104 involves a shift 122 of the distribution of values 114 learnt during the non-invertible phase 102 and a set of predicted functional response values (e.g., the set of first predicted functional response values 124-1) determined from the mechanistic model 110 based on the shifted distribution of values.

[0035] The non-invertible phase 102 seeks to learn a parameterization of the mechanistic model 110 (i.e., the distribution of values 114 for the input parameter vector 116). This parameterization results in the mechanistic model 110 producing predicted functional response values of the cardiac cell culture 108 which approximate empirical functional response values of the cardiac cell culture 108. The parameterization is learnt by the i parameter fitting algorithm 112 determining the distribution of values 114 which results in the mechanistic model 110 producing functional response values which closely match those of the plurality of in vitro responses 106. Once the distribution of values 114 has been determined, repeated predictions obtained from the mechanistic model 110 parameterized according to the distribution of values 114 allows accurate in silico predictions of cardiac function to be obtained. The mechanistic model 110 parameterized according to the distribution of values 114 thus acts as an in silico model of the cardiac cell culture 108.

[0036] Thus, the distribution of values 114 of the input parameter vector 116 provides an efficient featurization of the one or more conditions of the cardiac cell culture 108. This link between the distribution of values 114 and the one or more conditions allows the change in cardiac function between conditions to be encoded by a relative shift in distribution of values (e.g., the relative shift from a distribution associated with a first condition to a distribution associated with a second condition). Because the distributional shift is relative, different shifts can be directly compared to link and classify functional changes. As will be described in more detail below, this provides a powerful framework for encoding functional change in cardiac cell culture which can be utilized in applications such as predicting effects of unknown compounds and constructing a database of relative shifts for use in drug discovery and development.

[0037] The invertible phase 104 utilizes the mechanistic model 110 parameterized according to the distribution of values 114 (learnt during the non-invertible phase 102) to predict functional responses of the cardiac cell culture 108. Because the distribution of values 114 provides an accurate in silico model of the cardiac cell culture 108 under one or more conditions, shifts applied to the distribution of values 114 provide biologically plausible and meaningful predictions of how changes to the one or more conditions may affect the functional response of the cardiac cell culture 108. For example, a shift applied to a parameter associated with calcium binding may lead to a predicted increase in contractile force of the cardiac cell culture. Therefore, one or more distributions in the distribution of values 114 associated with one or more parameters of the input parameter vector 116 may be shifted until a predicted functional response value obtained from the mechanistic model 110 reaches a predetermined criterion or value. The resulting shift of the one or more distributions represents the change in function of a cardiac cell culture which may be required to achieve the desired change in functional response.

[0038] As stated previously, the relative shifts in parameter distributions provides an effective featurization, or signature, of the change in cardiac function. These relative shifts are then used to identify candidate agents or treatments which are predicted to provide a change in cardiac function.

[0039] The cardiac cell culture 108 is either a 2D culture (e.g., monolayers) or a 3D tissue formed from 3D culture. As described in more detail below in relation to Figure 12, the cardiac cell culture 108 is grown within a bioreactor (e.g., the bioreactor 1202 shown in Figure 12) from cells seeded within a well of the bioreactor.

[0040] The cardiac cell culture 108 is associated with one or more conditions which may generally be considered as a reference to the state(s) of the cardiac cell culture 108. As the condition (state) of a cardiac cell culture may change over time, the condition is time dependent. As such, the plurality of in vitro responses 106 are associated with the condition(s) of the cardiac cell culture 108 at the time point at which the in vitro responses 106 are obtained, or at which data from which the in vitro responses 106 were obtained.

[0041] The conditions may be reference conditions or perturbation conditions. In general, reference conditions refer to conditions which provide a baseline comparison to the perturbation conditions. In embodiments, a reference condition is a condition associated with a control setup or environment. As such, a reference condition may alternatively be referred to as a control condition or baseline condition. A reference condition may correspond to a cardiac cell culture in its default, natural, or unaltered state (i.e., without dosage of a drug or agent). Alternatively, a reference condition may correspond to vehicle treated cardiac cell culture. Perturbation conditions refer to conditions in which the cardiac cell culture has been perturbed in some way. Examples of perturbation conditions include the administration of a drug or compound (i.e., a perturbant), a disease state, a different cell line, or a physical perturbance applied to the cardiac cell culture. As such, perturbation conditions may alternatively be referred to as treatment conditions. In the case of perturbations involving a drug or compound, the conditions are further associated with an effect related to the drug or compound such as a mechanism of action or a toxicity. Given the range of different perturbation conditions, a cardiac cell culture may be associated with more than one perturbation condition (e.g., a diseased cardiac cell culture having been treated with a specific compound).

[0042] As will be described in more detail below, the link between the one or more conditions of a cardiac cell culture and the input parameter vector 116 of the mechanistic model 110 allows in silico comparisons and identifications of changes or shifts in cardiac function to be obtained.

[0043] The plurality of in vitro responses 106 obtained in the non-invertible phase 102 correspond to empirical measurements of the cardiac cell culture 108 under an associated condition or conditions. The plurality of in vitro responses 106 provide empirical data relating to the functional response of the cardiac cell culture 108 under the associated condition(s) and is used in the non-invertible phase 102 to fit a distribution of input parameters to the mechanistic model 110. As such, the plurality of in vitro responses 106 may alternatively be referred to as empirical responses, empirical data, experimental responses, experimental data, in vitro data, or empirical functional response data. The plurality of in vitro responses 106 comprise a first set of measurements 106-1 (observations or data points) associated with a first functional response of the cardiac cell culture 108. The plurality of in vitro responses 106 may further comprise a second set of measurements 106-2 (observations or data points) associated with a second functional response of the cardiac cell culture 108 and / or a third set of measurements 106-3 (observations or data points) associated with a third functional response of the cardiac cell culture 108.

[0044] Here, a functional response is to be understood as a biophysical response of a cardiac cell culture such as a contractile force, a calcium response or property (e.g., calcium transients), or an electrical response or property. As such, the plurality of in vitro responses 106 comprise measurements, or values, related to one or more of such functional responses of the cardiac cell culture 108. Thus, the functional response measurements within the plurality of in vitro responses 106 comprise one or more of: measurements related to a contractile force of the cardiac cell culture 108; measurements related to calcium properties of the cardiac cell culture 108; and measurements related to electrical properties of the cardiac cell culture 108. For example, the first set of measurements 106-1 may comprise contractile force measurements whilst the second set of measurements 106-2 and the third set of measurements 106-3 may comprise calcium property measurements and electrical property measurements respectively.

[0045] The plurality of in vitro responses 106 are extracted from one or more functional response waveforms of the cardiac cell culture 108. For example, a first waveform may capture the contractile force of a cardiac cell culture over a 30 second period whilst a second waveform may capture the calcium transients of the cardiac cell culture over the same period. As described in more detail below in relation to Figures 12 and 13, a cardiac cell culture within a bioreactor (such as the bioreactor 1202 shown in Figure 12) may be exposed to an electrical stimulation at a predetermined pacing frequency and the change in functional response (e.g., contractile force, calcium transients, etc.) of the cardiac cell culture over time recorded as a waveform. Alternatively, the waveform captures the change in functional response of the cardiac cell culture over time in the absence of stimulation (i.e., the spontaneous response of the cardiac cell culture). In either case, each value of the waveform corresponds to the functional response of the cardiac cell culture at a respective time point (e.g., a contractile force of 120 / zm at time point tlfa contractile force of llO n at time point t2, etc.). The measurements, or feature values, which form the plurality of in vitro responses 106 are extracted from the waveform using a feature extraction process. In an embodiment, peak analysis is performed on the waveform to extract one or more numerical features from each contraction-relaxation of the cardiac cell culture within the waveform. The numerical features extracted from the waveform include twitch amplitude, contraction time, maximum contraction slope, relaxation time, maximum relaxation slope, and twitch duration. As such, the plurality of in vitro responses 106 comprises multiple measurements or feature values for each peak within the functional response waveform. Alternatively, the measurements comprise summary statistics such as the mean, median, standard deviation, and the like derived from the waveform feature values. In another embodiment, a spectral transformation is applied to the waveform to extract a spectral representation of the functional response. The spectral representation takes the form of a spectral density which provides a frequency-based characterization of the functional response(s). Example spectral transformations include Fourier transforms and maximum entropy transforms.

[0046] In one embodiment, the plurality of in vitro responses 106 are obtained either directly or indirectly from a bioreactor containing the cardiac cell culture 108 (e.g., the bioreactor 1202 shown in Figure 12). When obtained directly, the feature extraction process is performed at the bioreactor and the plurality of in vitro responses 106 are obtained from the bioreactor. When obtained indirectly, the waveform from which the in vitro responses are extracted is obtained from the bioreactor and a secondary system (e.g., the control unit 1204 shown in Figure 12) performs the feature extraction process to obtain the plurality of in vitro responses 106. Beneficially, utilizing a bioreactor, such as that described in relation to Figure 12, to cultivate and maintain the cardiac cell culture allows large volumes of functional data to be obtained efficiently across a range of cardiac cell cultures under different conditions. This is particularly beneficial for the purpose of parameter fitting where a greater volume of data allows for improved estimation of the distribution of values 114 for the input parameter vector 116.

[0047] The plurality of in vitro responses 106 are associated with the one or more conditions (i.e., the state) of the cardiac cell culture 108 at the time the functional response waveforms from which they derived were obtained. As such, the conditions may be considered labelling information (i.e., metadata) associated with the cardiac cell culture 108. As will be described in more detail below, this information is used when identifying potential treatments or effects based on comparisons of distributional shifts.

[0048] The plurality of in vitro responses 106 provide high-fidelity empirical measurements of the behavior of the cardiac cell culture under the set of one or more conditions (i.e., reference conditions or perturbation conditions). Therefore, the plurality of in vitro responses provide an efficient, high-fidelity, and high-density set of data from which input parameters of the mechanistic model 110 may be fit to determine a distribution, or distributions, of values of the input parameter vector 116.

[0049] The mechanistic model 110 is an in silico model of cardiac function (i.e., an in silico model of the function of the cardiac cell culture 108). The mechanistic model 110 takes as input one or more input parameters in the form of an input parameter vector 116 and determines an estimated functional response value, or values, (e.g., the set of first estimated functional response values 118-1) as output. The input parameter vector 116, along with the initial conditions of the model, determine the dynamical behavior of the mechanistic model 110. As described in more detail below, the parameter values are a priori unknown and are therefore estimated from the plurality of in vitro responses 106 (i.e., the input parameter vector 116 is fit to the plurality of in vitro responses 106). As the plurality of in vitro responses 106 are associated with the condition(s) of the cardiac cell culture 108 at the time at which the responses are obtained or derived, the distribution of values 114 for the input parameter vector 116 are also associated with the condition(s) of the cardiac cell culture 108. The distribution of values 114 thus provide an in silico parameterization of the condition of the cardiac cell culture 108 such that predicted functional response value produced by the mechanistic model 110 based on the input parameter vector 116 taking values from the distribution of values 114 will approximate empirical functional response values of the cardiac cell culture 108 when under the condition(s). That is, once learnt, the distribution of values 114 for the input parameter vector 116 allow the mechanistic model 110 to estimate the function of the cardiac cell culture 108 under the condition(s).

[0050] At a general level, the mechanistic model 110 is a mathematical model parameterized by the input parameter vector 116. In one embodiment, the mechanistic model 110 comprises one or more ordinary differential equations (ODEs). ODEs are well suited to modeling dynamical systems such as the heart or biological subsystems thereof because they allow various biochemical interactions which occur within such systems to be translated into one or more rate equations. Figure 2 shows a mechanistic model 200 of cardiac function according to an embodiment of the present disclosure. In one embodiment, the mechanistic model 200 corresponds to the mechanistic model 110 shown in Figure 1.

[0051] The mechanistic model 200 comprises a plurality of equations (ODEs) which model the dynamic contractile behavior of a cardiac cell culture or tissue so as to generate an estimation of contractile force at a given time point, t. The equations of the mechanistic model 200 are grouped into functional blocks, or groups, as shown in Figure 2. A first function block 202 estimates intracellular calcium transient that drives contraction, [Ca](t). A second functional block 204 estimates the fraction of troponin complexes with bound calcium, A. A third functional block 206 estimates the faction of cross-bridge (XB) groups engaged, GXB. A fourth functional block 208 estimates the total fraction of XBs in a force generating state, XBA. A fifth functional block 210 estimates the fraction of bound XBs within a group, XBC. A sixth functional block 212 estimates the mean XB strain, s. A seventh functional block 214 estimates the sarcomere length, SL. An eighth functional block 216 estimates the length dependence for thin filament, LDFthin( ). A ninth functional block 218 estimates the length dependence for thick filament, LDFthick(X). A tenth functional block 220 estimates the active tension, Ta. An eleventh function block 222 estimates the active force, FA.

[0052] At the first functional block 202 of the mechanistic model 200, the intracellular calcium transient that drives contraction, [Ca](t), at time point, t, is estimated as where

[0053] Here, Cadiastis the diastolic calcium level, tstartis the starting time point of the calcium transient, Caampis the amplitude of calcium transient, T1is a time constant for the upstroke of calcium transient, and T2is a time constant for the decay of calcium transient.

[0054] The intracellular calcium transient, [Ca](t), estimated at the first functional block 202 is used at the second functional block 204 to estimate the fraction of troponin complexes with bound calcium, A. The second functional block 204 estimates the value of A as

[0055] A — AH* LDFthin(X) + AL* (1 — LDFtflirl, (3) where

[0056] Here, AHis the fraction of bound high calcium affinity troponin sites, LDFthin(X) is the length dependence for thin filament estimated by the ninth functional block 218, ALis the fraction of bound low calcium affinity troponin sites, konTis a rate constant of calcium binding to troponin sites, koffHTis a rate constant of unbinding to high affinity sites, and koffLTis a rate constant of unbinding to low affinity sites.

[0057] The estimated fraction of troponin complexes with bound calcium, A, determined at the second functional block 204 is used to estimate the fraction of cross-binding (XB) groups engaged in force generation, GXB, at the third functional block 206. The fraction of XB groups engaged, GXB, is estimated by

[0058] Where

[0059] In the above equations, fG, gG, g, and gGmaxare model parameters (as described in more detail below, these parameter may either be variable or constant), nAis the Hill coefficient corresponding to the sensitivity or degree of cooperativity between subunits that bind calcium, Asois the half-saturation constant which corresponds to the threshold concentration for 50% response, s is the mean cross-binding strain estimated by the sixth functional block 212, and smodis the mean strain modified by XB power-stroke distortion which is defined as

[0060] Here, a is a parameter accounting for positive or negative strain, and x0is the distortion due to XB power-stroke (the step size of myosin power stroke).

[0061] At the fourth functional block 208, the total fraction of XBs in force-generating state, XBA, is estimated as XBA— GXB* XBC, (11) where GXBis the fraction of XB groups that are engaged in force generation, estimated at the third functional block 206, and XBCis the fraction of bound XBs within a group, estimated at the fifth functional block 210.

[0062] The fraction of bound XBs within a group, XBC, is estimated at the fifth functional block 210 by where

[0063] 9XB (S)=9XB *smod- (13)

[0064] Here, fXBand gXBare model parameters which can either be variable or constant. As stated above, s is the mean cross-binding strain estimated by the sixth functional block 212 and smodis the mean strain modified by XB power-stroke distortion (as described above).

[0065] At the sixth functional block 212, the mean XB strain, s, is estimated by ds 1 dSL 1 — XBCdt 2 dtJXBXBG(14) where fXBis a model parameter, SL is the sarcomere length estimated at the seventh functional block 214, and XBCis the fraction of bound XBs within a group estimated at fifth functional block 210.

[0066] The sarcomere length, SL, used at the sixth functional block 212 is estimated at the seventh functional block 214 according to:

[0067] SL = SLsiack* A, (15)

[0068] Here, SLslackis the sarcomere resting or slack length, A is the stretch ratio of a sarcomere, TTP is the time to maximum contraction, and s is the mean cross-binding strain estimated by the sixth functional block 212.

[0069] At the eighth functional block 216, the length dependence for thin filament, LDFthin(X), is estimated as is In the above equation, LDFthinmaxis the maximum length dependence for thin filament, Aas0> ^-asi are the slopes of the piecewise linear function, and Aan0< Aanlare nodes defining discontinuities.

[0070] At the ninth functional block 218, the length dependence for thick filament, LDFthick(A') , is estimated as

[0071] In the above equation, LDFthickmaxis the maximum length dependence for thick filament, Ams0> ^-msi are the slopes of the piecewise linear function, and Amn0< Amnlare nodes defining discontinuities.

[0072] The active tension, Ta, is then estimated at the tenth functional block 220 according to

[0073] Ta=a * LDFthick(A') * XBA* (s + XQ'). (19)

[0074] Here, Sais a scaling factor for tension generated by sarcomere, LDFthick(A') is the length dependence for thick filament estimated at the ninth functional block 218, XBAis the total fraction of XBs in a force-generating state estimated at the fourth functional block 208, s is the mean cross-binding strain estimated at the sixth functional block 212, and x0is the distortion due to XB power-stroke (the step size of myosin power stroke).

[0075] At the eleventh functional block 222, the active tension Ta, estimated at the tenth functional block 220, is converted to active force, FA, according to

[0076] FA= Ta* ST, (20) where STis a scaling factor for cell culture or tissue force.

[0077] The mechanistic model 200 is thus parameterized according to one or more variable parameters (which form an input parameter vector, such as the input parameter vector 116 shown in Figure 1) and one or more constant parameters. As described in more detail below, whilst the constant parameters of the mechanistic model 200 are a prior known and thus fixed, a distribution of values for each of the variable parameters (i.e., each parameter in the input parameter vector) is determined using empirical data (e.g., the plurality of in vitro responses 106 shown in Figure 1).

[0078] In one embodiment, the variable parameters— i.e., the parameters which form the input parameter vector— are the amplitude of calcium transient Caampe [0.5,2] / zM, the diastolic calcium level Cadiaste [0.05,0.4] / zM, the decay of transient time constant T2e [20,140] ms, the calcium binding to troponin sites rate constant konTe [10,70] / zM-1s-1, the unbinding to high affinity sites rate constant koffHTe [5, 70] s-1, the unbinding to low affinity sites rate constant koffLTe [20, 1400] s-1, the Hill coefficient nAe [3, 15] au, the half-saturation constant X50e [0.4, 1.2] au, and the parameters fce [5,1500] ms"1, gce [5e - 3, 5e - 2] ms-1, gXBe -1 -1s, £ {0 < < < 1}), g = 3 au, gGmax= 5e + 6 s-1, x0= 0.07 urn, a = 0.05 for positive strain and a = 1 for negative strain, SLsiack= 1.9 gm, Sa= 250e - 6 N gm~3, and ST= 1000. The variables AH, AL, smod, and A are time dependent and determined using the above parameters according to equations (4), (5), (10), (15), and (16) respectively (as described above).

[0079] Referring once again to Figure 1, the parameter fitting algorithm 112 is used to determine the distribution of values 114 for the input parameter vector 116 of the mechanistic model 110 (as described above in relation to Figure 2) based on the plurality of in vitro responses 106. For each parameter within the input parameter vector 116 (e.g., the amplitude of calcium transient, the diastolic calcium level, etc.), the parameter fitting algorithm 112 will determine a distribution of values for that parameter. The distribution of values 114 may alternatively be referred to as a distribution, a parameter distribution, a distribution set, or a parameter distribution set. The parameter fitting algorithm 112 determines the distribution of values 114 such that estimated functional response values obtained from the mechanistic model 110 based on input values obtained from the distribution of values 114 approximate measurements from the plurality of in vitro responses 106 (e.g., the set of first estimated functional response values 118-1 approximate the set of first functional response values 106-1). That is, the estimated or predicted distribution of functional responses approximate, or match, the empirical distribution determined from the plurality of in vitro responses 106.

[0080] In one embodiment, the parameter fitting algorithm 112 comprises a Markov Chain Montel Carlo (MCMC) algorithm as illustrated in Figure 3.

[0081] Figure 3 shows an input parameter vector 302, a mechanistic model 304 of cardiac function, a plurality of in vitro responses 306, and a distribution of values 308 for the input parameter vector 302. In one embodiment, the input parameter vector 302, the mechanistic model 304, the plurality of in vitro responses 306, and the distribution of values 308 correspond to the input parameter vector 116, the mechanistic model 110, the plurality of in vitro responses 106, and the distribution of values 114 shown in Figure 1.

[0082] The input parameter vector 302 comprises a first parameter 310 and may further comprise a second parameter 312 and a third parameter 314. The mechanistic model 304 determines a set of first estimated functional response values 304-1 associated with a first functional response based on the input parameter vector 302. For example, the mechanistic model 304 may determine an estimated contractile force value based on the input parameter vector 302. In one embodiment, the mechanistic model 304 further determines a set of second estimated functional response values 304-2 associated with a second functional response and / or a set of third estimated functional response values 304- 3 associated with a third functional response. The plurality of in vitro responses 306 comprise a first set of measurements 306-1 associated with the first functional response. In one embodiment, the plurality of in vitro responses 306 further comprise a second set of measurements 306-2 associated with the second functional response and / or a third set of measurements 306-3 associated with the third functional response.

[0083] Markov chain Monte Carlo (MCMC) algorithms are Bayesian approaches to estimating the full posterior distribution of parameters for a model or process. At a general level, an MCMC algorithm will draw a sample set of input parameters from a prior distribution of the input parameters and evaluate the likelihood of the functional response outputs from the mechanistic model given the sample set of input parameters. An acceptance / rejection strategy based on Bayes law is then used to determine whether to keep the sample set of parameters and update the prior distribution or to discard them. The MCMC algorithm will then draw a new set of parameters and repeat the process until a termination criterion is reached (e.g., the number of parameters retained reaches a threshold amount). Once the termination criterion is reached, the parameters which were kept approximate the posterior distribution of parameters for the mechanistic model and repeated sampling will produce sample values of the input parameter vector under the target posterior distribution.

[0084] The MCMC algorithm is either unconstrained or constrained. The unconstrained MCMC algorithm treats the parameters within the input parameter vector, 0, as random variables rather than unknown constants. Starting with a certain prior distribution density q(0), the aim is to update the prior distribution density through the data, X, to obtain the posterior distribution density q(0| ), which is proportional to L(0,y, / z, <r) q(0) (Bayes' formula). Here, L(e,y,ii,a) is the likelihood of the mechanistic model:

[0085] Here, y corresponds to the output of the mechanistic model given the input parameter vector 0, and / z and a are obtained from the observed data X. In one embodiment, X and y are log transformed prior to computing / z and <r. In one embodiment, the prior q(0) is chosen as a uniform distribution.

[0086] IB In one embodiment, the MCMC algorithm comprises the Metropolis-Hastings algorithm. The posterior density q(0| ) is obtained as the equilibrium distribution density TT(0) of a Markov chain (0fc) where the next state 0k+1depends only on the present state 0k. In the Metropolis-Hastings algorithm, the Markov chain is implemented using an acceptance-rejection sampling method. Namely, given the current state 6 of the chain, a new candidate state O' is generated according to a proposal density TT(0' |0), which is accepted with probability

[0087] In the present disclosure, the proposals are sampled from a uniform distribution centered at the current state 6 of the Markov chain, with standard deviation set initially as a small positive number. Since such a proposal density is symmetric, TT(0' |0) = TT(0|0'), the acceptance probability of Eq. (22) is reduced to

[0088] The above acceptance-rejection sampling method is repeated until a termination criterion is met. In one embodiment, the termination criterion comprises a maximum number of iterations (e.g., 1000 iterations, 10000 iterations, 100000 iterations, etc.). In another embodiment, the termination criterion comprises an equilibrium criterion such that the sampling method terminates after an equilibrium has been reached (e.g., as identified using a method such as the Gelman-Rubin convergence diagnostic).

[0089] After the termination criterion has been reached, continued performance of the MCMC algorithm produces (random) sample values of the input parameter vector 6 under the target posterior distribution q(G| ). Input parameters for the mechanistic model may be obtained from the fitted distribution by taking the posterior mean (also called the Bayesian estimate) or the posterior median, both of which are determined empirically on the basis of the posterior sample. Beneficially, the use of MCMC allows accurate point estimates of the input parameter vector to be obtained and also allows the entire posterior distribution to be determined.

[0090] The constrained MCMC algorithm follows a similar approach to the constrained MCMC algorithm but splits the input parameter vector 302 into shared and variable parameters. The distributions for the shared parameters are shared across treatment groups, or conditions, whilst the variable parameters are separate for each treatment group or condition thereby allowing them to change per treatment group or condition. The split of the input parameter vector 302 into shared and variable parameters may be determined by the plurality of in vitro responses 306 or manually identified. In Figure 3, the first parameter 310 and the third parameter 314 are shared parameters which would be learnt across treatment groups or conditions, whilst the second parameter 312 is a variable parameter which would be learnt separately for each treatment group or condition. As an example of the constrained MCMC algorithm, consider a situation involving in vitro responses of a cardiac cell culture under a reference condition (i.e., control) and in vitro responses of the cardiac cell culture under a perturbation condition. When applying the constrained MCMC algorithm to learn the distribution for each parameter of an input parameter vector, the reference condition responses and the perturbation condition responses are both used to determine the distributions for the shared parameters (e.g., the first parameter 310 and the third parameter 314), whilst distributions for variable parameters are learnt independently (e.g., a reference second parameter 312-1 is learnt from the reference condition responses and a perturbation second parameter 312-2 is learnt from the perturbation responses). Therefore, the distribution of values for the reference condition and the distribution of values for the perturbation condition would have the same distributions for the shared parameters but different distributions for the variable parameters.

[0091] Beneficially, the constrained approach to the MCMC algorithm increases the available data for common parameters whilst allowing parameters relative to a treatment or condition to vary. This helps provide improved estimates of the input parameter vector 302 which in turn leads to improvements in downstream drug discovery and development tasks which utilize the input parameter vector 302.

[0092] In one embodiment, the parameter fitting algorithm 112 in Figure 1 comprises a hierarchical Bayesian algorithm as illustrated in Figure 4.

[0093] Figure 4 shows an input parameter vector 402, a mechanistic model 404 of cardiac function, a plurality of in vitro responses 406, and a distribution of values 408 for the input parameter vector 402. In one embodiment, the input parameter vector 402, the mechanistic model 404, the plurality of in vitro responses 406, and the distribution of values 408 correspond to the input parameter vector 116, the mechanistic model 110, the plurality of in vitro responses 106, and the distribution of values 114 shown in Figure 1. Figure 4 further shows a set of priors 410 associated with the input parameter vector 402.

[0094] The input parameter vector 402 comprises a first parameter 412, a second parameter 414 and optionally comprises a third parameter 416. The first parameter 412 and the third parameter 416 are shared, or common parameters, whilst the second parameter 414 is a variable parameter. The set of priors 410 comprises a first prior distribution 418 associated with the first parameter 412, a second prior distribution 420 associated with the second parameter 414, and optionally comprises a third prior distribution 422 associated with the third parameter 416.

[0095] As in the MCMC approach described in relation to Figure 3 above, the mechanistic model 404 determines a set of first estimated functional response values 404-1 associated with a first functional response based on the input parameter vector 402. In one embodiment, the mechanistic model 404 further determines a set of second estimated functional response values 404-2 associated with a second functional response and / or a set of third estimated functional response values 404-3 associated with a third functional response. The plurality of in vitro responses 406 comprise a first set of measurements 406-1 associated with the first functional response. In one embodiment, the plurality of in vitro responses 406 further comprise a second set of measurements 406-

[0096] 2 associated with the second functional response and / or a third set of measurements 406-

[0097] 3 associated with the third functional response.

[0098] In general, the hierarchical Bayesian approach uses different levels to approximate the full posteriors of the parameters in the input parameter vector 402 across multiple groups. Here, the groupings are associated with the in-vitro data which is used to fit the parameters if the mechanistic model 110 (e.g., the plurality of in vitro responses 406). For example, the in vitro data may comprise data obtained from one or more cardiac cell cultures within a control group and one or more cardiac cell cultures within a treatment group. Alternatively, the in vitro data may comprise data collected across different time periods (e.g., across different days). In one embodiment, the groupings are made based on one or more features or patterns within the plurality of in vitro responses 406. In the example shown in Figure 4, the hierarchical Bayesian approach is applied to two groups such that a distribution for the variable parameter (i.e., the second parameter 414) is learnt for each group. As such, the input parameter vector 402 includes a second parameter 414-1 associated with the first group and a second parameter 414-2 associated with the second group. Both the second parameter 414-1 associated with the first group and the second parameter 414-2 associated with the second group have associated prior distributions 420-1.

[0099] The hierarchical Bayesian approach assumes shared population level priors for both groups and then allows the posterior for each group to vary. As an example, consider an input parameter vector, 0, composed of a set of shared parameters, a, and one or more variable parameters b such that 6 = [a,b]. In the case of two groups, the hierarchical Bayesian approach fits the input parameter vector 6 = [a.b^b^ where brcorresponds to the one or

[0100] 11 more variable parameters for the first group and b2corresponds to the one or more variable parameters for the second group. For in vitro (empirical) data associated with the first group the model parameters being fit are [a.b- , whilst for in vitro (empirical) data associated with the second group the model parameters are [a,b2]. The parameters in the input parameter vector 6 are fit using a Markov chain Monte Carlo (MCMC) approach as described above in relation to Figure 3. However, unlike the above described approach, a separate Markov chain is associated with each parameter group (i.e., a separate Markov chain will be associated with each of the parameters or parameter groups a.b^b^. This allows different posterior distributions to be learnt for the variable parameters across both groups whilst maintaining the same posterior distribution for the common parameters.

[0101] In the hierarchical Bayesian approach, differences in the posterior distributions can be investigated once the parameters have been fit by adjusting the prior distributions (i.e., adjusting the prior distributions within the set of priors 410). Moreover, comparing the posterior distributions of the parameters for each of the groups allows significant differences between the groups to be identified.

[0102] In one embodiment, the parameter fitting algorithm 112 in Figure 1 comprises a generative adversarial network (GAN) 500 as illustrated in Figure 5.

[0103] The GAN 500 comprises a generator network 502 and a first discriminator network 504. Figure 5 further shows an estimated input parameter vector 506, a mechanistic model 508 of cardiac function, a plurality of in vitro responses 510, and a random variable 512. In one embodiment, the GAN 500 further comprises a second discriminator network 514 and a simulated input parameter vector 516.

[0104] At a general level, the GAN 500 is trained to transform random variables with a normal distribution to input parameter vectors such that the estimated, or predicted, functional response values determined by the mechanistic model 508 based on the input parameter vectors approximate the plurality of in vitro responses 510.

[0105] In one implementation, the generator network 502 comprises 8 hidden layers with 160 nodes per hidden layer and the first discriminator network 504 comprises 8 hidden layers with 80 nodes per layer. Both networks use ReLU activation functions and the first discriminator network 504 utilizes dropout with a dropout rate of 0.01. The second discriminator network 514 comprises the same architecture as the first discriminator network 504. In an embodiment, the GAN 500 is trained using an ADAM solver which has an initial learning rate of le-3 with early stopping based on validation loss. A training data set with 10,000 training samples and 2,000 validation samples is used.

[0106] In one embodiment, the input parameter vector is split into shared and variable parameters (in a similar way as described above in relation to the constrained MCMC approach in Figure 3 and the hierarchical Bayesian approach in Figure 4). In such an embodiment, multiple generator networks are used— one for each parameter group. For example, a first generator network is used for the shared parameters, a second generator network is used for a first variable parameter under a first condition, and a third generator network is used for the first variable parameter under a second condition.

[0107] Referring once again to Figure 1, the output of the non-invertible phase 102 is the distribution of values 114 of the input parameter vector 116 of the mechanistic model 110 determined by the parameter fitting algorithm 112. The distribution of values 114 may be output to another process or system (e.g., output to the invertible phase 104 or to the database 120 for storage therein). Additionally, or alternatively, the distribution of values 114 is saved to a persistent storage such as a non-volatile memory, a non- transitory medium, or the like. The distribution of values 114 are output, or saved, in conjunction with the conditions associated with the cardiac cell culture 108.

[0108] According to an aspect of the present invention, a first distribution of values obtained during the non-invertible phase 102 as described above (e.g., the distribution of values 114) is compared to a second distribution of values obtained during the non- invertible phase 102. The first distribution of values is associated with a cardiac cell culture under a first condition and the second distribution of values is associated with the cardiac cell culture under a second, different, condition. In one embodiment, the first condition is a reference or control condition, and the second condition is a perturbed condition associated with a perturbation. As described above, example perturbations include drug treatments, disease states or models, different cell lines, and the like. Comparing the first and the second distribution of values therefore identifies the relative distribution shift in parameters of the mechanistic model 110 from the first condition to the second condition. The relative distribution shift is thus indicative of the change in function of the cardiac cell culture due to the change from the first condition to the second condition (e.g., due to the perturbation associated with the perturbed condition). The relative distribution shift may then be used as a feature, or signature, of the change from the first condition to the second condition. Because the parameters of the mechanistic model 110 encode the dynamical behavior of the in silico model of cardiac function, the relative shift in the distribution of values for the input parameter vector acts as a proxy for the change in cardiac function due to the change in conditions.

[0109] In one embodiment, the relative distribution is saved to the database 120 along with the condition information. The database 120 is generated from cardiac cell cultures under a range of different treatments, disease models, cell lines, and other perturbations using the above described methodology. Each entry in the database corresponds to a relative distribution shift associated with a relative shift in cardiac function from a first state to a second state. For example, a shift in cardiac function from control conditions to conditions involving a specific compound, or a shift in cardiac function from disease conditions to conditions involving the disease with the application of an agent. The database may then be queried to identify similar relative shifts thereby allowing the identification of possible treatment candidates (as described in more detail below).

[0110] In some embodiments, one or more outputs may be generated based on a change in function or condition of the cardiac cell culture from a first condition (e.g., reference condition) to a second condition (e.g., a perturbed condition). The one or more outputs may be used to identify, or may be indicative of, one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds.

[0111] For example, the relative distribution shift also provides a mechanism by which an effect (e.g., a toxicity, a mechanism of action, and the like) associated with an unknown compound or agent may be predicted in silico. In one example, a first relative distribution shift is generated from a distribution associated with a cardiac cell culture under control conditions and a distribution associated with the cardiac cell culture under perturbation conditions associated with a dosage of an unknown compound. Querying a database of relative distribution shifts (e.g., the database 120) with the first relative distribution shift identifies a second relative distribution shift associated with a shift from control conditions to perturbation conditions associated with a first drug. If the first drug has a known mechanism of action and / or toxicity, then the similarity in relative distribution shifts indicates that the unknown compound may share the same effects as the first drug because the relative distribution shift encodes the change in cardiac function due to the change in conditions. Therefore, as the unknown compound and the first agent result in the same or similar changes in cardiac function, it can be inferred that the unknown compound and the first agent may share the same or similar effects (e.g., mechanisms of action and / or toxicity). The non-invertible phase 102 therefore provides a framework for quickly and efficiently identifying potential effects of an unknown compound or agent which can reduce the need to perform costly and time consuming in vitro tests to identify such effects.

[0112] 9 In the invertible phase 104, the distribution of values 114 is used in conjunction with the mechanistic model 110 to determine estimated functional response values. A shift 122 (e.g., a relative shift) made to the distribution of values 114 results in a change of estimated functional response values. By matching the shift 122 to previously computed shifts stored in relation to specific conditions and effects, the invertible phase 104 allows fast and effective in silico discovery of potential agents or treatments which may result in a desired change of functional response.

[0113] Figure 6 illustrates inverse mechanistic modelling, as performed at the invertible phase 104 of Figure 1, according to an aspect of the present disclosure.

[0114] Figure 6 shows a distribution of values 602 for an input parameter vector of a mechanistic model 604 of cardiac function. The distribution of values 602 comprises a first distribution 606 for a first parameter of the input parameter vector and may further comprise a second distribution 608 for a second parameter of the input parameter vector and / or a third distribution 610 for a third parameter of the input parameter vector. Also shown in Figure 6 is a relative shift 612, a shifted first distribution 614, a first set of predicted functional response values 616, and a second set of predicted functional response values 618. Figure 6 further shows a database 620 and a first agent 622. In one embodiment, the distribution of values 602, the mechanistic model 604, the first set of predicted functional response values 616, and the database 620 correspond to the distribution of values 114, the mechanistic model 110, the set of first predicted functional response values 124-1, and the database 120 shown in Figure 1.

[0115] In general, the invertible phase shown in Figure 6 provides an in silico mechanism for predicting functional changes in a cardiac cell culture. The distribution of values 602 for the input parameter vector of the mechanistic model 604 corresponds to a distribution of values learnt during the non-invertible phase (as described above in relation to Figures 3- 5). The distribution of values 602 is associated with a cardiac cell culture under an associated condition such as a reference condition (i.e., the distribution was learnt from a cardiac cell culture under control conditions) or a perturbation condition (e.g., the distribution was learnt from a cardiac cell culture under a specific disease state). As such the distribution of values 602 provides a realistic distribution of the input parameter vector for an in silico model of cardiac cell culture under the associated condition. A shift applied to the distribution of values 602— e.g., applying a shift to one or more of the distributions associated with one or more of the parameters of the input parameter vector— may result in a change in the predicted functional response values produced by the mechanistic model 604. In the example shown in Figure 6, the relative shift 612 applied to the first parameter of the input parameter vector results in a change of predicted functional

[0116] 15 response values from the first set of predicted functional response values 616 to the second set of predicted functional response values 618. The difference between the first set of predicted functional response values 616 and the second set of predicted functional response values 618 corresponds to the predicted functional change of the cardiac cell culture occurring as a result of the relative shift 612.

[0117] By exploring the space of shifts applied to the distribution of values 602, a relative distribution shift which results in a desired, or target, change in predicted functional response can be identified. That is, one or more of the distributions for the input parameter vector can be iteratively and incrementally adjusted until one or more of the estimated functional response values meet a predetermined criterion. For example, a distribution within the distribution of values 602 associated with calcium binding is shifted until a predicted contractile force value exceeds a predetermined threshold value. The database 620 can then be queried using the relative distribution shift (e.g., the relative shift 612) to identify a matching relative distribution shift within the database 620. The matching relative distribution shift has a shift which is the same as, or similar to, the shift of the query relative distribution shift. Because the matching relative distribution shift is associated with a change in a cardiac cell culture from a first condition to a second condition (e.g., from a control condition to a treatment condition involving an agent), the first agent 622, or treatment, associated with the second condition is identified as a candidate agent. That candidate agent can be applied to a cardiac cell culture with a view to producing the desired change in predicted functional response.

[0118] For example, the distribution of values 602 may have been learnt from an engineered cardiac tissue under a perturbation condition associated with a disease state of hypertrophic cardiomyopathy. The first set of predicted functional response values 616 would thus correspond to values of the first functional response, corresponding to contractile force, when the engineered cardiac tissue is in this disease state. In this example, it is desirable to increase the contractile force of the engineered cardiac tissue as one of the hallmarks of hypertrophic cardiomyopathy is a decrease in contractile force of the heart muscle. Therefore, one or more shifts are applied to the distribution of values 602, or specific distributions within the distribution of values associated with specific parameters, to identify a shift which results in an increased contractile force (i.e., the second set of predicted functional response values 618 is an improvement over the first set of predicted functional response values 616). Once a suitable shift has been identified (e.g., the relative shift 612) it may be considered to represent the physiological change in the engineered cardiac tissue required to produce the functional change in contractile force (e.g., a lowering of calcium concentration). Because the shift is relative— i.e., it represents a relative distributional change in the input parameter vector from the disease state to a state associated with the change in contractile force— the shift can be used to search for a treatment (e.g., a compound or drug) which may affect such a functional change. The relative shift 612 is used to query the database 620 to identifying a similar shift associated with an agent (or treatment), this agent may then be identified as a candidate agent to increase the contractile force of the engineered cardiac tissue.

[0119] Beneficially, the relative nature of the distributional shifts in input parameter vectors allow such shifts to be directly compared thereby allowing them to be utilized for identification and classification of potential treatments and effects. Moreover, by learning the distribution of values for the input parameter vector from large volumes of high-fidelity data obtained from a bioreactor (such as that described in relation to Figure 12), the distributions can be shifted in biologically plausible and meaningful ways to produce accurate estimations of the change(s) in functional response. The invertible phase shown in Figure 6 thus provides a mechanism for quickly and efficiently identifying candidate agents or treatments.

[0120] In some embodiments, further validation of the candidate agent (or treatment) is performed to validate the in silico predictions and determine possible further effects associated with the candidate agent. For example, if the in silico predictions indicate that the candidate agent would produce an increase in contractile force, the additional validation would help identify whether contractile force was increased and whether other effects were also observed (e.g., an increase / decrease in calcium transients). Given a first plurality of in vitro responses comprising functional response measurements of a first cardiac cell culture under a first set of conditions, a second plurality of in vitro responses are obtained. The second plurality of in vitro responses comprise functional response measurements of a second cardiac cell culture under a second set of conditions associated with a perturbation of the second cardiac cell culture involving the candidate agent. The second cardiac cell culture can either be the same as the first cardiac cell culture or a different cardiac cell culture. For example, the first and second cardiac cell cultures are the same in situations where the first cardiac cell culture (which was used to obtain the in vitro responses which led to the distribution shift which identified the candidate agent) is under diseased conditions and the application of the candidate agent to the first cardiac cell culture will help test the efficacy of the candidate agent. The second plurality of in vitro responses provide an empirical representation of the cardiac cell culture's response to the candidate agent. This response is compared against one or more criteria to determine an effect associated with the candidate agent. For example, if the candidate agent was predicted to increase the contractile force to an amount, Flrthen the empirical l contractile force of the cardiac cell culture captured in the second plurality of in vitro responses are compared to to determine if this increase has been achieved. The one or more criteria would therefore comprise a threshold criterion which is met if the empirical contractile force matches or exceeds the predicted contractile force. The effect associated with the candidate agent would then be that the candidate agent did produce the predicted change in contractile force.

[0121] In one embodiment, a relative change of the predicted and empirical functional responses are compared to determine an effect. The relative change of the predicted, or desired, functional responses are determined by comparing the first set of predicted functional response values 616 and the second set of predicted functional response values 618. The relative change of the empirical functional responses are obtained by comparing in vitro responses obtained under a first condition (e.g., control, disease state, etc.) to the second plurality of in vitro responses which are obtained under conditions involving the candidate agent.

[0122] In one embodiment, a relative distribution shift is compared to the relative shift 612 to determine the effect. The relative distribution shift is obtained in a similar manner as described in relation to the non-invertible phase 102 above, and represents the shift from a first condition (e.g., control, disease state, etc.) to a second condition involving the candidate agent. The comparison of the predicted shift (i.e., the relative shift 612) and the empirical shift is then used to validate the predicted shift and determine whether the predicted effect was observed.

[0123] A description will now be provided of methods which are used in conjunction with the above described architectures to perform inverse modelling of cardiac function.

[0124] Figure 7 shows a method 700 for determining a change in cardiac function according to an aspect of the present disclosure.

[0125] The method 700 comprises the steps of obtaining 702 a first plurality of in vitro responses, obtaining 704 a second plurality of in vitro responses, obtaining 706 a mechanistic model, determining 708 a first distribution of values, determining 710 a second distribution of values, and determining 712 a first relative distribution shift. The method 700 further comprises the optional step of outputting 714 the first relative distribution shift.

[0126] At the step of obtaining 702, a first plurality of in vitro responses of a first cardiac cell culture are obtained (e.g., the plurality of in vitro responses 106 of the cardiac cell culture 108 shown in Figure 1). The first plurality of in vitro responses comprise measurements of a first functional response of the first cardiac cell culture under reference conditions (e.g., the first set of measurements 106-1 shown in Figure 1). Here, a functional response is to be understood as a biophysical response of a cardiac cell culture such as a contractile force of the cardiac cell culture, a calcium response or property of the cardiac cell culture, or an electrical response or property of the cardiac cell culture. As such, the first plurality of in vitro responses comprise measurements, or values, related to one or more of such functional responses of the first cardiac cell culture.

[0127] As stated in more detail above, the first cardiac cell culture is either a 2D culture (e.g., monolayers) or a 3D tissue formed from 3D culture. The first plurality of in vitro responses correspond to empirical measurements of the cardiac cell culture under a reference condition or conditions. The reference condition may be a control condition (e.g., the cardiac cell culture is vehicle treated prior to the first plurality of in vitro responses being obtained), or the reference condition may be a condition which acts as a reference to the condition(s) associated with the second plurality of in vitro responses (e.g., the reference condition corresponds to the cardiac cell culture being in a disease state with no agent or treatment having been applied).

[0128] The measurements of the first functional response comprise one or more waveform feature values such as a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value. Alternatively, the one or more waveform feature values comprise a spectral feature value. The one or more waveform feature values are determined from a first functional response waveform of the first cardiac cell culture, obtained over a first time period, under reference conditions.

[0129] At the step of obtaining 704, a second plurality of in vitro responses are obtained. The second plurality of in vitro responses comprise measurements of the first functional response of the first cardiac cell culture under a perturbed condition. The perturbed condition is associated with a first perturbation of the first cardiac cell culture. The first perturbation of the first cardiac cell culture comprises one or more of: a drug treatment; a disease model; or a different cell line.

[0130] The second plurality of in vitro responses comprise measurements, or values, related to one or more of the functional responses of the first cardiac cell culture. For example, if the first plurality of in vitro responses comprise contractile force related measurements, then the second plurality of in vitro responses also comprise contractile force related measurements. The measurements of the first functional response comprise one or more waveform feature values such as a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value. Alternatively, the one or more waveform feature values comprise a spectral feature value. The one or more waveform feature values are determined from a second functional response waveform of the first cardiac cell culture, obtained over a second time period, under the perturbed condition.

[0131] In one embodiment, the first plurality of in vitro responses and the second plurality of in vitro responses are obtained from a bioreactor containing the first cardiac cell culture (e.g., the bioreactor 1202 shown in Figure 12). Alternatively, the first plurality of in vitro responses and the second plurality of in vitro responses are obtained or derived from data obtained from the bioreactor containing the first cardiac cell culture. Beneficially, utilizing a bioreactor, such as that described in relation to Figure 12, to cultivate and maintain the cardiac cell culture allows large volumes of functional data to be obtained efficiently across a range of cardiac cell cultures under different conditions. This is particularly beneficial for the purpose of parameter fitting where a greater volume of data allows for improved estimation of the distribution of values for the input parameter vector.

[0132] At the step of obtaining 706, a mechanistic model of cardiac function is obtained (e.g., the mechanistic model 110 shown in Figure 1). The mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector (e.g., the first estimated functional response values 118-1 determined from the mechanistic model 110 based on the input parameter vector 116 shown in Figure 1). In one embodiment, the mechanistic model also determines one or more estimated values of a second functional response and / or one or more estimated values of a third functional response based on the input parameter vector.

[0133] The mechanistic model is an in silico model of cardiac function where the input parameter vector, along with the initial conditions of the model, determine the dynamical behavior of the mechanistic model (i.e., the dynamical behavior of the in silico cardiac model). The input parameter vector comprises a plurality of input parameters, each of which take an input value. For example, the input parameter vector may comprise a parameter associated with calcium binding, a parameter associated with the gating properties of cardiac ion channels, and the like. The mechanistic model is a mathematical model parameterized by the input parameter vector and the mechanistic model in one embodiment comprises one or more ordinary differential equations (ODEs). More details are provided in relation to Figure 2 above.

[0134] The distribution for the input parameter is a priori unknown and is learnt from the empirical (in vitro) functional response data. The functional response data (i.e., the plurality of in l vitro responses) capture different conditions of cardiac cell cultures and so different distributions for the input parameter vector are learnt for each different condition.

[0135] At the step of determining 708, a first distribution of values for the input parameter vector (e.g., the distribution of values 114 shown in Figure 1) is determined such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses.

[0136] At the step of determining 710, a second distribution of values for the input parameter vector is determined such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses.

[0137] The first and second distribution of values comprise a distribution for each of parameter of the input parameter vector. For example, if the input parameter vector comprises three parameters, then both the first and the second distribution of values will comprise three distributions each of which being associated with a respective parameter of the input parameter vector. The first and the second distribution of values are determined using a learning algorithm. As described in more detail above in relation to Figures 3-5, the learning algorithm is one of a constrained or unconstrained Markov chain Monte Carlo (MCMC) algorithm, a hierarchical Bayesian algorithm, or a generative adversarial network (GAN).

[0138] At the step of determining 712, a first relative distribution shift is determined based on a comparison of the first distribution of values and the second distribution of values. The first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

[0139] The first relative distribution shift is used as a feature, or signature, of the change from the reference condition to the perturbed condition. Because the parameters of the mechanistic model encode the dynamical behavior of the in silico model of cardiac function, the first relative shift in the distribution of values for the input parameter vector acts as an efficient proxy for the change in cardiac function due to the change in conditions.

[0140] In some embodiments, one or more outputs may be generated based on a change in function or condition of the cardiac cell culture from the reference condition to the perturbed condition. The one or more outputs may be used to identify, or may be indicative of, one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds. At the optional step of outputting 714, the first relative distribution shift is output. In one embodiment, outputting the first relative distribution shift comprises storing, or saving, the first relative distribution shift along with the relevant condition information in a database or other structured or unstructured store (e.g., the database 120 shown in Figure 1). This allows a database to be constructed from a wide variety of different compounds and conditions. Alternatively, outputting the first relative distribution shift comprises saving the first relative distribution shift to a persistent storage such as a nonvolatile memory, a non-transitory medium, or the like. Additionally, or alternatively, outputting the first relative distribution shift comprises transmitting or displaying the first relative distribution shift for review by a user.

[0141] Figure 8 shows a first set of steps 800 that are performed in conjunction with the method 700 of Figure 7 according to embodiments of the present disclosure.

[0142] In one embodiment, the first set of steps 800 are performed after the steps of the method 700 have been performed. Particularly, the first set of steps 800 are performed after the step in method 700 of determining 712 is performed. The first set of steps 800 comprise comparing 802 the first relative distribution shift to a plurality of distribution shifts and determining 804 a first effect. The first set of steps 800 further comprises the optional step of outputting 806 the first effect.

[0143] In general, the first set of steps 800 shown in Figure 8 provide a method for identifying a potential effect for a compound or treatment which has an unknown effect. For example, the first set of steps 800 can be used to identify a potential mechanism of action for a cardiac cell culture treated using an agent with an unknown mechanism of action.

[0144] At the step of comparing 802, the first relative distribution shift is compared to a plurality of relative distribution shifts associated with a plurality of perturbations. Each of the plurality of perturbations have a known effect. For example, the first relative distribution shift is compared to the distribution shifts stored in a database such as the database 120 shown in Figure 1. Because the distribution shifts are relative, direct comparisons between the various shifts can be made.

[0145] At the step of determining 804, a first effect associated with the first perturbation of the first cardiac cell culture is determined based on the comparing 802. For example, the most similar relative distribution shift within the plurality of relative distribution shifts is identified and the effect associated with this relative distribution shift is determined. Here, the most similar relative distribution shift may be the relative distribution shift having the highest similarity score to the first relative distribution shift, or a relative distribution shift which has a similarity score to the first relative distribution shift which is above predetermined threshold value. The first effect comprises one or more of a mechanism of action, a toxicity, and the like.

[0146] At the optional step of outputting 806, the first effect is output. Outputting the first effect comprises saving the first effect to a persistent storage such as a non-volatile memory, a non-transitory medium, or the like. Additionally, or alternatively, outputting the first effect comprises transmitting or displaying the first effect for review by a user.

[0147] Figure 9 shows a second set of steps 900 that are performed in conjunction with the method 700 of Figure 7 according to embodiments of the present disclosure.

[0148] In one embodiment, the second set of steps 900 are performed after the steps of the method 700 have been performed. Particularly, the second set of steps 900 are performed after the step in method 700 of determining 712 is performed. The second set of steps 900 comprise obtaining 902 a second relative distribution shift, comparing 904 the first relative distribution shift and the second relative distribution shift, and validating 906 the first distribution of values or the second distribution of values.

[0149] In general, the second set of steps 900 shown in Figure 9 provide a method for validating a distribution shift.

[0150] At the step of obtaining 902, a second relative distribution shift is obtained. The second relative distribution shift is associated with a second cardiac cell culture and the perturbed condition. The second relative distribution shift is obtained in the same manner as described in relation to the first relative distribution shift in Figure 7. That is, in vitro responses for the cardiac cell culture under both reference conditions and the perturbed condition are obtained. Distributions of values for the input parameter vector of the mechanistic model are determined from each set of in vitro responses, and the second relative distribution shift is determined from the two distribution of values.

[0151] At the step of comparing 904, the first relative distribution shift and the second relative distribution shift are compared. Because the distribution shifts are both relative, a direct comparison between the first and the second relative distribution shifts can be made.

[0152] At the step of validating 906, the first distribution set or the second distribution set are validated based on the comparing 904. For example, if the comparison revealed that the two relative distribution shifts were the same or similar, then this indicates that the first and the second relative distribution shifts provide accurate in silico representations of the change in cardiac function between the reference condition and the perturbed condition. Figure 10 shows a method 1000 for inverse mechanistic modelling of cardiac function according to an aspect of the present disclosure.

[0153] The method 1000 comprises the steps of obtaining 1002 a first plurality of in vitro responses, obtaining 1004 a mechanistic model, determining 1006 a first distribution of values, determining 1008 a shifted distribution of values, and determining 1010 a first relative distribution shift. The method 1000 further comprises the optional step of outputting 1012 the first relative distribution shift.

[0154] At the step of obtaining 1002, a first plurality of in vitro responses are obtained. The first plurality of in vitro responses comprise measurements of at least one functional response of a first cardiac cell culture under a first set of conditions. Example functional responses include contractile force, calcium transients, and electrical responses.

[0155] The first plurality of in vitro responses correspond to empirical measurements of the first cardiac cell culture (e.g., a 2D culture or a 3D tissue formed from 3D culture) under a first set of conditions (e.g., reference conditions). The measurements of the at least one functional response comprise one or more waveform feature values such as a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value. Alternatively, the one or more waveform feature values comprise a spectral feature value. The one or more waveform feature values are determined from a first functional response waveform of the first cardiac cell culture, obtained over a first time period, under the first set of conditions.

[0156] In one embodiment, the first plurality of in vitro responses are obtained from a bioreactor containing the first cardiac cell culture (e.g., the bioreactor 1202 described in relation to Figure 12). Alternatively, the first plurality of in vitro responses are obtained or derived from data obtained from the bioreactor containing the first cardiac cell culture.

[0157] At the step of obtaining 1004, a mechanistic model of cardiac function is obtained. The mechanistic model predicts one or more values of the at least one functional response based on an input parameter vector.

[0158] The mechanistic model is an in silico model of cardiac function where the input parameter vector, along with the initial conditions of the model, determines the dynamical behavior of the mechanistic model (i.e., the dynamical behavior of the in silico cardiac model). The input parameter vector comprises a plurality of input parameters, each of which takes an input value. The mechanistic model is a mathematical model parameterized by the input parameter vector and the mechanistic model in one embodiment comprises one or more i ordinary differential equations (ODEs). More details are provided in the description in relation to Figure 2 above.

[0159] At the step of determining 1006, a first distribution of values for the input parameter vector is determined such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses. That is, the predicted distribution of functional response values approximate, or match, the distribution of empirical functional response values from the first plurality of in vitro responses.

[0160] The first distribution of values is determined using a learning algorithm. As described in more detail above in relation to Figures 3-5, the learning algorithm is one of a Markov chain Montel Carlo (MCMC) algorithm which may be constrained or unconstrained, a hierarchical Bayesian algorithm, or a generative adversarial network (GAN).

[0161] At the step of determining 1008, a shifted first distribution of values for the input parameter vector is determined such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the shifted first distribution of values meet a predetermined functional response criterion. For example, the distribution of values are shifted until the at least one functional response obtained from the mechanistic model meets a threshold value (i.e., is greater than the threshold value or is less than the threshold value). As a further example, the distribution of values are shifted until the at least one functional response obtained from the mechanistic model falls within a predetermined range of values. Here, shifting the first distribution of values may comprise applying a shift operation to a distribution associated with one parameter of the input parameter vector (e.g., shifting the distribution associated with a calcium binding parameter). Alternatively, shifting the distribution of values may comprise applying multiple shift operations to multiple distributions associated with multiple parameters of the input parameter vector. In one embodiment, the first relative distribution shift is determined based a shift of one or more prior distributions.

[0162] At the step of determining 1010, a first relative distribution shift is determined based on a comparison of the first distribution of values and the shifted first distribution of values. The first relative distribution shift is indicative of a predicted change in cardiac function from the first set of conditions to a set of conditions associated with the predetermined functional response criterion.

[0163] Beneficially, the method 1000 provides a fast and efficient mechanism for searching through the space of distributional shifts of the input parameter vector to identify shifts

[0164] 15 which produce desired, or target, changes to the functional response(s) of a cardiac cell culture. This in turn may help reduce the cost and time associated with identifying target treatments or agents during drug discovery and development processes.

[0165] At the optional step of outputting 1012, the first relative distribution shift is output. Outputting the first relative distribution shift comprises saving the first relative distribution shift to a persistent storage such as a non-volatile memory, a non-transitory medium, or the like. Additionally, or alternatively, outputting the first relative distribution shift comprises transmitting or displaying the first relative distribution shift for review by a user.

[0166] Figure 11 shows a first set of steps 1100 that are performed in conjunction with the method 1000 of Figure 10 in some embodiments.

[0167] In embodiments, the first set of steps 1100 are performed after the steps of the method 1000 have been performed. Particularly, the first set of steps 1100 are performed after the step in method 1000 of determining 1010 is performed. The first set of steps 1100 comprise comparing 1102 the first relative distribution shift to a plurality of distribution shifts, identifying 1104 a first agent, obtaining 1106 a second plurality of in vitro responses, comparing 1108 the second plurality of in vitro responses to a predetermined functional response criterion, and identifying 1110 an effect. The first set of steps 1100 further comprise the optional step of outputting 1112 the effect.

[0168] At the step of comparing 1102, the first relative distribution shift is compared to a plurality of relative distribution shifts. The plurality of relative distribution shifts are associated with a corresponding plurality of agents. In one embodiment, the plurality of relative distribution shifts are stored within a persistent store or database (e.g., the database 120 shown in Figure 1). The plurality of relative distribution shifts are determined from cardiac cell cultures across a range of conditions and treatments using the non-invertible approach described in relation to Figure 7.

[0169] At the step of identifying 1104, a first agent is identified from the corresponding plurality of agents based on the comparing 1102. For example, the most similar relative distribution shift within the plurality of relative distribution shifts is identified and the agent associated with this relative distribution shift is determined (i.e., the agent associated with the perturbed condition from which the relative distribution shift was generated). Here, the most similar relative distribution shift may be the relative distribution shift having the highest similarity score to the first relative distribution shift, or a relative distribution shift which has a similarity score to the first relative distribution shift which is above predetermined threshold value. At the step of obtaining 1106, a second plurality of in vitro responses are obtained. The second plurality of in vitro responses comprise measurements of the at least one functional response of a second cardiac cell culture under a second set of conditions. The second set of conditions are associated with a perturbation of the second cardiac cell culture involving the first agent. In one embodiment, the first cardiac cell culture and the second cardiac cell culture are the same.

[0170] The second plurality of in vitro responses correspond to empirical measurements of the second cardiac cell culture under a second set of conditions (e.g., perturbed conditions). The measurements of the at least one functional response comprise one or more waveform feature values such as a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value. Alternatively, the one or more waveform feature values comprise a spectral feature value. The one or more waveform feature values are determined from a second functional response waveform of the second cardiac cell culture, obtained over a second time period, under the second set of conditions.

[0171] The second plurality of in vitro responses are obtained from a bioreactor containing the second cardiac cell culture (e.g., the bioreactor 1202 described in relation to Figure 12). Alternatively, the second plurality of in vitro responses are obtained or derived from data obtained from the bioreactor containing the second cardiac cell culture.

[0172] At the step of comparing 1108, the second plurality of in vitro responses are compared to the predetermined functional response criterion. In one embodiment, the at least one functional response comprises a first functional response and a second functional response, and the predetermined functional response criterion is associated with the second functional response.

[0173] At the step of identifying 1110, an effect associated with the first agent is identified based on the comparing 1108. The effect is associated with a change in functional response (e.g., a change in the first functional response, a change in the second functional response, etc.); specifically, a change in the predicted functional response as determined as a result of the shift performed at the step of determining 1008 in Figure 10 and the empirical functional response within the second plurality of in vitro responses.

[0174] At the optional step of outputting 1112, the effect is output. In one embodiment, outputting the effect comprises storing, or saving, the effect in a database or other structured or unstructured store. Alternatively, outputting the effect comprises saving the effect to a persistent storage such as a non-volatile memory, a non-transitory medium, or l the like. Additionally, or alternatively, outputting the effect comprises transmitting or displaying the effect for review by a user.

[0175] Figure 12 shows a system 1200 for obtaining cardiac cell culture functional response data according to an aspect of the present disclosure.

[0176] The system 1200 comprises a bioreactor 1202 and a control unit 1204. The bioreactor 1202 comprises a device 1206 for growing cardiac cell cultures, a sensor assembly 1208, and an interface 1210. The control unit 1204 comprises a feature extractor 1212. The interface 1210 communicatively couples the bioreactor 1202 and the control unit 1204 such that data may be exchanged between the bioreactor 1202 and the control unit 1204. In one embodiment, the control unit 1204 is configured to perform the above methods shown in Figure 7-11.

[0177] As shown in the expanded portion 1206-1 of the device 1206, the device 1206, or substrate, comprises one or more wells, such as the well 1214, one or more cell culture wells, such as the cell culture well 1216, a pair of electrodes including a first electrode 1218-1 and a second electrode 1218-2, and a pair of elements including a first element 1220-1 and a second element 1220-2. The well 1214 is positioned within the cell culture well 1216 and has a bottom on the device 1206, a first end 1222-1, and a second end 1222-2. The well 1214 is configured for growing a cardiac cell culture 1224 from cells seeded therein. Culture medium may be added to the cell culture well 1216 for growing and / or sustaining the cardiac cell culture 1224. In one embodiment, the cardiac cell culture is a 2D culture (e.g., monolayers). In an alternative embodiment, the cardiac cell culture is a 3D tissue (i.e., an engineered tissue) formed from 3D cell cultures.

[0178] The pair of electrodes are separated by a gap within which the well 1214 is positioned. The pair of electrodes are configured to apply an electrical stimulation to cell cultures within the one or more wells of the device 1206 (e.g., the cardiac cell culture 1124 within the well 1214 shown in the expanded portion 1206-1). During maturation of the cell cultures within the device 1206, the pair of electrodes apply stimulation to the cell cultures according to a multi-week electrical stimulation protocol. After the cell cultures are matured, the pair of electrodes may be configured to stimulate the cell cultures (e.g., the cardiac cell culture 1224) at a set frequency, or pacing frequency. In one embodiment, the frequency, or pacing frequency, at which the cell cultures are stimulated is set by the control unit 1204. As such, the control unit 1204 may be configured to send an instruction 1226 to the bioreactor 1202 to cause the bioreactor 1202 to stimulate the cardiac cell culture(s) within the device 1206 at a set pacing frequency. The first element 1220-1 and the second element 1220-2 are disposed across the well 1214 such that there is a gap between the bottom of the well 1214 and the pair of elements. The first element 1220-1 and the second element 1220-2 are configured to: (a) permit attachment of the cardiac cell culture 1224 formed therebetween, thereby suspending the cardiac cell culture 1224 above the bottom of the well 1214, and (b) deform in response to the contractile force exerted on the pair of elements by the cardiac cell culture 1224, thereby simulating a physiological environment that is native to the cardiac cell culture 1224 and / or permitting measurement of the contractile force (e.g., by the sensor assembly 1208). For example, the pair of electrodes may subject the cardiac cell culture 1224 to an electrical stimulation at a frequency of 0.1Hz. The cardiac cell culture 1224 will contract in response to this electrical stimulation causing deformation of at least one of the first element 1220-1 and the second element 1220-2. Measuring the deformation of the pair of elements allows the functional response of the cardiac cell culture 1224 when stimulated at 0.1Hz to be recorded.

[0179] The sensor assembly 1208 is configured to detect one or more functional responses of a cardiac cell culture within the device 1206 (e.g., one or more functional responses of the cardiac cell culture 1224). In one embodiment, the sensor assembly 1208 comprises an optical sensor. The optical sensor is configured to detect a deformation of the first element 1220-1 and / or the second element 1220-2 (e.g., occurring as a result of contractile force exerted on the first element 1220-1 and / or the second element 1220-2 by the cardiac cell culture 1224). Detecting the deformation of the first element 1220-1 and / or the second element 1220-2 allows one or more functional responses such as a displacement, or contractile displacement, of the cardiac cell culture 1224 or a contractile force of the cardiac cell culture 1224 to be determined. Additionally, or alternatively, the optical sensor of the sensor assembly 1208 is configured to detect a fluorescence intensity of the cardiac cell culture 1224. Detecting the fluorescence intensity of the cardiac cell culture 1224 allows one or more functional responses such as a transient calcium response of the cardiac cell culture 1224 or a change in membrane potential of the cardiac cell culture 1224 to be determined. Additionally, or alternatively, the optical sensor of the sensor assembly 1208 is configured to detect a change in dimensions of the cardiac cell culture 1224 over a time frame. Detecting the change in dimensions of the cardiac cell culture 1224 over the time frame allows one or more functional responses such as the displacement, or contractile displacement, of the cardiac cell culture 1224 or the contractile force of the cardiac cell culture 1224 to be determined.

[0180] The optical sensor of the sensor assembly 1208 is configured to obtain a plurality of image-based representations of the one or more functional responses of a tissue (e.g., the cardiac cell culture 1224) over a time frame or time period. For example, the optical sensor may be configured to capture an image, or frame, of a tissue every n seconds. Here, n is associated with a predetermined rate at which the images or frames are to be captured. For example, when n = 1 then one image of the tissue is captured per second. Any suitable value of n may be chosen such as n = {1 / 60, 1 / 50,1 / 30,1 / 24, 1 / 12 , 1 / 4,1 / 2, 1,2} and the like. In one embodiment, the frame rate is determined according to the frequency at which the tissues within the device are being stimulated. The sequences of images or frames of a tissue over a time frame therefore captures one or more functional responses of the tissue over the time frame.

[0181] In one embodiment, the bioreactor 1202 is configured to transform the sequence of images which capture the one or more functional responses of the tissue over the time frame to a waveform representation. For example, the sensor assembly 1208, the interface 1210, or another component of the bioreactor 1202 may process an image within the sequence of images to extract features relating to the functional response of the tissue at a time point associated with the image. Features relating to the functional response of the tissue extracted from the sequence of images may then be combined to form a waveform comprising the one or functional responses of the tissue over time. The waveform, such as the waveform 1228, may then be output from the bioreactor 1202. In an alternative embodiment, the raw image or frame data is output from the bioreactor 1202 and a separate unit— e.g., the control unit 1204 or an image analysis unit (not shown)— processes this data to determine the time-series functional response data.

[0182] The time-series functional response data produced by the bioreactor 1202 (e.g., the waveform 1228) provides a high fidelity and high information density representation of a functional response of an engineered tissue over a predetermined time period (e.g., the contractile force produced by a first tissue in response to a pacing frequency of 1Hz over a 30 second period). To obtain such waveform data from the bioreactor 1202 for the cardiac cell culture 1224, a command may be sent to the bioreactor 1202 (e.g., from the control unit 1204) to begin stimulating the cardiac cell culture 1224 at a pacing frequency. Alternatively, no electrical stimulation is applied so as to observe the spontaneous response of the cardiac cell culture 1224. The sensor assembly 1208 then captures a sequence of images of the cardiac cell culture 1224 over the predetermined time period. Decisively, the sequence of images capture the response (e.g., deformation) of the first element 1220-1 and / or the second element 1220-2 as a result of the contractile response of the cardiac cell culture 1224. The sequence of images are then processed to extract the response of the first element 1220-1 and / or the second element 1220-2 over the predetermined time period and convert the elements' responses over time to a time-series of functional response over time. For example, the displacement of the first element 1220-1 and / or the second element 1220-2 may be used to determine the force of the contractile response of the cardiac cell culture 1124. The time-series (e.g., the waveform 1228) is then output from the bioreactor 1202 for further processing and / or analysis. The feature extractor 1212 of the control unit 1204 extracts one or more waveform features (i.e., functional response values or features) from the waveform 1228 and outputs a plurality of measurements 1230. The features extracted by the feature extractor 1212 include, for each peak within the waveform 1228, a twitch amplitude, a contraction time, a maximum contraction slope, a relaxation time, a maximum relaxation slope, and a twitch duration. The feature extractor 1212 is also configured to extract spectral features from the waveform 1228 using a spectral transformation algorithm such as a Fourier transform.

[0183] A tissue within the bioreactor 1202 (e.g., the cardiac cell culture 1224) may be periodically dosed with a drug or compound and the functional response of the tissue after dosing recorded in the form of a waveform. Alternatively, the functional response of the tissue in the absence of any external dosing regimen may be periodically recorded. In either case, the changes in functional response of the tissue are captured in subsequent waveforms, as illustrated in Figure 13.

[0184] Figure 13 shows a waveform 1302 comprising a functional response of a tissue over a predetermined time period.

[0185] The waveform 1302 is obtained from a bioreactor such as the bioreactor 1202 shown in Figure 12 as described above. The waveform 1302 provides a high fidelity and high information density representation of the functional response of the tissue over the time frame to t2. The waveform 1302 comprises a plurality of peaks corresponding to the contractile response of the tissue over the time frame (e.g., 30s, 40s, etc.). A magnification of a peak within the portion 1304 of the waveform 1302 is shown in the expanded portion 1304-1.

[0186] Typically, a plurality of features are extracted from each peak of the waveform 1302 (e.g., using the feature extractor 1212 shown in Figure 12) to characterize the waveform 1302 and thereby allow for further processing or analysis of the waveform 1302. As shown in the expanded portion 1304-1, the features extracted from a single peak include peak (or twitch) amplitude 1306, time to peak amplitude 1308 (or contraction time), time to peak decline 1310 (or relaxation time), duration 1312 (or twitch duration), maximum rate of development 1314 (or maximum contraction slope), maximum rate of declination 1316 (or maximum relaxation slope), and passive tension 1318. Figure 14 shows an example computing system for carrying out the methods of the present disclosure. Specifically, Figure 14 shows a block diagram of an embodiment of a computing system according to example embodiments of the present disclosure.

[0187] Computing system 1400 can be configured to perform any of the operations disclosed herein such as, for example, any of the operations discussed with reference to the functional modules described in relation to Figure 1A. Computing system includes one or more computing device(s) 1402. Computing device(s) 1402 of computing system 1400 comprise one or more processors 1404 and memory 1406. One or more processors 1404 can be any general purpose processor(s) configured to execute a set of instructions. For example, one or more processors 1404 can be one or more general-purpose processors, one or more field programmable gate array (FPGA), and / or one or more application specific integrated circuits (ASIC). In one embodiment, one or more processors 1404 include one processor. Alternatively, one or more processors 1404 include a plurality of processors that are operatively connected. One or more processors 1404 are communicatively coupled to memory 1406 via address bus 1408, control bus 1410, and data bus 1412. Memory 1406 can be a random access memory (RAM), a read only memory (ROM), a persistent storage device such as a hard drive, an erasable programmable read only memory (EPROM), and / or the like. Computing device(s) 1402 further comprise I / O interface 1414 communicatively coupled to address bus 1408, control bus 1410, and data bus 1412.

[0188] Memory 1406 can store information that can be accessed by one or more processors 1404. For instance, memory 1406 (e.g., one or more non-transitory computer-readable storage mediums, memory devices) can include computer-readable instructions (not shown) that can be executed by one or more processors 1404. The computer-readable instructions can be software written in any suitable programming language or can be implemented in hardware. Additionally, or alternatively, the computer-readable instructions can be executed in logically and / or virtually separate threads on one or more processors 1404. For example, memory 1406 can store instructions (not shown) that when executed by one or more processors 1404 cause one or more processors 1404 to perform operations such as any of the operations and functions for which computing system 1400 is configured, as described herein. In addition, or alternatively, memory 1406 can store data (not shown) that can be obtained, received, accessed, written, manipulated, created, and / or stored. The data can include, for instance, the data and / or information described herein in relation to Figures 1 to 13. In some implementations, computing device(s) 1402 can obtain from and / or store data in one or more memory device(s) that are remote from the computing system 1400. Computing environment 1400 further comprises storage unit 1416, network interface 1418, input controller 1420, and output controller 1422. Storage unit 1416, network interface 1418, input controller 1420, and output controller 1422 are communicatively coupled to computing device(s) 1402 via I / O interface 1414. Storage unit 1416 is a computer readable medium, preferably a non-transitory computer readable medium, comprising one or more programs, the one or more programs comprising instructions which when executed by the one or more processors 1404 cause computing environment 1400 to perform the method steps of the present disclosure. Alternatively, storage unit 1416 is a transitory computer readable medium. Storage unit 1416 can be a persistent storage device such as a hard drive, a cloud storage device, or any other appropriate storage device.

[0189] Network interface 1418 can be a Wi-Fi module, a network interface card, a Bluetooth module, and / or any other suitable wired or wireless communication device. In an embodiment, network interface 1418 is configured to connect to a network such as a local area network (LAN), or a wide area network (WAN), the Internet, or an intranet.

Claims

PCT PATENT APPLICATIONAttorney Ref: 33719-58833 PCCLAIMSWhat is claimed is:

1. A method for predicting change in cardiac function, the method comprising: obtaining, by one or more processors, a first plurality of in vitro responses comprising measurements of a first functional response of a first cardiac cell culture under reference conditions; obtaining, by the one or more processors, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determining, by the one or more processors, a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; and determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

2. The method of claim 1 further comprising: outputting, by the one or more processors, the first relative distribution shift.

3. The method of claim 1 wherein the first perturbation of the first cardiac cell culture comprises one or more of: a drug treatment; a disease model; or a different cell line.

4. The method of claim 1 further comprising: comparing, by the one or more processors, the first relative distribution shift to a plurality of relative distribution shifts associated with a plurality of perturbations, each of the plurality of perturbations having a known effect; and determining, by the one or more processors, a first effect associated with the first perturbation of the first cardiac cell culture based on the comparing.

5. The method of claim 4 further comprising: outputting, by the one or more processors, the first effect.

6. The method of claim 4 wherein the first effect comprises a mechanism of action.

7. The method of claim 4 wherein the first effect comprises a toxicity.

8. The method of claim 1 further comprising: obtaining, by the one or more processors, a second relative distribution shift associated with a second cardiac cell culture and the perturbed condition; comparing, by the one or more processors, the first relative distribution shift and the second relative distribution shift; and validating, by the one or more processors, the first distribution set or the second distribution set based on the comparing.

9. The method of claim 1 wherein measurements of the first functional response comprise one or more waveform feature values.

10. The method of claim 9 wherein the one or more waveform feature values comprise one or more of a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value. is11. The method of claim 9 wherein the one or more waveform feature values comprise a spectral feature value.

12. The method of claim 9 wherein the one or more waveform feature values for the first plurality of in vitro responses are determined from a first functional response waveform of the first cardiac cell culture under reference conditions obtained over a first time period.

13. The method of claim 9 wherein the one or more waveform feature values for the second plurality of in vitro responses are determined from a second functional response waveform of the first cardiac cell culture under the perturbed condition over a second time period.

14. The method of claim 1 wherein the first plurality of in vitro responses and the second plurality of in vitro responses are obtained from a bioreactor containing the first cardiac cell culture.

15. The method of claim 1 wherein the first cardiac cell culture comprises a 2D cardiac cell culture.

16. The method of claim 1 wherein the first cardiac cell culture comprises a 3D cardiac tissue.

17. The method of claim 1 wherein the mechanistic model comprises a mathematical model.

18. The method of claim 17 wherein the mathematical model comprises one or more ordinary differential equations.

19. The method of claim 1 wherein the input parameter vector comprises a plurality of input parameters each of which taking an input value.

20. The method of claim 19 wherein the first distribution of values comprises a distribution for each of the plurality of input parameters.

21. The method of claim 19 wherein the second distribution of values comprises a distribution for each of the plurality of input parameters.

22. The method of claim 1 wherein the first distribution of values for the input parameter vector is determined using a first learning algorithm.

23. The method of claim 22 wherein the second distribution of values for the input parameter vector is determined using the first learning algorithm.

24. The method of claim 22 wherein the first learning algorithm comprises a Markov chain Monte Carlo (MCMC) algorithm.

25. The method of claim 24 wherein the MCMC is constrained according to one or more groupings of parameters within the input parameter vector.

26. The method of claim 22 wherein the first learning algorithm comprises a generative adversarial network.

27. The method of claim 22 wherein the first learning algorithm comprises a hierarchical Bayesian algorithm or model.

28. The method of claim 27 wherein the hierarchical Bayesian model comprises a plurality of prior distributions associated with one or more groupings of parameters within the input parameter vector.

29. The method of claim 1 wherein the first plurality of in vitro responses and the second plurality of in vitro responses further comprise measurements of a second functional response of the first cardiac cell culture.

30. The method of claim 29 wherein the mechanistic model determines one or more estimated values of the second functional response based on the input parameter vector.

31. The method of claim 1 wherein the first functional response comprises a contractile force of the first cardiac cell culture.

32. The method of claim 1 wherein the first functional response comprises a calcium transient response of the first cardiac cell culture.

33. The method of claim 1 wherein the first functional response comprises an electrical response of the first cardiac cell culture.

34. A non-transitory machine readable medium storing instructions which, when executed by one or more processors of a device, causes the one or more processors of the device to: obtain a first plurality of in vitro responses comprising measurements of a first functional response of a first cardiac cell culture under reference conditions; obtain a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtain a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determine a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; and determine a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

35. A device comprising: one or more processors; anda memory storing instructions; wherein the instructions, when executed by the one or more processors, cause the one or more processors to: obtain a first plurality of in vitro responses comprising measurements of a first functional response of a first cardiac cell culture under reference conditions; obtain a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtain a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determine a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; and determine a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition.

36. A method for inverse mechanistic modelling of cardiac function, the method comprising: obtaining, by one or more processors, a first plurality of in vitro responses comprising measurements of at least one functional response of a first cardiac cell culture under a first set of conditions;obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model predicts one or more values of the at least one functional response based on an input parameter vector; determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determining, by the one or more processors, a shifted first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the shifted first distribution of values meet a predetermined functional response criterion; and determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the shifted first distribution of values, wherein the first relative distribution shift is indicative of a predicted change in cardiac function from the first set of conditions to a set of conditions associated with the predetermined functional response criterion.

37. The method of claim 36 further comprising: outputting, by the one or more processors, the first relative distribution shift.

38. The method of claim 36 further comprising: comparing, by the one or more processors, the first relative distribution shift to a plurality of relative distribution shifts, wherein the plurality of relative distribution shifts are associated with a corresponding plurality of agents; and identifying, by the one or more processors, a first agent from the corresponding plurality of agents based on the comparing.

39. The method of claim 38 further comprising: obtaining, by the one or more processors, a second plurality of in vitro responses comprising measurements of the at least one functional response of a second cardiac cell culture under a second set of conditions, wherein the second set ofconditions are associated with a perturbation of the second cardiac cell culture involving the first agent.

40. The method of claim 39 wherein the first cardiac cell culture and the second cardiac cell culture are the same.

41. The method of claim 39 further comprising: comparing, by the one or more processors, the second plurality of in vitro responses to the predetermined functional response criterion; and identifying, by the one or more processors, an effect associated with the first agent based on the comparing.

42. The method of claim 41 further comprising: outputting, by the one or more processors, the effect.

43. The method of claim 41 wherein the at least one functional response comprises a first functional response and a second functional response.

44. The method of claim 43 wherein the predetermined functional response criterion is associated with the second functional response.

45. The method of claim 44 wherein the effect is associated with a change in the second functional response.

46. The method of claim 36 wherein measurements of the at least one first functional response comprise one or more waveform feature values.

47. The method of claim 46 wherein the one or more waveform feature values comprise one or more of a twitch amplitude value, a contraction time value, a maximum contraction slope value, a relaxation time value, a maximum relaxation slope value, and a twitch duration value.

48. The method of claim 46 wherein the one or more waveform feature values comprise a spectral feature value.

49. The method of claim 46 wherein the one or more waveform feature values for the first plurality of in vitro responses are determined from a first functional response waveform of the first cardiac cell culture under the first set of conditions obtained over a first time period.

50. The method of claim 36 wherein the first plurality of in vitro responses are obtained from a bioreactor containing the first cardiac cell culture.

51. The method of claim 36 wherein the first cardiac cell culture comprises a 2D cardiac cell culture.

52. The method of claim 36 wherein the first cardiac cell culture comprises a 3D cardiac tissue.

53. The method of claim 36 wherein the mechanistic model comprises a mathematical model.

54. The method of claim 53 wherein the mathematical model comprises one or more ordinary differential equations.

55. The method of claim 36 wherein the input parameter vector comprises a plurality of input parameters each of which taking an input value.

56. The method of claim 55 wherein the first distribution of values comprises a distribution for each of the plurality of input parameters.

57. The method of claim 36 wherein the first distribution of values for the input parameter vector is determined using a first learning algorithm.

58. The method of claim 57 wherein the first learning algorithm comprises a Markov chain Monte Carlo (MCMC) algorithm.

59. The method of claim 58 wherein the MCMC is constrained according to one or more groupings of parameters within the input parameter vector.

60. The method of claim 57 wherein the first learning algorithm comprises a generative adversarial network.

61. The method of claim 57 wherein the first learning algorithm comprises a hierarchical Bayesian algorithm.

62. The method of claim 61 wherein the hierarchical Bayesian model comprises one or more prior distributions associated with one or more groupings of parameters within the input parameter vector.

63. The method of claim 62 wherein shifted first distribution of values for the input parameter vector are determined by shifting one or more of the one or more prior distributions.

64. The method of claim 36 wherein the at least one functional response comprises a contractile force of the first cardiac cell culture.

65. The method of claim 36 wherein the at least one functional response comprises a calcium transient response of the first cardiac cell culture.

66. The method of claim 36 wherein the at least one functional response comprises an electrical response of the first cardiac cell culture.

67. A non-transitory machine readable medium storing instructions which, when executed by one or more processors of a device, causes the one or more processors of the device to: obtain a first plurality of in vitro responses comprising measurements of at least one functional response of a first cardiac cell culture under a first set of conditions; obtain a mechanistic model of cardiac function, wherein the mechanistic model predicts one or more values of the at least one functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses;S3determine shifted first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the shifted first distribution of values meet a predetermined functional response criterion; and determine a first relative distribution shift based on a comparison of the first distribution of values and the shifted first distribution of values, wherein the first relative distribution shift is indicative of a predicted change in cardiac function from the first set of conditions to a set of conditions associated with the predetermined functional response criterion.

68. A system comprising: one or more processors; and a memory storing instructions, wherein the instructions, when executed by the one or more processors, causes the one or more processors to: obtain a first plurality of in vitro responses comprising measurements of at least one functional response of a first cardiac cell culture under a first set of conditions; obtain a mechanistic model of cardiac function, wherein the mechanistic model predicts one or more values of the at least one functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determine shifted first distribution of values for the input parameter vector such that estimated values of the at least one functional response obtained from the mechanistic model based on input values obtained from the shifted first distribution of values meet a predetermined functional response criterion; and determine a first relative distribution shift based on a comparison of the first distribution of values and the shifted first distribution of values, wherein the firstBirelative distribution shift is indicative of a predicted change in cardiac function from the first set of conditions to a set of conditions associated with the predetermined functional response criterion.

69. A method for predicting change in cardiac function, the method comprising: obtaining, by one or more processors from a bioreactor containing a first cardiac cell culture, a first plurality of in vitro responses comprising measurements of a first functional response of the first cardiac cell culture under reference conditions; obtaining, by the one or more processors from the bioreactor, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtaining, by the one or more processors, a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determining, by the one or more processors, a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determining, by the one or more processors, a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; determining, by the one or more processors, a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition; and generating , based the change in function of the first cardiac cell culture due to the perturbed condition, one or more outputs identifying or indicative of one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds. s70. A system configured to predict change in cardiac function, the system comprising: one or more bioreactors configured for growing a cardiac tissue therein; and a control unit communicatively coupled to the bioreactor, and comprising one or more processors configured to execute instructions that causes the one or more processors to: obtain, from the bioreactor containing a first cardiac cell culture of the cardiac tissue, a first plurality of in vitro responses comprising measurements of a first functional response of the first cardiac cell culture under reference conditions; obtain, from the bioreactor, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtain a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determine a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; and determine a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition; and generate, based the change in function of the first cardiac cell culture due to the perturbed condition, one or more outputs identifying or indicative ofBone or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds71. A non-transitory computer readable medium storing instructions for predicting change in cardiac function, which, when executed by one or more processors of a device, causes the one or more processors of the device to: obtain, from a bioreactor containing a first cardiac cell culture, a first plurality of in vitro responses comprising measurements of a first functional response of the first cardiac cell culture under reference conditions; obtain, from the bioreactor, a second plurality of in vitro responses comprising measurements of the first functional response of the first cardiac cell culture under a perturbed condition, wherein the perturbed condition is associated with a first perturbation of the first cardiac cell culture; obtain a mechanistic model of cardiac function, wherein the mechanistic model determines one or more estimated values of the first functional response based on an input parameter vector; determine a first distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the first distribution of values approximate measurements from the first plurality of in vitro responses; determine a second distribution of values for the input parameter vector such that estimated values of the first functional response obtained from the mechanistic model based on input values obtained from the second distribution of values approximate measurements from the second plurality of in vitro responses; determine a first relative distribution shift based on a comparison of the first distribution of values and the second distribution of values, wherein the first relative distribution shift is indicative of a change in function of the first cardiac cell culture due to the perturbed condition; and generate, based the change in function of the first cardiac cell culture due to the perturbed condition, one or more outputs identifying or indicative of one or more of: (a) target molecules as potential drug candidates, and / or (b) potential effects of unknown compounds.Bl

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