A method and system for combined analysis of energy metabolism and behavior based on response delay correction

Abstract

The application discloses a kind of energy metabolism and behavior combined analysis method and system based on response delay correction, method includes: the original energy metabolism data and video data of small animal are collected;Response delay model of metabolism detection is constructed, and the response parameter of response delay model is calibrated or estimated based on metabolism data and video data acquisition processing energy metabolism data and behavior time series;Response convolution model of behavior state is constructed based on behavior time series, and discrete response function and response correction behavior sequence are obtained;Metabolism-behavior combined regression model is constructed based on processing energy metabolism data and response correction behavior sequence;Based on the potential metabolic signal of system response function, the potential real-time metabolism sequence is obtained by inversion;Behavior state conditional metabolism phenotype index model is constructed based on metabolism-behavior combined regression model and potential real-time metabolism sequence, and combined analysis report is generated based on behavior state conditional metabolism phenotype index model.

Description

Technical Field

[0001] This invention belongs to the fields of small animal energy metabolism detection, indirect calorimetry, video behavior recognition, time-series signal processing and biomedical data technology, and specifically relates to a method and system for joint analysis of energy metabolism and behavior based on response delay correction. Background Technology

[0002] Existing metabolic monitoring systems can calculate an animal's energy expenditure by measuring oxygen consumption and carbon dioxide production, and existing video behavior recognition systems can continuously identify animal behavior. However, although behavioral and metabolic signals can be synchronized in sampling time, for example, both output with a time resolution of 1 second, they do not naturally have an instantaneous correspondence in a true physiological sense.

[0003] Behavioral signals are directly acquired from video and can approximately reflect the actual time when animal behavior occurs; however, metabolic signals require processes such as animal respiration, air mixing in the cage, airway delivery, and sensor response. Therefore, the observed energy consumption curve has a time delay and signal smoothing phenomenon relative to the metabolic changes induced by actual behavior. Summary of the Invention

[0004] This invention aims to address the shortcomings of existing technologies by proposing a joint detection device and analysis method for energy metabolism and behavior. By establishing a response function for the metabolic detection system, response delay correction, convolution modeling, deconvolution inversion, and state conditional index extraction are performed on the behavioral state sequence and metabolic observation sequence. This enables the analysis of metabolic characteristics of the same animal under different behavioral states, as well as the comparison of metabolic differences between different treatment groups of animals under the same behavioral state.

[0005] To achieve the above objectives, the present invention provides the following solution: A joint analysis method for energy metabolism and behavior based on response delay correction includes the following steps: Collect raw energy metabolism data and video data of small animals; The video data is subjected to computer vision analysis to identify the animal's behavioral state and generate a behavioral time series. The raw energy metabolism data is preprocessed to obtain processed energy metabolism data; Construct a response delay model for metabolic detection, and calibrate or estimate the response parameters of the response delay model; A behavior-state-response convolutional model is constructed based on the behavior time series, and a discrete response function and a response-corrected behavior sequence are obtained based on the behavior-state-response convolutional model. A joint regression model of metabolism and behavior is constructed based on the processed energy metabolism data and the response correction behavior sequence. The potential instantaneous metabolic sequence is obtained by inverting the potential metabolic signal based on the system response function. Based on the metabolism-behavior joint regression model and the potential real-time metabolic sequence, a behavior state-conditionalized metabolic phenotypic index model is constructed, and a joint analysis report is generated based on the behavior state-conditionalized metabolic phenotypic index model.

[0006] Preferably, the method for obtaining the raw energy metabolism data and the video data includes: The raw energy metabolism data are obtained by collecting data on oxygen concentration at the inlet end, oxygen concentration at the outlet end, carbon dioxide concentration at the inlet end, carbon dioxide concentration at the outlet end, gas flow rate, temperature, humidity, and pressure at a preset sampling frequency. Animal behavior videos are collected, and timestamps are generated for each frame or each second of video segment to obtain the video data.

[0007] Preferably, the method for obtaining the behavioral time series includes: The video data is analyzed using computer vision to identify the animal's behavioral state; Construct a sequence of probabilistic behavioral events based on the behavioral state. ; Based on the behavioral probability event sequence Construct the behavior probability vector at each time point when there are K mutually exclusive behavior states. and satisfy The behavior probability vector is used as the behavior time series.

[0008] Preferably, the preprocessing method includes: For the original energy metabolism data, delete the data from the preheating stage and the initial gas equilibrium stage in the cage to obtain the deleted data; The outliers in the deleted data are identified, marked, and processed, and short-term missing data is interpolated to obtain interpolated data. Based on the gas concentration, flow rate, temperature, humidity, and pressure in the interpolated data, the energy consumption value is calculated to obtain the processed energy metabolism data.

[0009] Preferably, the method for obtaining the response parameters includes: Construct a behavior activity-driven sequence based on the aforementioned behavior time series: , in, Represents a sequence of behavioral activities. Indicates the first k Activity intensity weights for various behaviors; The behavioral activity-driven sequence and the processed energy metabolism data are subjected to mean-reducing processing, and within a preset lag range... Inside, calculate the cross-correlation function: , , , in, This represents the mean-removed behavior-driven sequence. This represents the observed energy consumption sequence after removing the mean. This represents the energy metabolism data after processing. mean This indicates that the arithmetic mean was calculated within the valid time range of the analysis. Represents the cross-correlation function. l Indicates the lag time; When cross-correlation function At a certain lag When the value is reached, the initial estimated delay of behavioral activity change relative to observed metabolic change is considered to be . ; The initial estimated delay is For reference, candidate sets for fixed delays are determined respectively. Candidate set of time constant The response parameters are determined based on two candidate sets: , , , , in, Indicates candidate parameters, This represents the activity-driven sequence obtained by convolution with the response function under candidate parameters. This represents the convolution operation. Represents the system response function. A This represents the original behavioral activity-driven sequence. This represents the baseline term estimated by least squares under candidate parameters. This indicates that the activity-driven metabolic contribution coefficient is estimated by the least squares method under candidate parameters. Indicates the baseline term. This represents the activity-driven metabolic contribution coefficient. This represents the sum of squared residuals corresponding to the candidate parameters. This represents the set of valid time points for fitting. This represents the response parameters.

[0010] Preferably, the method for obtaining the discrete response function and the response correction behavior sequence includes: The obtained system response function According to sampling interval t Discretization yields the discrete response function. To ensure that the convolution process only changes the temporal distribution of the behavioral influence, without artificially amplifying or reducing the total probability of the behavior, the discrete response function... Normalization was performed, where, Indicates the historical lag sequence number relative to the current point in time. M Indicates the length of the system response window; Based on the normalized discrete response function and the behavior time series, the response-corrected behavior sequence is obtained: , in, This represents a sequence of response correction behaviors.

[0011] Preferably, the metabolism-behavior joint regression model is: , in, Indicates the baseline term. Indicates the first k The metabolic contribution coefficient corresponding to the row state Represents the coefficients of the covariates. Indicates the first m One covariate, Represents the residual.

[0012] Preferably, the method for obtaining the potential immediate metabolic sequence includes: Based on the convolution operation of the system response function, the processed energy metabolism data, and the real real-time energy consumption sequence: , in, Represents a real-time energy consumption sequence. Indicates observation noise; Based on the processed discrete response function Constructing convolutional matrices H The convolution operation is then rewritten in matrix form: , in, Y Represents the observed energy consumption vector. E This represents the candidate potential immediate metabolic sequence to be solved. Represents the observation noise vector; Construct the optimization objective function based on the aforementioned matrix form: , in, Indicates reference metabolic level. W Represents the data weight matrix. D Represents the difference matrix. T To represent the transpose of a matrix, and Represents the regularization coefficient; The potential instantaneous metabolic sequence is obtained by inverting the optimization objective function: , in, Indicates by E The estimated potential immediate metabolic sequence, I Represents the identity matrix.

[0013] The present invention also provides a joint analysis system for energy metabolism and behavior based on response delay correction. The system applies the above-mentioned method and includes: a data acquisition module, a visual analysis module, an energy data processing module, a response parameter calibration module, a response function and behavior sequence acquisition module, a regression model construction module, an inversion module, and an index analysis module. The data acquisition module is used to collect raw energy metabolism data and video data of small animals; The visual analysis module is used to perform computer vision analysis on the video data, identify the animal's behavioral state, and generate a behavioral time series. The energy data processing module is used to preprocess the raw energy metabolism data to obtain processed energy metabolism data; The response parameter calibration module is used to construct a response delay model for metabolic detection and to calibrate or estimate the response parameters of the response delay model. The response function and behavior sequence acquisition module constructs a behavior state response convolution model based on the behavior time series, and obtains a discrete response function and a response correction behavior sequence based on the behavior state response convolution model; The regression model construction module constructs a joint regression model of metabolism and behavior based on the processed energy metabolism data and the response correction behavior sequence. The inversion module performs inversion based on the potential metabolic signal of the system response function to obtain the potential real-time metabolic sequence. The indicator analysis module constructs a behavioral state-conditionalized metabolic phenotype indicator model based on the metabolism-behavior joint regression model and the potential real-time metabolic sequence, and generates a joint analysis report based on the behavioral state-conditionalized metabolic phenotype indicator model.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention no longer simply maps the behavior label of the same second to the observation EE of the same second, but considers the response delay and smoothing effect caused by the metabolic detection system; (2) This invention establishes a quantitative relationship between the behavior occurrence time and the metabolic observation time through the system response function; (3) This invention retains the uncertainty of behavior identification through probability labels, and improves the analysis accuracy of behavior switching and mixed behavior stages; (4) This invention converts the behavior sequence into an explanatory variable that matches the observed metabolic signal through the behavior state response convolution model; (5) This invention estimates the contribution of different behavior states to energy consumption through the metabolism-behavior joint regression model; (6) This invention recovers or estimates potential instantaneous metabolic changes through the regularized deconvolution method; (7) This invention distinguishes between changes in behavior composition and changes in metabolic cost per unit behavior through behavior state conditional metabolic phenotypic indicators; (8) This invention can be used for small animal experimental research on obesity, diabetes, aging, neurobehavioral abnormalities, drug intervention, gene editing and environmental intervention. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 In this embodiment, as Figure 1 As shown, a joint analysis method for energy metabolism and behavior based on response delay correction includes the following steps: S1. Collect raw energy metabolism data and video data of small animals.

[0020] The methods for obtaining raw energy metabolism data and video data include: collecting data on oxygen concentration at the inlet end, oxygen concentration at the outlet end, carbon dioxide concentration at the inlet end, carbon dioxide concentration at the outlet end, gas flow rate, temperature, humidity, and pressure at a preset sampling frequency to obtain raw energy metabolism data; and collecting videos of animal behavior and generating timestamps for each frame or each second of video to obtain video data.

[0021] In this embodiment, experimental animals are placed in metabolic cages, and data on oxygen concentration at the inlet, oxygen concentration at the outlet, carbon dioxide concentration at the inlet, carbon dioxide concentration at the outlet, gas flow rate, temperature, humidity, and pressure are collected at a preset sampling frequency. Animal behavior videos are simultaneously collected, and timestamps are generated for each frame or each second of video footage.

[0022] In one implementation, both metabolic data and video data are output with a time resolution of 1 second. In other implementations, metabolic data and video data may use different sampling frequencies and be unified to a common time axis through resampling.

[0023] S2. Perform computer vision analysis on the video data to identify the animal's behavioral state and generate a behavioral time series.

[0024] Methods for obtaining behavioral time series include: performing computer vision analysis on video data to identify the behavioral state of animals; constructing a sequence of behavioral probability events based on the behavioral state; and constructing a behavioral probability vector at each time point when there are K mutually exclusive behavioral states based on the sequence of behavioral probability events, and using the behavioral probability vector as the behavioral time series.

[0025] In this embodiment, behavioral states include, but are not limited to, being still, sleeping, walking, running, eating, drinking, exploring, standing, grooming, turning around, climbing, stretching, and abnormal behavior.

[0026] This implementation preferably uses probability labels to express animal behavioral states. For the first... k Various behavioral states are used to construct behavioral probability time series. ,in, Indicates the time of animals t Belongs to the k The probability of a certain behavioral state, ranging from 0 to 1.

[0027] Given K mutually exclusive behavioral states, the behavioral probability vector at each time point is: , And satisfy: .

[0028] When the video recognition model outputs results in frames, while subsequent metabolic analysis is performed in seconds, the behavior probabilities of all video frames within the same second can be averaged to obtain the behavior probability for that second. , in, Indicates the first f Frame belongs to the k The probability of a certain behavioral state. This represents summing the probabilities of all behavioral states. Indicates time t The corresponding number of video frames per second.

[0029] The advantage of using probabilistic labels is that, in situations involving behavior transitions, occlusion, pose ambiguity, or overlapping behavioral features, the system does not forcibly categorize animal behaviors into a single class, but rather preserves the uncertainty of behavior recognition. For example, the transition of a mouse from rest to walking can simultaneously possess both a probability of rest and a probability of walking; similarly, the head movements a mouse makes while eating can simultaneously retain probabilistic information for both eating and walking behaviors. These probabilistic labels can then be used as weights in subsequent convolutional modeling, regression analysis, and indicator extraction.

[0030] In another embodiment, hard-labeling can also be used to express the animal's behavioral state. Hard-labeling directly assigns each time point a unique behavioral category; for example, the behavior with the highest probability is taken as the behavioral label for that time point. .

[0031] The advantages of hard-labeling are intuitive results, simple calculation, and ease of manual verification; the disadvantage is that it loses the uncertainty of behavior recognition and is prone to misassignment during behavior switching or mixed behavior stages. The advantages of probabilistic labeling are that it can preserve model confidence and mixed behavior states, making it more suitable for weighted modeling with continuous metabolic signals; the disadvantage is that the calculation and interpretation are relatively complex.

[0032] S3. Preprocess the raw energy metabolism data to obtain processed energy metabolism data.

[0033] The preprocessing methods include: for the original energy metabolism data, deleting the data from the preheating stage and the initial gas equilibrium stage in the cage to obtain the deleted data; identifying, marking and processing outliers in the deleted data, and interpolating short-term missing data to obtain the interpolated data; and calculating the energy consumption value based on the gas concentration, flow rate, temperature, humidity and pressure in the interpolated data to obtain the processed energy metabolism data.

[0034] In this embodiment, the raw energy metabolism data is processed by deleting data from the preheating phase and the initial gas equilibration phase within the cage, resulting in the deleted data. Specifically, after the experiment begins, the oxygen sensor, carbon dioxide sensor, gas flow control module, and the gas environment within the metabolic cage typically require a period of time to reach a stable state. Therefore, data from the instrument preheating phase and the initial gas mixing and equilibration phase within the cage are deleted before formal analysis. The preheating and equilibration phases include the time periods when sensor readings are unstable, gas flow is unstable, the gas within the cage is not fully replaced, and the concentration difference between the inlet and outlet has not yet reached stable detection conditions. In one implementation, data from the period immediately following the start of the experiment can be deleted according to a preset time. Minute-by-minute data. In another implementation, the equilibrium end time can be automatically determined based on the stability of the gas concentration curve. For example, when the rate of change of oxygen concentration, carbon dioxide concentration, and gas flow rate are all below a preset threshold for a continuous period of time, the system is determined to have entered the stable detection phase.

[0035] Outliers in the deleted data are identified, marked, and processed, and short-term missing data are interpolated to obtain interpolated data. Specifically, outliers in metabolic data are identified. Outliers include, but are not limited to, sudden changes in gas flow rate, sudden changes in oxygen concentration, sudden changes in carbon dioxide concentration, energy consumption values ​​exceeding physiological range, abnormal sensor communication values, and abnormal fluctuations caused by cage opening. In one implementation, a threshold method is used to identify outliers; for example, when the deviation of a data point from the median in the adjacent time window exceeds a preset multiple, it is marked as an outlier. The standard deviation method, the absolute deviation of the median method, or the sliding window method can also be used to identify outliers. Marked outliers are not directly used for system response parameter estimation and regression model fitting. If the duration of the outlier or missing data is short, linear interpolation, spline interpolation, or local interpolation is performed using adjacent valid data; if the outlier or missing data duration is long, the time period is marked as an invalid interval and removed in subsequent analysis.

[0036] Based on the gas concentration, flow rate, temperature, humidity, and pressure in the interpolated data, energy consumption is calculated to obtain processed energy metabolism data. Specifically, the gas flow rate is first corrected to standard temperature, standard pressure, and dry conditions. Let the measured gas flow rate be... Environmental pressure is The temperature is The relative humidity is The saturated vapor pressure of water at this temperature is Then the standard state flow rate for drying can be expressed as: , in, Indicates standard pressure, It is 273.15 K. If the pressure unit is kPa, then A value of 101.325 kPa can be used; if the pressure unit is mmHg, then... A reading of 760 mmHg is acceptable.

[0037] Let the oxygen volume fraction at the inlet be... The oxygen volume fraction at the outlet is The volume fraction of carbon dioxide at the intake end is The volume fraction of carbon dioxide at the outlet is All gas volume fractions are expressed in decimal form, for example, 20.95% is expressed as 0.2095.

[0038] In a preferred embodiment, nitrogen balance correction is used to calculate oxygen consumption and carbon dioxide production. Let the standard flow rate for drying at the outlet be... The equivalent flow rate at the intake end is... This can be obtained from the conservation of nitrogen: , Oxygen consumption for: , Will After substituting, we get: .

[0039] carbon dioxide production for: , Will After substituting, we get: .

[0040] in, and The unit is consistent with the gas flow rate unit. If The unit is L / min, then and The unit is L / min.

[0041] Energy consumption value is calculated based on oxygen consumption and carbon dioxide production. In one implementation, the Weir formula is used: , when and When the unit is L / min, the unit of EE(t) is kcal / min. If you need to output kcal / d, you can convert it to: , If the system outputs the energy consumption per second with a time resolution of one second, then kcal / min can be divided by 60 to obtain kcal / s.

[0042] Simultaneously, the respiratory exchange rate can be calculated. : .

[0043] In another simplified implementation, when the inlet and outlet air flow rates are approximately equal and the accuracy requirement is low, the concentration difference can also be used for approximate calculation: , .

[0044] However, in the preferred embodiment, the aforementioned nitrogen balance correction formula is used.

[0045] S4. Construct a response delay model for metabolic detection and calibrate or estimate the response parameters of the response delay model.

[0046] Since behaviorally induced metabolic changes are not immediately reflected in the observed signals of the metabolic detection unit, this step establishes a response delay model for the metabolic detection system and calibrates or estimates its response parameters. Sources of response delay in metabolic detection include animal respiration gas expulsion, cage air mixing, gas delivery, and sensor response. These factors are then collectively expressed as a system response function. .

[0047] In one implementation, the system response function employs a first-order exponential response model with a fixed delay: , , in, d Indicates a fixed delay. t Represents the time constant. Fixed delay. d It mainly reflects the overall lag caused by gas path transmission and sampling calculation, the time constant. t It mainly reflects the smoothing effect caused by gas mixing inside the cage and sensor response.

[0048] For a discrete-time series, let the sampling interval be Δ. t , usually Δ t =1s, then the discrete response function can be expressed as: , , in, m This represents the discrete-time lag index. Z Let be the normalization coefficient, so that .

[0049] In this embodiment, the method for obtaining the response parameters includes: Based on the obtained behavioral probability sequence Constructing behavioral activity-driven sequences . It can be obtained by weighting the probabilities of behaviors related to changes in energy metabolism: , in, Represents a sequence of behavioral activities. Indicates the first k The activity intensity weights are assigned to different behaviors; for example, sleep and inactivity receive lower weights, while walking, exploring, and running receive higher weights. In another implementation, It can also be obtained from continuous motion intensity indicators such as the animal's center of mass velocity, movement distance, key point movement amplitude, posture change amplitude, or activity area change in the video.

[0050] The behavioral activity-driven sequences and processed energy metabolism data were subjected to mean-reduced processing and within a preset lag range. Inside, calculate the cross-correlation function. Specifically, [the following will be done]. Energy metabolism data after processing After removing the mean, we get: , , Within the preset lag range Inside, calculate the cross-correlation function: , in, This represents the mean-removed behavior-driven sequence. This represents the observed energy consumption sequence after removing the mean. This represents the energy metabolism data after processing. mean This indicates that the arithmetic mean was calculated within the valid time range of the analysis. Represents the cross-correlation function. l Indicates the lag time; when the cross-correlation function At a certain lag When the value is reached, the initial estimated delay of behavioral activity change relative to observed metabolic change is considered to be . The lag It is not directly equivalent to all system response parameters, but is treated as a fixed delay. d and time constant t Optimize the initial reference for the search.

[0051] With the initial estimated delay as For reference, candidate sets for fixed delays are determined respectively. Candidate set of time constant The response parameters are determined based on two candidate sets. Specifically, the initial delay is obtained from cross-correlation analysis. For reference, candidate sets for fixed delays are determined respectively. Candidate set of time constant For each set of candidate parameters Construct the corresponding response function and drive the sequence of behavioral activities. Convolving with it, we get: , in, Indicates candidate parameters, This represents the activity-driven sequence obtained by convolution with the response function under candidate parameters. This represents the convolution operation. Represents the system response function. A This represents the original behavioral activity-driven sequence; This represents the response function corresponding to the candidate parameters when the candidate parameters take their optimal values. When the optimal response function is obtained, The following text will be abbreviated as Therefore, the above formula can also be written as: .

[0052] In fixed Under the given conditions, the baseline term is estimated using the least squares method. and activity-driven metabolic contribution coefficient : , in, This represents the baseline term estimated by the least squares method under the given candidate parameters. This indicates that the activity-driven metabolic contribution coefficient is estimated by the least squares method under this candidate parameter. Indicates the baseline term. This represents the activity-driven metabolic contribution coefficient. This represents the set of valid time points involved in the fitting. Further calculation of the sum of squared residuals corresponding to this set of candidate parameters is then performed: , in, This represents the sum of squared residuals for each candidate parameter. The candidate parameter with the smallest sum of squared residuals is determined as the optimal response parameter. , in, This represents the response parameters.

[0053] In another implementation, multiple behavior probability sequences can be used for fitting. This avoids the sum of the behavior probabilities becoming... l The resulting perfect collinearity, select the first r This behavior is used as a reference behavior, and the convolutional sequence corresponding to this reference behavior is not included in the model while retaining the intercept term: , For each group of candidates The least squares method is used to estimate and each And select the one with the smallest sum of squared residuals. .in, This indicates the metabolic level under reference behavioral conditions. Indicates the first k The metabolic increment of this behavior relative to the reference behavior.

[0054] After optimization, the system response function is obtained. Fixed delay d Time constant t The response window length M and the fitting error index. The response window length M can be set to 3. t Up to 5 t , or take The length of time it takes for the decay to fall below a preset threshold.

[0055] In another embodiment, the empty cage gas replacement calibration method can also be used to estimate the system response parameters. Specifically, in the absence of animals, the metabolic cage is placed in a stable gas environment, and then over time... The intake gas is changed from the initial concentration Switch to step concentration Alternatively, a standard gas of known concentration can be input into the inlet, and the concentration change curve detected by the sensor at the outlet can be recorded. .

[0056] Normalize the output concentration to a step response curve: .

[0057] For a first-order system with a fixed delay, its step response can be expressed as: , , By minimizing the following error estimate d and t : , in, For the measured normalized response curve, This is the model response curve.

[0058] Parameters can also be estimated based on the time it takes for the response curve to reach a specific proportion. Let... for Reaching the proportion p The time is then: .

[0059] For example, when p When =0.632: ; when p When =0.90: .

[0060] Therefore, it can be derived from and estimate: , , If the system needs to estimate cage mixing, gas path transmission, and sensor response separately, the overall response function can be expressed as: , in, Indicates the mixed response of the cage. Indicates the gas transmission response. This indicates the sensor response. The fixed delay in the gas path can be estimated from the gas path volume and gas flow rate. , in, Indicates the volume of the sampling pipeline. Q This represents the gas flow rate. The mixing time constant in the cage can be approximated as: , in, This represents the effective gas volume of the metabolic cage. The above parameters can be used as initial values ​​and then corrected through step response experiments.

[0061] S5. Construct a behavior-state-response convolution model based on the behavior time series, and obtain the discrete response function and response-corrected behavior sequence based on the behavior-state-response convolution model.

[0062] Based on the obtained behavioral probability time series and system response function A behavioral state-response convolutional model is constructed. This model converts the behavioral probability sequence along the actual timeline of animal behavior into response-corrected behavioral explanatory variables along the observation timeline of the metabolic monitoring system. This step resolves the issue of the incomplete correspondence between the behavior occurrence time and the metabolic observation time, enabling subsequent metabolism-behavior joint regression models to utilize and process post-energy metabolism data (observed energy consumption sequences). Matching behavioral explanatory variables.

[0063] In this embodiment, the method for obtaining the discrete response function and the response correction behavior sequence includes: The obtained system response function According to sampling interval t Discretization yields the discrete response function. ,in, Indicates the historical lag sequence number relative to the current point in time. M This represents the length of the system response window. To ensure that the convolution process only changes the temporal distribution of the behavioral influence, without artificially amplifying or reducing the total probability of the behavior, the discrete response function... Perform normalization to ensure that it satisfies: , At the same time, to satisfy the causality constraint, we set: , This constraint means that future actions cannot affect current or past metabolic observations, and the energy consumption currently observed can only be contributed by the current and past behavioral states.

[0064] When the system response function adopts a first-order exponential response model with a fixed delay, its discrete form can be expressed as: , , in, d For a fixed delay, t It is a time constant. Z These are normalization coefficients used to ensure... .

[0065] For the k Given a behavioral state, its behavioral probability time series is... With system response function Perform convolution to obtain the response-corrected behavior sequence: , In discrete-time form, the above equation can be expressed as: , in, This represents a sequence of response correction behaviors. Indicates the animal at the current time t The previous m The sampling point belongs to the first k The probability of a certain behavioral state. This is obtained from... This indicates that, after considering the response delay and smoothing effect of the metabolic detection system, the first... k Behavioral state versus time t Observed energy consumption value The extent of its potential contribution. Therefore, This is not equivalent to animals in time. t Original behavior probability Instead, it represents the behavioral explanatory variable that matches the observed metabolic signal after the behavioral state has undergone a transformation in response to the metabolic detection system. For example, when an animal is in a certain time... When running occurs, the probability of the original behavior Will The level is elevated in the vicinity; however, due to delays and smoothing effects in metabolic detection systems, the impact of this running behavior on observed energy expenditure values ​​may be limited. It then gradually appears and gradually decays over a subsequent period. Therefore, the result obtained through convolution calculations... It can reflect the delayed contribution of running behavior on the observed metabolic timeline.

[0066] In this embodiment, the boundary time points, invalid time periods, and missing data of the response correction behavior sequence also need to be processed. Specifically, in the calculation... At that time, for the initial stage of the experiment or near the starting point of valid data, when When the effective time range for the behavior is exceeded, the following methods can be used to handle it: (1) Remove the time range that exceeds the effective time range. Set to 0; (2) Use the behavior probability near the effective start time point to fill the boundary; (3) Directly mark the incomplete start time period of the response window as the boundary invalid interval and remove it in the subsequent model fitting.

[0067] In a preferred embodiment, to avoid boundary filling causing deviations in model fitting, the initial step after the experiment begins... M Each sampling point is marked as a convolution boundary interval and is not used for subsequent fitting of the metabolism-behavior joint regression model. For metabolic time periods that have been marked as instrument malfunction, cage opening malfunction, long-term absence, or other invalid states, their corresponding... The calculation results can be retained, but will not be used as valid samples in subsequent model fitting. For short-term missing behavior probability data, interpolation can be performed using adjacent valid behavior probabilities, or smooth completion can be performed based on the output results of the video recognition model at previous and subsequent time points. If the missing behavior data time exceeds a preset threshold, the time period will be marked as an invalid behavior interval and removed in subsequent analysis.

[0068] Output response corrected behavior explanatory variable matrix: for all K Perform the above convolution calculation on each of the behavioral states to obtain the behavioral explanatory variables after response correction: , Organize them into a matrix of behavioral response explanatory variables: , In this matrix, each column corresponds to a response convolution sequence for a specific behavioral state, and each row corresponds to a valid time point. This matrix serves as the primary independent variable input to the subsequent metabolism-behavior joint regression model, used to interpret the observed energy consumption sequence. .

[0069] Through this step, the original behavior probability sequence It is converted into a sequence of response correction behaviors that match the observed characteristics of the metabolic detection system. This allows for the alignment and correction between the behavioral timeline and the metabolic observation timeline. In another embodiment, different behavioral states can also utilize behavior-specific response functions. ,Right now: , in, Indicates the first k The response function corresponds to different behavioral states. This approach is suitable when it is assumed that the rate, duration, or recovery process of metabolic responses induced by different behaviors differs significantly. However, in a preferred embodiment, a uniform system response function is used. Because gas mixing, gas transmission, and sensor response within the cage are primarily characteristics of the detection system, they share a common delaying and smoothing effect on changes in metabolic gases from different sources.

[0070] S6. Construct a joint regression model of metabolism and behavior based on processed energy metabolism data and response correction behavior sequences.

[0071] The metabolism-behavior joint regression model is as follows: , in, Indicates the baseline term. Indicates the first k The metabolic contribution coefficient corresponding to the row state Represents the coefficients of the covariates. Indicates the first m One covariate, Represents the residual.

[0072] In this embodiment, the model construction steps are as follows: (1) Organize the dependent variables The preprocessed energy consumption sequence is used as the dependent variable: , in, to To ensure effective analysis of time points, time points marked as instrument malfunction, opening abnormality, long-term missing time, or other invalid states are not included in the model fitting.

[0073] (2) Organize the independent variables The response correction sequence corresponding to each behavioral state is used as the independent variable: , Simultaneously organize the covariate sequence Covariates may include animal weight, ambient temperature, day / night time, experimental treatment, cage number, gas flow rate, body temperature, or other variables that require correction.

[0074] (3) Constructing the design matrix Construct the design matrix Z: , The first column contains constant terms, used for estimation. .

[0075] Since the probability label usually satisfies at each time point After convolution with normalized response functions, multiple There may also be summation constraints between them. To avoid collinearity, in one implementation, a reference behavioral state, such as sleep or quiescent behavior, can be selected, and its corresponding... Add it to the design matrix. At this point, This indicates the basal energy expenditure level under the reference behavioral state, and others. This represents the metabolic increment relative to a reference behavioral state. In another implementation, all behavioral states may also be retained. However, no intercept item is set. ,at this time It can be directly interpreted as the absolute energy consumption contribution in the corresponding behavioral state.

[0076] (4) Perform parameter estimation The model parameters are estimated using the least squares method: , , in, This represents the estimated parameter vector. In the presence of outliers, heteroscedasticity, or discrepancies in behavior recognition confidence, weighted least squares can be used. , in, W This is the weight matrix. The weights can be determined based on the quality of metabolic data, the confidence level of behavior recognition, or the validity of the experiment. For example, when the confidence level of behavior recognition is low at a certain time point, the weight of that time point in the model fitting can be reduced.

[0077] In another implementation, regularized regression can be used to improve model stability: , in, l The regularization coefficient is . R For example, a positive semidefinite penalty matrix. .

[0078] (5) Obtaining behavioral metabolic contribution After fitting, the metabolic contribution coefficient corresponding to each behavioral state can be obtained. If a reference behavior model is used, then Indicates the first k The energy consumption increment of this behavior relative to the reference behavior. If no intercept term is used and all behavior states are retained, then Indicates the first k The model can also output the absolute metabolic level corresponding to a given behavioral state. , By comparison and This allows us to evaluate the model's ability to interpret observed metabolic curves.

[0079] S7. Invert the potential metabolic signal based on the system response function to obtain the potential instantaneous metabolic sequence.

[0080] In addition to the convolution fitting path described above, this embodiment also provides a potential metabolic signal inversion method based on response function, which is used to recover or estimate potential real real-time energy consumption sequences of animals from observed metabolic signals.

[0081] Methods for obtaining potential immediate metabolic sequences include: Convolution operation based on system response function, processed energy metabolism data, and real real-time energy consumption sequence: , in, Represents a real-time energy consumption sequence. This indicates observation noise.

[0082] Based on the processed discrete response function Constructing convolutional matrices H And rewrite the convolution operation in matrix form: , in, Y Represents the observed energy consumption vector; E This represents the candidate potential immediate metabolic sequences to be solved during the optimization process. This represents the observation noise vector, composed of the observation noise at each time point. composition; H Each row represents a specific observation time point. From multiple previous time points According to response weight Weighted formation.

[0083] Since direct deconvolution easily amplifies noise, this embodiment uses a regularized deconvolution method to solve the problem. Construct the optimization objective function in matrix form: , in, Indicates reference metabolic level. W Represents the data weight matrix. D Represents the difference matrix. T To represent the transpose of a matrix, and This represents the regularization coefficient.

[0084] Among them, the first item Used to ensure After convolution with the system response function again, it can approximate the actual observation as closely as possible. The second item Used to restrict Avoid excessive fluctuations between adjacent time points to prevent deconvolution from amplifying noise. D It can be a first-order difference matrix or a second-order difference matrix. The third term... Used to limit the range of solutions and improve solution stability.

[0085] In one implementation, nonnegativity constraints and physiological range constraints may also be added: , , in, and These represent the preset lower and upper limits of physiologically reasonable energy consumption, respectively.

[0086] Without adding nonnegativity constraints, the regularized deconvolution problem can be solved using linear equations to obtain the potential instantaneous metabolic sequence: , in, This represents the value that minimizes the regularization objective function. E The estimated value, i.e., the potential immediate metabolic sequence; I Represents the identity matrix. When nonnegativity constraints or physiological range constraints are added, nonnegativity least squares, constrained least squares, or other convex optimization methods can be used to solve the problem. Regularization coefficient. and Cross-validation can be used. L Determined by curve method, residual analysis or preset empirical parameters.

[0087] get Then, it is convolved again with the system response function to obtain the reconstructed observed metabolic curve: , Compare Compared with actual observed metabolic curves Y The difference is considered. If the reconstruction error is less than the preset threshold, the inversion result is considered valid; if the error is too large, the response function parameters, regularization coefficient, or abnormal time periods are removed and the solution is recalculated. The result obtained through this step... This refers to the potential immediate metabolic sequence after delay and smoothing correction, which can be used for subsequent behavioral state conditional metabolic index modeling.

[0088] S8. Construct a behavioral state-conditionalized metabolic phenotypic index model based on the metabolism-behavior joint regression model and potential real-time metabolic sequences, and generate a joint analysis report based on the behavioral state-conditionalized metabolic phenotypic index model.

[0089] In this embodiment, the results are based on the obtained metabolic-behavioral joint regression or on the obtained potential immediate metabolic sequences. Establish a behavioral state-conditional metabolic phenotypic index model.

[0090] The core of this step is not simply listing multiple indicators, but rather constructing state-specific metabolic phenotypic indicators based on "behavioral state exposure" and "corresponding metabolic contribution." Among these, the most basic and core indicator is the probability-weighted average energy expenditure value under a given behavioral state.

[0091] For the k The behavioral state and the conditional metabolic indicators of the behavioral state can be obtained according to the two analytical paths mentioned above.

[0092] When using a combined metabolism-behavior regression path, the metabolic level corresponding to each behavioral state is determined based on the fitted behavioral-metabolic contribution coefficient. If sleep or quiescent behavior is used as the reference behavior, the metabolic level of the reference behavior is... , No. k The metabolic level of non-reference behavior is ,in, Indicates the first k The energy consumption increment of this behavior relative to the reference behavior.

[0093] When using a potential metabolic signal inversion pathway, assume the metabolic sequence used for analysis is the obtained potential immediate metabolic sequence. ( Then the first... k The probability-weighted average energy consumption under each behavioral state is: .

[0094] This formula indicates that, based on the fact that the underlying metabolic sequence has already undergone response delay and smoothing correction, according to each time point belonging to the [missing information]... k The probability of each behavioral state is weighted to obtain the average energy consumption level corresponding to that behavioral state.

[0095] Based on this, we can further obtain the first... k Cumulative exposure time for each behavioral state: , in, The sampling interval. k The cumulative energy consumption corresponding to a certain behavioral state can be expressed as: , Therefore, the fundamental logic of behavioral state-conditioned metabolic indicators is: first use behavioral probabilities... Describe the degree to which an animal is in a certain behavioral state at different points in time, and then use... Energy consumption sequence We then weight the data to obtain the average metabolic rate, cumulative metabolic consumption, and relative metabolic increment under this behavioral state.

[0096] In obtaining Then, the metabolic increment relative to the reference behavioral state can be calculated. Let the reference behavior be sleep or resting behavior, with an average energy expenditure of... Then the first k The metabolic increment for this behavior is: , This indicator is used to represent the first k This behavior represents the additional energy expenditure compared to the baseline state. The metabolic cost per unit time for this behavior can then be calculated. , If we are concerned with the total metabolic cost of a certain behavioral event, we can calculate the incremental energy consumption area within the interval where the behavioral event occurs: , in, This represents the extra energy consumed by a certain action or event relative to the reference state.

[0097] For behavioral events with clear start and end times, such as running, eating, drinking, or exploring, event-level metabolic response features can also be extracted. Specifically, taking the start time of the behavioral event as 0, multiple similar behavioral events... Alignment is performed, and the average event-triggered metabolic curve is calculated. Based on this curve, metabolic rise delay, peak energy expenditure, peak occurrence time, recovery time, and area under the curve are extracted.

[0098] Among them, the metabolic rise delay indicates that after the behavior occurs The time at which the metabolic response begins to be significantly higher than the baseline; peak energy expenditure represents the maximum value of the behavior-induced metabolic response; recovery time represents the time required for the metabolic curve to return to near the baseline; and the area under the curve represents the cumulative additional metabolic expenditure caused by the behavioral event.

[0099] oxygen consumption Carbon dioxide production and respiratory exchange rate The same probability-weighted logic can also be used to construct behavioral state conditional indicators: , , , This allows us to obtain characteristics of oxygen consumption, carbon dioxide production, and substrate utilization under different behavioral states. When comparing different treatment groups, these characteristics can be calculated separately for each animal. , , , , and Then, statistical comparisons are made between groups based on indicators such as these.

[0100] In one implementation, the following statistical model is used to analyze metabolic differences among different treatment groups under the same behavioral state: , in, Metabolic indicators representing behavioral states under conditioned conditions. Indicates the state of behavior. Indicates experimental treatment, This represents the interaction between behavioral states and experimental treatments. This represents covariates such as body weight, day / night time, and ambient temperature. This indicates random effects on individual animals.

[0101] The model can distinguish the following situations: (1) The increase in total energy consumption is due to the increase in animal activity time; (2) The increase in total energy consumption is due to the increase in unit metabolic cost under the same behavior; (3) The treatment factors only affect metabolism under certain specific behavioral states; (4) The treatment factors change basal metabolism but do not change behavior-induced metabolism; (5) The treatment factors change behavioral composition but do not change metabolic efficiency within behavioral states.

[0102] Based on the aforementioned steps, a joint analysis report on energy metabolism and behavior is generated.

[0103] The report includes: (1) the original energy consumption curve and the original behavioral state timeline; (2) the preprocessed energy consumption curve; (3) the behavioral probability time series; and (4) the system response parameters, including fixed delay. d Time constant t and response function (5) Results of behavioral state response convolution; (6) Parameters of metabolism-behavior joint regression model; (7) Results of potential instantaneous metabolic signal inversion; (8) Probability-weighted average energy consumption under each behavioral state; (9) Metabolic increment of each behavioral state relative to the reference behavior; (10) Metabolic response curves, peak values, delays, recovery times and cumulative metabolic costs of each behavioral event; (11) Metabolic differences between different treatment groups under the same behavioral state; (12) Visual charts and statistical analysis results.

[0104] This report allows users to obtain the metabolic characteristics of animals under different behavioral states and determine whether different genotypes, drug treatments, disease models, dietary interventions, environmental interventions, or aging states alter the energy metabolism patterns under specific behavioral states.

[0105] Example 2 In this embodiment, a joint analysis system for energy metabolism and behavior based on response delay correction is also provided, including: a data acquisition module, a visual analysis module, an energy data processing module, a response parameter calibration module, a response function and behavior sequence acquisition module, a regression model construction module, an inversion module, and an index analysis module.

[0106] The data acquisition module collects raw energy metabolism data and video data from small animals. The visual analysis module performs computer vision analysis on the video data to identify the animal's behavioral states and generate behavioral time series. The energy data processing module preprocesses the raw energy metabolism data to obtain processed energy metabolism data. The response parameter calibration module constructs a response delay model for metabolic detection and calibrates or estimates the response parameters of the response delay model. The response function and behavioral sequence acquisition module constructs a behavioral state response convolution model based on the behavioral state response convolution model and obtains a discrete response function and a response-corrected behavioral sequence based on the behavioral state response convolution model. The regression model construction module constructs a metabolism-behavior joint regression model based on the processed energy metabolism data and the response-corrected behavioral sequence. The inversion module inverts the underlying metabolic signal based on the system response function to obtain a potential real-time metabolic sequence. The index analysis module constructs a behavioral state-conditionalized metabolic phenotypic index model based on the metabolism-behavior joint regression model and the potential real-time metabolic sequence, and generates a joint analysis report based on the behavioral state-conditionalized metabolic phenotypic index model.

[0107] Example 3 In this embodiment, an energy metabolism and behavior joint analysis device based on response delay correction is also provided, including: an energy metabolism detection unit, a video behavior acquisition unit, a behavior recognition and analysis unit, a time synchronization unit, a system response parameter estimation unit, a metabolism-behavior joint analysis unit, and a report generation unit.

[0108] The energy metabolism detection unit includes an animal metabolism cage, an air inlet channel, an air outlet channel, a gas flow control module, an oxygen concentration detection module, a carbon dioxide concentration detection module, a temperature and humidity detection module, a pressure detection module, and a data acquisition module. It is used to collect gas parameters at the air inlet and outlet ends and calculate the animal's oxygen consumption, carbon dioxide production, and energy consumption.

[0109] The video behavior acquisition unit includes a visible light camera, an infrared camera, a supplementary lighting module, a video acquisition module, and a video storage module, which are used to continuously acquire videos of animal behavior in the metabolic cage.

[0110] The behavior recognition and analysis unit is used to perform computer vision analysis on video data and output the probability that the animal belongs to different behavioral states at different time points.

[0111] The time synchronization unit is used to unify metabolic data, video data, and behavior recognition data onto the same timeline.

[0112] The system response parameter estimation unit is used to estimate the fixed delay, cage mixing time constant, gas path transmission delay, and sensor response time constant of the metabolic detection system.

[0113] The response delay correction unit is used to perform convolution correction on the behavioral state sequence based on the system response function, or to perform deconvolution inversion on the observed metabolic signal.

[0114] The metabolism-behavior joint analysis unit is used to establish a metabolism-behavior joint regression model and extract behavioral state-conditional metabolic phenotypic indicators.

[0115] The report generation unit is used to generate metabolic curves, behavioral state timelines, delay correction results, behavioral metabolic indicators, intergroup comparison results, and visualization reports.

[0116] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A joint analysis method for energy metabolism and behavior based on response delay correction, characterized in that, Includes the following steps: Collect raw energy metabolism data and video data of small animals; The video data is subjected to computer vision analysis to identify the animal's behavioral state and generate a behavioral time series. The raw energy metabolism data is preprocessed to obtain processed energy metabolism data; Construct a response delay model for metabolic detection, and calibrate or estimate the response parameters of the response delay model; A behavior-state-response convolutional model is constructed based on the behavior time series, and a discrete response function and a response-corrected behavior sequence are obtained based on the behavior-state-response convolutional model. A joint regression model of metabolism and behavior is constructed based on the processed energy metabolism data and the response correction behavior sequence. The potential instantaneous metabolic sequence is obtained by inverting the potential metabolic signal based on the system response function. Based on the metabolism-behavior joint regression model and the potential real-time metabolic sequence, a behavior state-conditionalized metabolic phenotypic index model is constructed, and a joint analysis report is generated based on the behavior state-conditionalized metabolic phenotypic index model.

2. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 1, characterized in that, The methods for obtaining the raw energy metabolism data and the video data include: The raw energy metabolism data are obtained by collecting data on oxygen concentration at the inlet end, oxygen concentration at the outlet end, carbon dioxide concentration at the inlet end, carbon dioxide concentration at the outlet end, gas flow rate, temperature, humidity, and pressure at a preset sampling frequency. Animal behavior videos are collected, and timestamps are generated for each frame or each second of video segment to obtain the video data.

3. The energy metabolism and behavior joint analysis method based on response delay correction according to claim 1, characterized in that, Methods for obtaining the behavioral time series include: The video data is analyzed using computer vision to identify the animal's behavioral state; Construct a sequence of probabilistic behavioral events based on the behavioral state. ; Based on the behavioral probability event sequence Construct the behavior probability vector at each time point when there are K mutually exclusive behavior states. and satisfy The behavior probability vector is used as the behavior time series.

4. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 1, characterized in that, The preprocessing method includes: For the original energy metabolism data, delete the data from the preheating stage and the initial gas equilibrium stage in the cage to obtain the deleted data; The outliers in the deleted data are identified, marked, and processed, and short-term missing data is interpolated to obtain interpolated data. Based on the gas concentration, flow rate, temperature, humidity, and pressure in the interpolated data, the energy consumption value is calculated to obtain the processed energy metabolism data.

5. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 1, characterized in that, The methods for obtaining the response parameters include: Construct a behavior activity-driven sequence based on the aforementioned behavior time series: ， in, Represents a sequence of behavioral activities. Indicates the first k Activity intensity weights for various behaviors; The behavioral activity-driven sequence and the processed energy metabolism data are subjected to mean-reducing processing, and within a preset lag range... Inside, calculate the cross-correlation function: ， ， ， in, This represents the mean-removed behavior-driven sequence. This represents the observed energy consumption sequence after removing the mean. This represents the energy metabolism data after processing. mean This indicates that the arithmetic mean was calculated within the valid time range of the analysis. Represents the cross-correlation function. l Indicates the lag time; When cross-correlation function At a certain lag When the value is reached, the initial estimated delay of behavioral activity change relative to observed metabolic change is considered to be . ; The initial estimated delay is For reference, candidate sets for fixed delays are determined respectively. Candidate set of time constant The response parameters are determined based on two candidate sets: ， ， ， ， in, Indicates candidate parameters, This represents the activity-driven sequence obtained by convolution with the response function under candidate parameters. This represents the convolution operation. Represents the system response function. A This represents the original behavioral activity-driven sequence. This represents the baseline term estimated by least squares under candidate parameters. This indicates that the activity-driven metabolic contribution coefficient is estimated by the least squares method under candidate parameters. Indicates the baseline term. This represents the activity-driven metabolic contribution coefficient. This represents the sum of squared residuals corresponding to the candidate parameters. This represents the set of valid time points for fitting. This represents the response parameters.

6. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 5, characterized in that, The methods for obtaining the discrete response function and the response correction behavior sequence include: The obtained system response function According to sampling interval t Discretization yields the discrete response function. To ensure that the convolution process only changes the temporal distribution of the behavioral influence, without artificially amplifying or reducing the total probability of the behavior, the discrete response function... Normalization was performed, where, Indicates the historical lag sequence number relative to the current point in time. M Indicates the length of the system response window; Based on the normalized discrete response function and the behavior time series, the response-corrected behavior sequence is obtained: ， in, This represents a sequence of response correction behaviors.

7. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 6, characterized in that, The metabolism-behavior joint regression model is as follows: ， in, Indicates the baseline term. Indicates the first k The metabolic contribution coefficient corresponding to the row state Represents the coefficients of the covariates. Indicates the first m One covariate, Represents the residual.

8. The joint analysis method for energy metabolism and behavior based on response delay correction according to claim 7, characterized in that, Methods for obtaining the potential immediate metabolic sequence include: Based on the convolution operation of the system response function, the processed energy metabolism data, and the real real-time energy consumption sequence: ， in, Represents a real-time energy consumption sequence. Indicates observation noise; Based on the processed discrete response function Constructing convolutional matrices H The convolution operation is then rewritten in matrix form: ， in, Y Represents the observed energy consumption vector. E This represents the candidate potential immediate metabolic sequence to be solved. Represents the observation noise vector; Construct the optimization objective function based on the aforementioned matrix form: ， in, Indicates reference metabolic level. W Represents the data weight matrix. D Represents the difference matrix. T To represent the transpose of a matrix, and Represents the regularization coefficient; The potential instantaneous metabolic sequence is obtained by inverting the optimization objective function: ， in, Indicates by E The estimated potential immediate metabolic sequence, I Represents the identity matrix.

9. A joint analysis system for energy metabolism and behavior based on response delay correction, wherein the system applies the method described in any one of claims 1-8, characterized in that, include: The system includes a data acquisition module, a visual analysis module, an energy data processing module, a response parameter calibration module, a response function and behavior sequence acquisition module, a regression model construction module, an inversion module, and an index analysis module. The data acquisition module is used to collect raw energy metabolism data and video data of small animals; The visual analysis module is used to perform computer vision analysis on the video data, identify the animal's behavioral state, and generate a behavioral time series. The energy data processing module is used to preprocess the raw energy metabolism data to obtain processed energy metabolism data; The response parameter calibration module is used to construct a response delay model for metabolic detection and to calibrate or estimate the response parameters of the response delay model. The response function and behavior sequence acquisition module constructs a behavior state response convolution model based on the behavior time series, and obtains a discrete response function and a response correction behavior sequence based on the behavior state response convolution model; The regression model construction module constructs a joint regression model of metabolism and behavior based on the processed energy metabolism data and the response correction behavior sequence. The inversion module performs inversion based on the potential metabolic signal of the system response function to obtain the potential real-time metabolic sequence. The indicator analysis module constructs a behavioral state-conditionalized metabolic phenotype indicator model based on the metabolism-behavior joint regression model and the potential real-time metabolic sequence, and generates a joint analysis report based on the behavioral state-conditionalized metabolic phenotype indicator model.

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