Applying complex mathematical models of physiological systems is challenging due to the large number of parameters. Identifying these parameters through experimentation is difficult, and although procedures for fitting and validating models are reported, no integrated strategy exists. Additionally, the complexity of optimization is generally neglected when the number of experimental observations is restricted, obtaining multiple solutions or results without physiological justification. This work proposes a fitting and validation strategy for physiological models with many parameters under various populations, stimuli, and experimental conditions. A cardiorespiratory system model is used as a case study, and the strategy, model, computational implementation, and data analysis are described. Using optimized parameter values, model simulations are compared to those obtained using nominal values, with experimental data as a reference. Overall, a reduction in prediction error is achieved compared to that reported for model building. Furthermore, the behavior and accuracy of all the predictions in the steady state were improved. The results validate the fitted model and provide evidence of the proposed strategy’s usefulness. Mathematical modeling is an interdisciplinary field that, applied to medicine, has allowed a better understanding of physiological functions and relationships. Its support in this field has been related to the education and training of clinical staff, the identification, monitoring, and treatment of diseases, and equipment development ,2,3,4,5.The cardiorespiratory system stands out as one of the most relevant physiological systems regarding the diagnosis, treatment, monitoring, and prevention of diseases, mainly due to the importance and usefulness of their related variables for the identification of the correct state and functioning of the organism ,10,11. TPhysical exercise is a natural stimulus that generates significant cardiorespiratory variations that cannot be evidenced under resting conditions and constitute a well-defined characteristic pattern in healthy human subjects ,16. SeveAlthough mathematical models can describe the physiological response under a specific stimulus, their computational simulation using parameters’ nominal values constrains their use in populations with the same characteristics and conditions used during their development ,23. FittDifferent techniques to solve the fitting problem of models with many parameters have been proposed. They all focused on identifying the minimum number of parameters that must be fitted to correctly predict the experimental response. In , a deterThe validation procedure aims to verify whether the model predictions agree with the experimental data for the defined conditions and disturbances. For this purpose, measures that consider the transient and steady-state response features of the analyzed physiological variables are usually implemented. Although there is no consensus on the proper methodology for validating mathematical models of physiological systems, different works coincide with the criteria proposed by . Such crThis work aims to propose a fitting and validation strategy for physiological models with many parameters that consider different populations and stimuli. This strategy includes several techniques and approaches to classify, select, and optimize model parameters under steady-state conditions. A model validation methodology is also presented. Some described methods are new proposals or correspond to improvements to previously reported methods. The strategy application in a cardiorespiratory model during dynamic aerobic exercise is presented and described as a case study.This paper is structured as follows. First, the fitting and validation strategies are presented. It describes in detail the procedures for the classification, selection, and optimization of parameters and methodology validation. Second, a case study is presented. It includes a qualitative description of the cardiorespiratory model and the simulation, fitting, and validation. Third, predictions at different levels of aerobic exercise, both with the fitted model and the nominal values, are compared with experimental data obtained from healthy subjects under a cardiopulmonary exercise test . FinallyThe strategy proposed in this work consists of applying three main procedures or steps that must be done sequentially: (a) classification and selection of parameters, (b) model fitting, and (c) model validation. The first procedure involves classifying the model parameters according to some predefined roles in the model  and selecting the most relevant ones according to different model-fitting approaches. The second one consists of four sequential stages of parameter value identification related to the model fitting regarding the available experimental information, the overall accuracy, the specific prediction of each variable, and the predictions’ behavior concerning the evaluated stimulus. The final procedure focuses on validating the fitted model regarding its predictions’ accuracy, behavior, and transient and steady-state regimes. Each procedure is presented in This procedure aims to highlight and select the parameters that can be considered best-fit candidates. The selection of parameters is justified according to their relationship to available experimental data, role in the model, identifiability, sensitivity to variations, and their relationship to the stimulus evaluated. Initially, it reduces the number of parameters depending on their role in the model and the objective of fitting predictions in steady-state conditions. Subsequently, the resulting parameters are classified and selected according to two reported techniques and established criteria regarding the model fitting approaches.Classification and Selection of Parameters by RoleIt consists of an initial classification of the model parameters according to their roles. It comprises five parameter classes generally found in structured models of physiological systems. They correspond to (i) time constants, i.e., parameters related to transient response; (ii) conversion parameters, which are constant values related to equivalences among measurement units; (iii) covariates, corresponding to values that allow defining simulation conditions regarding external disturbances, environment conditions, and features of the population to be simulated; (iv) initial values, corresponding to initial conditions of the model variables, usually required as initial states of integrators and whose action mainly affect the temporal characteristics of the responses before reaching the model steady state; and (v) gain and thresholds, that either module or saturate variables related to model mechanisms, i.e., the weighting of the chemoreceptors response to set the parasympathetic and sympathetic activity regarding the regulation of peripheral resistances in cardiovascular control models.The selection of parameters comprises choosing those parameters that mainly define the steady-state behavior of the cardiorespiratory system response and, therefore, can be used to fit the model response in such a condition. The time constant parameters and initial values are discarded, considering that the proposed fitting procedure focuses on the response once the steady state is reached. Conversion parameters do not need fitting because of their nature and meaning. Therefore, only gain and threshold parameters, whose variations have physiological sense, and are correlated with experimental conditions, and covariates will be considered for the subsequent selection procedures and fitting process. Covariates are only used for the standardization of the simulation conditions.Parameter Classification TechniquesThe proposed strategy involves modifying and implementing two of the most widely implemented parameter classification techniques for fitting physiological models ,23. A deSubset Selection of ParametersIt is a technique based on the classification of model parameters according to how well-conditioned or ill-conditioned they can be identified . Well-coIn this study, the subset selection of parameters is based on QR Factorization with the Column Pivoting method . It was This technique is complemented by integrating the different stimulus exercise levels  and variations in the parameters previously selected in the appropriate physiological range . These additions would allow the selection of parameters that are more consistent with the desired fit.According to the above, the Jacobian is calculated according to Equation (1).tion (4) .(4)σjklThe parameters associated with the The standard 2-norm of the normalized singular value for each parameter in each ranking obtained for each parameter variation must be determined to obtain a general ranking independent of the stimulus level, as presented in Equation (8).Finally, the result of this technique corresponds to the presented in Equation (9).This technique is usually implemented with sensitivity analysis techniques because their approaches complement each other regarding the problem solution. QR decomposition identifies the parameters to which the model is sensitive as a group, while sensitivity analysis finds the parameters to which the model is individually sensitive .Sensitivity AnalysisSensitivity analysis involves the integration and improvement of the techniques introduced by ,8,23. ItThe model variable’s sensitivity regarding each parameter variation is based on the standard local differential equation described by  and usedThis work proposes modifying the measurement of relative sensitivity to make it independent of the time and dependent on the stimulus. Therefore, an approach based on steady-state conditions at different stimulus levels is used. Relative sensitivity is evaluated by varying each parameter over a range around its nominal value, while the others are kept at their nominal values. Equation (11) shows the proposed relative sensitivity measure. Time independence avoids significant differences between sensitivity measures due to time lags, considering that the fitting model procedure is focused on minimizing the steady-state differences between the experimental measurements and the model predictions. The evaluation of the stimulus is included by considering the influence of its variations on sensitivity measures.Deriving sensitivity equations can be tedious and error-prone for large systems, mainly when they involve nonlinear features, such as those analyzed in this case study. Alternatively, Equation (11) can be solved using a computational approach consisting of a simple finite difference method. A numerical approximation of the derivatives, which also considers the variation of the parameter relative to its nominal value, is expressed in Equation (12).Standard 2-norm is applied to The stimulus level independency relative sensitivity is calculated according to Equation (15).The model’s total sensitivity to each parameter is calculated according to Equation (19).Parameter Selection CriteriaThis procedure focuses on applying the selection criteria of the classified parameters concerning four different fitting approaches.Selection for the Standardization of Simulation ConditionsIt consists of selecting the model’s parameters, which can be determined from the available experimental data. It involves those related to the subjects’ characteristics, the stimulus evaluated, or the environmental conditions. They can be established by direct equivalence or by applying previously validated equations.Selection for the Base Fitting ApproachIt comprises selecting the set of parameters for which the model has the highest global sensitivity. This selection aims to reduce the model’s total prediction error by considering the parameter’s overall effect on model behavior. They correspond to the union of the set of parameters obtained in subset selection ) and total sensitivity techniques ). In this work, this selection is defined according to the following criteria.Parameters from the subset selection ranking are chosen according to the criterion defined in Equation (4), considering rocedure .Parameters from the total sensitivity ranking are chosen in descending order until at least one is obtained for each system and controller of the model, including those already selected in the previous step.Selection for a Specific Fitting ApproachIt corresponds to the set of parameters for each variable’s highest sensitivity at the individual level. Its optimization aims to modify each variable’s predictability to bring it closer to the respective experimental data without significantly affecting the other predictions. It is based on relative sensitivity measures independent of the stimulus level (Equation (15)). Based on the following criteria, only one parameter is selected by each ranking obtained for the evaluated physiological variables.Remove the parameters selected for the base fitting approach from each variable ranking.Remove the parameters of systems and controllers that are not directly related to regulating the variable of interest.Select only those parameters whose sensitivity is high for the variable of interest and low for the remaining ones. Parameters with high sensitivity for other variables could be selected if those variables belong to or are dependent on the same system or controller of the variable of interest.Selection for the Stimulus-Related Fitting ApproachThis corresponds to the parameter selection criteria that relate the stimulus to the regulation mechanisms addressed in the model under study. Their selection is based on the parameters’ role concerning the mechanisms mainly associated with the stimulus, highlighting the weighting factors or gains that link them to regulatory activities.Eight mechanisms directly related to the exercise stimulus were evaluated in this work. Only one parameter per mechanism was selected.Fitting a parametric model involves solving an optimization problem in which the values of the set of parameters minimizing the differences between experimental data and model predictions are identified . The ideStandardization of Simulation ConditionsIts objective is to bring the simulation conditions close to the data used as a fitting reference. To do this, it proposes modifying some model parameters using the values obtained from the experimental data. It replaces the selected parameters’ values with the direct equivalences or results of applying previously validated equations. Its implementation has been previously presented in works on the design and fitting of physiological models, e.g., for the estimation of blood volumes and mechanical characteristics of cardiovascular and respiratory systems ,34,35. IOptimization AlgorithmDifferent optimization algorithms reported could be applied for the fitting of physiological models. They are divided into those that use deterministic or stochastic methods. Their correct selection depends on the model’s specific characteristics under study and the validation requirements ,36.In this paper, an evolutionary strategy with a covariance matrix and adaptation (CMA-ES) was selected. It is a stochastic global optimization algorithm based on adaptive and evolutionary strategies . This alParameterization of the Optimization AlgorithmThis corresponds to the parameter assignment of the selected optimization algorithm. It is generally related to the number of evaluations, iterations, and error tolerances. These parameters are specific to the algorithm and must be defined based on the fitting’s strictness and computational cost.The parameter values used for implementing the CMA-ES algorithm are presented in Evaluation Ranges of the ParametersThe optimization algorithms seek to identify model parameters through strategic variations of their values. The variation ranges should depend on the parameter’s specific function concerning the associated model mechanism since not all possible values provide a consistent result. For physiological models, in addition to obtaining predictions close to experimental data, it is desirable to find optimized values that reflect consistent physiological conditions or characteristics, further constraining the optimization problem .Determine an initial variation range for each parameter in proportion to its nominal value. The range bounds depend on the expected closeness between the optimized and nominal values. Such closeness can be estimated overall by considering the parameter’s relationship with the condition for which its nominal value was defined and the nature of the experimental dataset for which it is intended to optimize, e.g., variation of respiratory mechanics parameters during rest and exercise . The varEvaluate the values’ constraints from the equations describing the model mechanisms associated with each parameter and redefine the previously established bounds.Redefine the variation range’s bounds if the reported information relates the parameter to the experimental conditions. Since not all model parameters are directly related to physiological measures, i.e., those from empirical equations that have been fitted to experimental data, evaluating their variations considering different works in which it has been used is necessary.According to the above, this work proposes the following criteria to determine the evaluation range for each selected parameter:Performance EvaluationIt uses a metric that compares the model’s predictions with the experimental data. The optimization algorithm uses this measure as a criterion function to identify the goodness of fit of the model predictions for each parameter’s optimization. Different metric options have been applied in several works related to physiological models. However, the most commonly used is based on the root mean square error (RMSE) ,12,33, aThis paper modified the RMSE metric to consider all analyzed variables at different stimulus levels, as expressed in Equation (23).The error between predictions and experimental data is initially computed by obtaining a dimensionless measurement of each variable’s difference at each stimulus level. Subsequently, the standard 2-norm is calculated regarding stimulus levels to measure each variable’s mean trend. Finally, the global error is calculated as the mean value of every variable’s errors.Fitting StagesThis work proposes fitting the model using three approaches. They involve those presented in the parameter selection procedure’s subsections and represent stages sequentially applied to obtain a complete fit of the case study model. In one stage, the previously fitted parameters remained fixed, and only those selected for the current one are optimized.The first stage corresponds to a base fitting approach. It optimizes the parameters with the highest total sensitivity, whose variations have the most significant overall impact on the controllers and system outputs.The second stage corresponds to a specific fitting approach. Each variable comprises the parameters’ optimization with the highest relative sensitivity and the least side effect for the remaining variables. This is focused on minimizing the prediction error of each variable individually.The third stage involves a model mechanisms’ fitting approach. It optimizes the mechanisms’ parameters, mainly associated with the evaluated stimulus, to improve the predictions’ behavior.This procedure assesses the model predictions under conditions and disturbances that match the experimental data. Although there is no consensus on a defined validation methodology for mathematical models of physiological systems, most of the evaluations described in related works generally coincide with the criteria proposed in . TherefoDifferent metrics can be used to evaluate the performance of a model in steady-state conditions, highlighting mean absolute error (MAE) and RMSE as the most common ones. Their selection must be related to the critical interpretation of the results and the statistical distribution of errors. However, there is no consensus on which of these is most appropriate ,40. In tThe PE measurement was selected because (a) it corresponds to the PE measure used in the structural evaluation work of the case study model , (b) it Regarding dynamic transitions, changes in magnitude and response speed are usually implemented to evaluate predictions under stimulus changes ,17,18. DThe cardiorespiratory model follows a multi-compartmental structure comprised of subsystems for cardiovascular circulation, respiratory mechanics and gas exchange processes, and controllers that allow cardiac and respiratory self-regulation. It results from adapting different published models to achieve a model that can correctly mimic the main cardiorespiratory variables of a healthy adult under incremental aerobic exercise. Its development, nominal parameter values, and complete description of mechanisms are not reported here for brevity. The reader can refer to the previous paper for full details .The cardiovascular system includes systemic circulation, pulmonary circulation, and the heart. Systemic circulation is divided into large arteries, peripheral and venous vessels, and the vena cava. Pulmonary circulation involves the pulmonary arteries, peripheral vessels, and veins. The heart differentiates elements of the left and right compartments, where the atriums are modeled as passive compliance and the ventricles’ activity as a variable-elastance model. Changes in the pressures, resistances, blood flows, and blood volumes of the different vascular beds are regulated in response to cardiovascular regulation and exercise stimulus.The cardiovascular control response is initially mediated by the activity of afferent pathways , the blood flow local control, the central nervous system to acute ischemic conditions, the central respiratory neuromuscular drive, and the mechanism of the central command . The efferent pathways modulate their actions as sympathetic and parasympathetic activities. Subsequently, these results, together with the central command response  is assumed to be equal to Tc) and the period of the muscular contraction-relaxation cycle (Tim) are parameters related to muscle contraction times involved in systemic circulatory activity and characterize different physical activity protocols. Other parameters can also be used to characterize the population or the subject whose cardiorespiratory system tries to be simulated, highlighting the anaerobic threshold (AT) and basal respiratory tidal volume (VTn) for the exercise stimulus.The model has different parameters that can be configured as inputs to simulate a healthy human subject’s response with specific characteristics under several stimuli, e.g., at different levels of aerobic exercise and environmental conditions. Carbon dioxide output ). The model predictions were obtained under simulated variations of Transient SimulationThe experimental data dynamic responses of the first exercise phase load step were compared with the simulation results under equivalent variations of Descriptions of the model parameters are presented in this section in order to elucidate their selection according to the different fitting approaches. The reader can see the model equations in the The cardiorespiratory model has 316 parameters  distributed according to the proposed classification presented in Only the parameters with the role of covariates, gain, and thresholds were considered for the model fitting. Among gains and thresholds, the maximal abdominal pressure parameter  is associated with the error contribution of the related variables .After applying the selection criteria, the number of parameters considered for this fitting procedure was reduced by 97.4%. The selected parameters, the corresponding model equations and mechanisms, and the possible variation range information are presented below.r system . Its nomr system ,22,47,48r system . Consideented in  concernin tissue  and alloeen used ,21,22,45een used ,49,50,51ervation . It is ttal data ,52. It htal data ,22,47,48pressure . It relapressure , a nominsubjects . Followiorted in ,53 for hexpected ,21,50,54ntroller . These pntroller ,21,22,55The results highlighted that not all the parameters selected for each variable corresponded to the first ranking positions, which shows the significant influence of the regulation results between the model’s different systems and controllers. This fact was presented mainly for variables not directly related to the controllers  . FollowiPmusc(t) ,33, a vad oxygen . Its nomd oxygen  and calcd oxygen , allowin and Qpp . It denothe lung ,50,51,63For this approach, the selected parameters relate to each of the eight mechanisms reported for the case study model . Only ontal data . No paraThe selected parameters, their corresponding mechanisms, and regulatory activity are presented in The related mechanisms and the information reported on the possible variation range of each selected parameter are presented below.mized in  to ensurmized in ,22. to 1 in  under thrding to ,20,33, aA general evaluation range of ±30% regarding the nominal value was defined for those selected parameters whose variation could not be established or constrained to reported values in the literature. For that, the following considerations were taken into account: (a) it is suitable for the constrictions of each associated mechanism of the model, and (b) it agrees with the expected closeness of the results for the nominal values. It was also considered that these parameter values are related to subjects with physiological characteristics similar to the subject’s experimental data . The evaluation ranges for the other parameters are presented in It should be noted that most of the selected parameters were adapted to the defined general evaluation range; the remaining ones were mainly related to the increase of either lower or upper bounds. Only For the Stimulus-related fitting approach, the following results were obtained: (a) a decrease of the sympathetic activity related to the regulation of peripheral resistances and heart elastances and an increase for the sympathetic activity for venous volumes due to the modifications in The steady-state results confirm the overall improvement of the model predictions after the fitting stages. The base fitting stage improves respiratory variables and gas exchange predictions during rest and exercise. Similar behaviors as nominal results are observed, but with an offset change, wherein the model results are closer to the experimental data’s mean trend. The predictions of cardiovascular variables showed only an improvement in PS. The model’s specific fitting improves most respiratory and cardiovascular predictions, evidencing behavior modifications under the stimulus’s increase concerning the base fitting results.The PE results confirm the steady-state predictions’ observations. The highest errors are obtained under nominal conditions, and the last fitting stage reduces the overall PE by 21.9%. The most significant PE value changes are presented for the predictions of respiratory variables and systemic blood pressure measurements, with statistically significant differences for In general, a significant decrease in PE was found at each fitting stage. Slight adverse effects were evidenced at the base and stimulus-related fitting approaches. Improvements associated with cardiovascular variables were mainly obtained in the last fitting stage. They were related to the effects of exercise mechanisms on systemic arterial pressures. The most significant results for gas exchange predictions were obtained after the model’s base fitting. The other stages do not present significant variations in PE, as The simulation results do not present significant variations for the different fitting stages, consistent with the proposed fitting strategies focused on predictions in the steady state. As part of the validation strategy, it is shown that the predictions had consistent behaviors regarding the dynamic response of the experimental data, mainly highlighting the similarity for HR and This work presents a methodology focused on selecting reduced sets of model parameters that can be reliably fitted in steady-state conditions following several classification approaches. The methodology is based on applying complementary and sequential techniques of parameter classification that evaluate criteria, such as the role in the model, identifiability, and sensitivity to its variation. It involves modifications to reported techniques that evaluate different stimulus levels, imply variations in the parameter values, and consider the experimental data by evaluating the error contribution.The parameters’ role classification initially constrained those parameters that should be considered for subsequent selection and fitting procedures. Five role classification groups of the parameters most commonly found in mathematical models of physiological systems were proposed. They were based on time constants, conversion parameters, covariates, initial values, and gain and thresholds that facilitated the case study model’s parameter selection.The parameter identifiability classification was based on Jacobian matrix analysis, which focused on determining which parameters can be reliably fit from available experimental data. Different stimulus levels were evaluated, considering their effects on the model’s prediction behavior. The first three parameters, classified as most identifiable for the case study, were selected a. Each oParameter sensitivity analysis is based on finite difference measurements. It evaluates model variable predictions in steady-state conditions under parameter variations and different stimulus levels. In particular, steady-state conditions allowed considering variable magnitude changes instead of changes to temporary lags among simulated variables, mainly observable in variables with oscillating dynamic behaviors such as  ranking b, consid ranking . For the systems h,i.Parameter selection based on the parameter’s classification according to their role in the model allowed a significant reduction of the complexity associated with subsequent selection and fitting procedures, mainly evidenced by the computational cost involved in the simulations. Its correct application depends on the model mechanisms’ knowledge, its parameters, and the conditions to be simulated because some parameter variations may not be adequate or relevant for the stimulus, environmental conditions, and population features to be represented. Only parameters related to the response in magnitude were selected in this work, which is consistent with the model predictions in steady state and allowed to reduce the PEs in the fitting stages . In applThe procedure results based on the base fitting approach were mainly related to the respiratory system parameters and controller parameters, which is coherent considering that the model predictions under nominal conditions provide the highest PE values . The modParameter selection based on the specific fitting approach was proposed to obtain optimal results focused on decreasing the PE values for each variable without negatively affecting the rest of the predictions, as usually happens under the traditional fitting approach. For the case study model predictions, a single parameter per variable was chosen based on its relative sensitivities . Most ofng stage .Parameter optimization under the stimulus-related fitting approach aims to improve the behavior of predictions. This procedure is justified for the case study, considering that although the model was previously evaluated , the mecThe fitting procedure was proposed as a sequential application of three stages based on different approaches that improved the model’s prediction capacity. The order of the stages was selected considering, firstly, reducing the overall PE, bringing the general trends of simulation results and experimental data closer; secondly, decreasing specific PEs with the least possible adverse effect between predictions; and finally, improving the behavior of the predictions regarding the stimulus. The stages’ results are related to the modification of the values of the selected parameters for each one, considering the constriction of the evaluation ranges for optimization according to the function in the model and the physiological sense  the relationship between the quantity and variety of experimental measures available regarding the number of parameters of the model to be fitted; (b) the model’s capacity to mimic the behaviors of the experimental data; and (c) proper knowledge of the physiological system and the mechanisms of the model. The lack of any of these aspects will constitute a limitation in the application of the strategy, and its consequences will be evident in the poor results of applying the procedures and techniques that compose the approach. A constrained number of experimental variables or a low relationship between them and the model parameters would affect the parameter classification techniques, obtaining low and similar sensitivity values and the different optimization stages, and encouraging multiple identification solutions. The inappropriate choice of a physiological model to represent the experimental data will impact the optimization stages, leading to a lack of precision and accuracy of the results in the validation. Finally, the lack of knowledge about physiological systems and the different mechanisms associated with the model will affect the proper classification, selection, and constraint of parameter values.Due to the improvement of the prediction capacity and the adequate validation results of the cardiorespiratory model of the case study, both the model and the proposed fitting and validation strategy could be implemented in future works related to diagnostic applications, including athlete evaluation studies, detection of cardiorespiratory diseases, and simulation of the cardiorespiratory response under therapeutic treatments. Furthermore, the application of this strategy regarding experimental data from longitudinal records over time could be considered the basis for developing a dynamic fitting strategy. In this sense, the information obtained from the role, sensitivity, evaluation ranges, and parameter optimization at each instant in time could be used to analyze the temporal evolution of physiological system parameters and predict their future value.The implementation of the proposed strategy mainly involves the development and execution of software based on data storage and processing. The storage corresponds to the digital recording of the data of physiological variables in databases. At the same time, the processing includes the execution of code and algorithms related to the mathematical model of the physiological system under study and the techniques, stages, and procedures defined by the strategy. The recording of physiological measurements and signals will involve the use of applications that concentrate data from different possible sources, such as personal health devices, laboratory equipment, or medical equipment from clinical environments. The execution of the processing software should be semi-supervised, considering the importance of knowledge of the physiological system and its mathematical model, although in future works, training based on artificial intelligence could be evaluated to fully automate the process. New findings, such as model improvements, new parameter classification techniques, optimization, or validation criteria, can be incorporated into the strategy as long as the order described in each main procedure is considered. The results obtained must be interpreted by medical staff and can support clinical decisions regarding diagnosis and health monitoring.This paper presents a strategy for fitting and validating physiological models with a large number of parameters under the consideration of different populations and stimuli. The strategy consists of different procedures and techniques that improve the model’s prediction capacity, considering the complexity reduction of the optimization problem, the results of parameter values with physiological justification, and minimization of the possibility of multiple fitting solutions.The validation results demonstrate that the case study model is adequate for predicting the cardiorespiratory response of healthy adult subjects under rest and aerobic exercise conditions with reasonable precision and accuracy. This model can constitute an analysis and diagnostic tool related to studies and evaluations of the cardiorespiratory system.


This paper first measures and compares the size of middle-income groups in China based on the subjective income evaluation method and the objective criteria. Second, it empirically investigates the differences in government trust of different income groups defined by the subjective evaluation method and the objective criteria. It is found that there is a significant difference between the results of the subjective evaluation of income and objective criteria. Compared with individuals in the middle-income group, individuals in the low-income group have a significantly worse overall evaluation of local government and a considerably lower trust in local government officials. On the other hand, individuals in the high-income group have a substantially better assessment of local government and a significantly higher trust in local government officials. However, the differences in trust in government across income groups defined by objective criteria are insignificant overall. In terms of policy insights, the effect of targeting low-income groups determined by subjective evaluation may be more effective in improving people’s trust in the government. In the 1970s and 1980s, the economy of developed countries fell into “stagflation.” Traditionally, most studies have used objective criteria to define middle-income groups, but there is no consensus on whether absolute, relative, or mixed criteria should be chosen and what interval should be selected for a particular criterion. Based on the reality of China, limited and inaccurate income statistics remain challenges in the selection of objective criteria. In rural and some underdeveloped areas of China, cash and in-kind economies are prevalent, informal employment is common, income information systems are missing, and household surveys are costly and low-quality . ChineseUnlike objective criteria, subjective evaluations of socioeconomic status do not rely on specifically defined intervals, do not require income surveys, are simple to operate, and can be experimentally manipulated.In this paper, first, based on the subjective income evaluation method and the objective criteria method, the size of middle-income groups in China is measured and compared. Second, we follow the classical hypothesis and research on social class theory on the existence of discontinuous social “class fragments” and the differences in lifestyles, social cognition, political attitudes and political participation of members of different social classes in 2.Traditionally, most studies have used objective criteria to define middle-income groups, but there is no consensus on whether absolute, relative, or mixed criteria should be chosen, and what measurement interval should be chosen under a particular criterion. Among them, developed countries more often choose relative or mixed criteria to define middle-income groups. For example, developed countries widely use the 75–125% median income range and 75–150% range as the criteria for determining the middle-income group . Some stThe absolute criteria mainly reflect the size of the population in a specific income range and its proportion, which is more suitable for developing or low- and middle-income countries. They can be used to explore the benefits of economic development for different income groups in these countries. It is also suitable for international comparative analysis, comparing the speed of economic development of different countries and the benefits of different economic development models. The relative criterion mainly reflects the size of the population with income in a specific quantile range and its proportion, which is more suitable for developed countries, where the level of economic development is higher and the size of middle-income groups accounts for a larger proportion of the population. Moreover, the relative criterion can explore the changes in the size of different groups brought about by fluctuations in income distribution in these countries.per capita household disposable income of 20,000–67,000 yuan, per capita annual household income of 35,000–120,000 yuan, and annual household income of 69,000–236,000 yuan, respectively, as the criteria for defining middle-income groups. In terms of the relative criteria, The criteria for defining China’s middle-income group are based on the fact that China has entered the ranks of middle-income countries with the dual characteristics of a growing and improving society. Hence, both the goal of moving toward a high-income country and the goal of achieving common prosperity should be considered. It is relevant to measure the size of China’s middle-income group, both in absolute and relative terms . In the The measurement results of the size of middle-income groups vary greatly depending on the choice of the objective criteria . And theWhile reflecting on the shortcomings of the objective criteria definition method, researchers seek other alternative or complementary methods. Drawing on the psychology of social class (PSG) findings, subjective methods of socioeconomic status evaluation have recently emerged in the field of social group-related research .The subjective evaluation method is a general evaluation of the individual’s relative position in the social hierarchy in terms of income level and social status with reference to others . CompareThe subjective assessment of socioeconomic status is simple and easy to administer, but its validity has been widely questioned. Typical questions include, first, whether individuals can identify their position on the “social ladder,” as measured by the MacArthur Subjective Social Class Scale, for example. If respondents are unable to identify their position on the “social ladder,” the dilemma faced by the subjective assessment method coincides with the shortcomings of objective criteria. Although subjective evaluation methods do not presuppose benchmarks to define different social classes or economic status, researchers can adopt contextualization strategies to guide respondents to reflect on and revise their internalized criteria. They can even manipulate the frame of reference so that respondents can make more precise assessments of their economic and social status . Second,In this research, we follow the hypothesis and research on on social class theory in However, many empirical studies have found differences between the subjective evaluation methods and objective criteria in different “scenarios.” For example, The existing research does not judge the merits of the subjective evaluation method and the objective criteria. The objective criteria have their inherent defects. The subjective evaluation method can partially overcome the weaknesses of the objective standard and is relatively simple and easy to implement. Differences in factors such as diversity, environment, and culture, as well as differences in the selection of reference objects, may lead to hidden limitations and risks in the subjective evaluation results of socioeconomic status. Following There is a vast literature on government trust. In summary, the main research objectives of this paper include the following. First, we compare the differences between subjective evaluation methods and objective criteria based on measuring the size of middle-income groups. Second, based on the study of government trust in different income groups, we compare the differences in government trust in different income groups defined by subjective evaluation methods and objective criteria. Third, we test the validity of the results of the two methods in assessing government trust. Fourth, based on the possible shortcomings of subjective criteria, the stability and validity of the subjective evaluation results are examined, and the robustness of government trust in different income groups is tested.3.3.1.This paper conducts an empirical study using data from the China Family Panel Studies (CFPS) 2018, a national, comprehensive social tracking survey project that aims to reflect social, economic, demographic, educational, and health changes in China by tracking and collecting data at three levels: individual, household, and community.3.2.per capita household income  with objective criteria (measured by income) measures.At the same time, the study shows that there is only a weak positive correlation between the subjective evaluation of income and the objective criteria. In particular, the correlation coefficient between the subjective evaluation of income and the relative standard measure results was 0.0265, and the correlation coefficient with the absolute standard measure results was 0.0459. Still, both were significant at the 1% significance level. The findings are similar to those of 4.The survey of respondents’ trust in government in the CFPS project was implemented through the following question “Your overall evaluation of the work of government in your county or county city/district last year was: 1. had a great achievement, 2. had some achievement, 3. did not have much achievement, 4. had no achievement, and 5. was worse than before.” In this paper, we construct a ranking model for empirical study, and the explanatory variables are individuals’ overall evaluation of the work of local government .The main explanatory variables are different income groups  defined according to the subjective evaluation of individual income and objective criteria, respectively. The selection of control variables draws on studies such as Combining the regression results in Second, there is no significant difference in the overall evaluation of local governments by different income groups defined according to relative criteria. Compared to the middle-income group, the overall evaluation of local governments by the low-income group defined by absolute criteria is significantly worse. The overall evaluation of local governments by the high-income group is not significantly different from that of the middle-income group.Third, the effect of individual other explanatory variables on the overall evaluation of local government is generally stable. Compared with females, males have a worse overall evaluation of local government. The relationship between an individual’s age and their overall evaluation of local government is “U” shaped, i.e., as an individual grows older, their overall evaluation of local government gradually becomes worse, and then gradually becomes better after reaching a certain age. Individuals with higher education levels have a significantly better overall evaluation of local government. Individuals with poorer health status also rated local governments worse overall. Married individuals rated local government worse overall compared to unmarried individuals. Individuals who are members of organizations such as the Communist Party, trade unions, religious faith associations, and individuals’ associations all have a better overall evaluation of local government. Individuals rated local governments poorly overall if they used mobile devices to access information online. They rated local governments better overall if they used computers to access information online or watched television for a more extended time each day. Compared to the Eastern region, individuals in the Northeastern region rated the local government less favorably overall. In contrast, individuals in the rural areas rated the local government more favorably overall compared to the urban areas.In summary, if the overall evaluation of local government is used as a measure of government trust, there are significant differences in government trust among different income groups defined based on subjective evaluation methods. However, the differences in government trust among different income groups defined based on objective criteria are generally insignificant.5.5.1.Although the subjective evaluation method of socioeconomic status is simple and easy to implement, its validity and stability need to be double-checked. For example, respondents’ emotions or emotional factors may affect the subjective evaluation results. In this paper, it is also necessary to test the stability and reliability of the subjective evaluation results.The CFPS project also included a survey on respondents’ self-assessment of their social status “On a scale of 1 for very low and 5 for very high, how would you rate your social status in your local area?” Logically, if a respondent scores high on the subjective assessment of income, he or she should also score high on the subjective assessment of social status. We matched respondents’ income subjective evaluation scores with their social status subjective evaluation scores , and we 5.2.As argued by We construct an empirical study using respondents’ trust in local government officials as the explanatory variable and construct a ranking model to test the robustness of government trust and influencing factors across income groups. At the same time, there may be endogeneity problems caused by omitted variables and other factors influencing government trust in the empirical study. We exclude the sample with only one family member and construct a household fixed effects model to conduct an empirical study to partially overcome the possible endogeneity problem and test the robustness of government trust and influencing factors across income groups.Comparing the results in 6.This paper measures and compares the size of middle-income groups in China based on the subjective evaluation of income and the objective criteria using survey data from the China Household Tracking Survey Project 2018. Furthermore, the differences in government trust of different income groups defined by subjective evaluation and the objective criteria are examined. Synthesizing the research in this paper, we have the following major findings.First, there are considerable differences between the results of the subjective evaluation of income and objective criteria. There is only a weak positive correlation between the two. In practice, although the choice of the objective criteria for defining middle-income groups is controversial or even flawed, if the established criteria are determined, the results mainly depend on the location of individual income (absolute or relative income level) in the overall income distribution. As argued in the binary structure theory of social class constructed by The findings of this paper are similar to those of Class status identification bias is more prevalent in China than in developed countries. For example, Second, relative to the objective criteria, there is a more significant association between the subjective evaluation of income and trust in government. If the overall evaluation of local government or trust in local government officials is used as a measure of trust in government, there are significant differences in trust in government among different income groups defined based on the subjective evaluation methods. Individuals in the higher income group have a significantly better overall evaluation of local government and a considerably higher trust in local government officials. However, the differences in trust in government among different income groups defined based on the objective criteria are insignificant overall. The above findings are similar to those of There is a paucity of research on the differences in trust in government across income groups as defined by subjective assessments of socioeconomic status and objective standard measures in China. However, related studies on other topics in China have yielded similar findings to this paper. For example, In practice, the objective criteria for defining middle-income groups are still widely debated in both developed and developing countries, and the choice of objective criteria faces even more difficulties based on the realities of China. The different objectives criteria may lead to the dilemma of ambiguity in the objectives of policies to expand the middle-income group. Moreover, the perceived socioeconomic status of individuals may be a key factor guiding their behavior. When the results of objective criteria  are not consistent with the subjective evaluation of individuals’ socioeconomic status (perception), the “label” of the group defined by objective criteria may lose its meaning. That is, the effectiveness of policies targeting the group defined by objective criteria may be greatly reduced. Of course, the subjective evaluation method can overcome the defects of objective criteria and is relatively simple and easy to implement, but it also has inherent defects or shortcomings. This paper argues that the subjective evaluation methods can be considered as a supplement or alternative to the objective criteria for defining middle-income groups in China. This is true especially when the objective criteria are difficult to determine or are highly controversial. The research in this paper provides a major policy insight. That is, to improve people’s trust in the government, there may be a dilemma in targeting different income groups defined by the objective criteria.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.This paper is supported by the China National Social Science Foundation’s project “Research on the size measurement and influence mechanism of middle-income group” (Project #: 17BJY042).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. 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Background and Objectives: Cultural beliefs influence the conceptualization, adaptation, and coping strategies for diseases. This study aimed to investigate the impact of cultural beliefs and customs on the willingness to undergo cataract surgery in Taiwan. Materials and Methods: The data were retrospectively retrieved from the national Longitudinal Health Insurance Database 2000 (LHID2000). From the national database, we enrolled patients that were diagnosed with cataracts and underwent cataract surgery from 2001 to 2010. All the patients were stratified according to their gender and living area. Gender was categorized as male or female, and the living area was classified as urban or rural. We compared the difference in the number of surgeries between stratified patient groups in each Chinese lunar month. Results: The number of cataract surgeries decreased significantly in the seventh and twelfth lunar months for both genders. There was a significant reduction in cataract surgeries in both the urban and rural groups during the seventh lunar month. Interestingly, only the seventh lunar month had an association with sex in different living areas, which meant that in the seventh month, there was a gender-specific difference in the surgical numbers. Conclusions: The Taiwanese population holds a belief that surgical procedures, including cataract surgery, during the lunar ghost month is inauspicious. Citizens tend to avoid elective surgery due to cultural practice, resulting in a decrease in surgical numbers during the period of the Chinese New Year. The authorities should consider these cultural behaviors when developing medical policies and allocating resources. Healthcare providers should be aware of these superstitions and take them into account when providing medical care and advice to patients. The impact of cultural beliefs on healthcare-seeking behavior has been documented in various studies all around the world. For instance, studies have shown that cultural beliefs and attitudes toward illness affect the decision to seek healthcare, the type of treatment preferred, and the level of trust in healthcare providers ,3,4,5,6.The Chinese lunar calendar and festivals have a significant influence on Asian cultures, not just in China, but also in other countries with sizable Chinese populations such as Taiwan, Hong Kong, Singapore, and Malaysia. The Chinese lunar year begins with the first new moon of the lunar calendar, usually in late January or early February. Each lunar month is associated with various cultures, festivals, and traditional beliefs, which are deeply rooted in Chinese culture. Among all the Chinese festivals, in Taiwan, Chinese New Year, the Qingming Festival , Moon Festival, and Mid-Autumn Festival are the most important ones. Due to traditional customs, national holidays are usually observed during these festivals, with five days for Chinese New Year and one day for the others. The period from the end of the twelfth lunar month to the next new lunar year is the most significant festival in Chinese culture. This time, also known as “Chinese New Year” or the “Spring Festival,” is a time of family gathering, celebration, and joy. The celebrations last for days and include various traditional customs and activities, such as worshiping the ancestors, giving red envelopes with money in to children, and preparing and enjoying traditional foods. People used to be blessed but busy in this period, due to lots of kinds of customs activities.In contrast, the seventh lunar month is known as the “Ghost Month”, when it is believed that the spirits of the dead return to the world of the living. During this month, there is no specific national holiday. Many Chinese people avoid making important decisions, getting married, or undergoing surgery because of the belief that it is an inauspicious time. It is similar to “Friday the 13th” in the United States.In this study, we examined the relationship between cultural beliefs and medical decision-making by analyzing the association of the Chinese lunar months on the number of cataract surgeries performed in Taiwan. Cataract surgery was chosen as the index of procedure as it is typically an elective procedure that is not affected by seasonal or weather-related factors. In Taiwan, cataract surgery is covered by the national health insurance by the government and there is no difference in the offers from health facilities each month. In addition, the decision to undergo cataract surgery is typically based on the degree of visual impairment and its impact on the patient’s quality of life. Modern cataract surgery is performed as an outpatient under local anesthesia and used to take less than half an hour. Cataract operations make up most ophthalmic surgery cases and are readily available in Taiwan ,8,9,10. This is a retrospective study, designed as a population-based review using the national Longitudinal Health Insurance Database 2000 (LHID2000). The LHID2000 is a valuable resource for conducting population-based studies in Taiwan, as it provides a representative sample of the population and allows for the investigation of various health conditions and interventions. The data contained in LHID2000 are randomly selected from a million subjects from Taiwan’s National Health Insurance Research Database (NHIRD) and made available for research purposes. Both the LHID2000 and NHIRD contain a lot of computerized records, including registration files, medication and treatment regimens, and information on surgery, which are provided to researchers in an electronically encrypted form. We officially obtained approval for the data obtained from the LHID2000. From the database, we collected the patients’ identification numbers, gender, diagnostic codes, operative procedure codes, dates for the operative procedure, and living areas. The diagnostic codes for the diseases are defined by the International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9-CM366) and the surgical procedure codes are defined according to the International Classification of Diseases operative procedure code (ICD-OP). The study was approved by the Institutional Review Board of Changhua Christian Hospital and all the research was performed in accordance with the relevant guidelines and regulations. This study was conducted in accordance with the Declaration of Helsinki and other relevant ethical guidelines.We enrolled patients with a diagnosis of cataracts, who underwent cataract surgery from 2001 to 2010. The number of cataract surgeries was counted according to the lunar months. To investigate whether gender and living area had any association on the frequency of cataract surgeries during different lunar months, the patients were stratified based on these two variables. Gender was categorized as male or female, and living area was classified as urban or rural. This allowed for more in-depth analysis of the potential factors influencing the frequency of cataract surgery during different lunar months.p value of <0.05 was considered to indicate statistical significance, and all tests were two-tailed.The statistical analysis was performed using SPSS software, version 23.5. We used the Wilcoxon signed rank test to compare the number of surgeries in each month vertically in all patients and each stratified group. The Mann–Whitney U tests and the Kruskal–Wallis test were applied to analyze differences in the frequency of cataract surgeries in stratified groups during different lunar months. Furthermore, we also utilized heterogeneous AR (1), a linear mixed model with a covariance structure, for the longitudinal data to investigate the differences in the frequency of cataract surgeries in the stratified groups during different lunar months. As the numbers of surgeries in conjoint lunar months were correlated, and the variance in each lunar month may be different, the covariance was set as heterogeneous AR (1) in the linear mixed model. The F statistic was used to test whether two or more means were equal. A p < 0.001; twelfth lunar month: mean = 64.00 ± 24.50, p < 0.001). This finding suggests that the lunar calendar might influence the frequency of cataract surgeries in Taiwan, with fewer surgeries occurring during certain months of the year. Additionally, gender was found to be a significant factor in the frequency of cataract surgeries. Women underwent significantly more cataract surgeries than men in all lunar months, except for the seventh and twelfth months .The average number of cataract surgeries in different lunar months from 2001 to 2010 are illustrated in p < 0.001) (p < 0.01), with the exception of the 12th month in females .When analyzing the association of the living environment on cataract surgery, only in the seventh lunar month was there a significant difference between urban and rural areas. In the seventh lunar month, the number of cataract surgeries in the rural area was much lower than in the urban areas (< 0.001) . We alsop < 0.001, rural p < 0.001); however, the interaction of gender with the twelfth lunar month was not significant . The above finding revealed that in the seventh month, there was a gender-specific difference in the surgical numbers.In the mixed model analysis, we chose the 1st, 7th, and 12th lunar months for comparison with the other lunar months due to the 1st and 12th lunar months representing the Chinese New Year and the 7th representing ghost month. From the results in Our study highlights the significant association of cultural behavior on medical decisions, even for relatively safe and quick outpatient surgeries, such as cataract surgery. We found a significant reduction in the number of cataract surgeries during the Chinese seventh and twelfth months. It is worth noting that the population in Taiwan consists of more females than males, with a mean sex ratio of 96.51 from 2001 to 2010, according to official data from the Department of Household Registration in Taiwan. Furthermore, the Ministry of Interior of Taiwan reports that women have a longer life expectancy than men. The average life expectancy for women in Taiwan increased from 78.1 years in 2001 to 80.8 years in 2010, while men’s average life expectancy increased from 72.7 years in 2001 to 76.2 years in 2010. The above demographic factors might have contributed to the higher number of cataract surgeries in women.Cultural beliefs influence the conceptualization, adaptation, and coping strategies for diseases . The infIn southern China, Hong Kong, and Taiwan, the seventh lunar month is known as the “Chinese Lunar Ghost Month” or “Hungry Ghost Festival”. During this month, it is believed that the gates of the afterlife are opened, and the spirits of the dead return to the living world. The lunar ghost month is believed to be a time of heightened spiritual activity. The cultural belief is that during the lunar ghost month, the world is filled with wandering spirits, and the spirits can cause accidents, unfortunate events, or harm to people. As a result, many people in Taiwan avoid certain activities during this time, including swimming, getting married, moving into a new house, starting a new business, and may postpone major surgical procedures until the end of this month ,12,13. WIn addition to the ghost month, the number of surgeries for cataracts was also reduced in the twelfth lunar month. This might be due to another custom. The twelfth lunar month is followed by Chinese New Year. It is a time for family gatherings, feasting, and celebrating the start of a new year. People believe that the New Year will bring good luck and that they cannot be absent from this festival. Patients may also be concerned about post-surgical recovery during a time when they would prefer to be spending time with their family and participating in festive activities. As a result, the turn-of-the-year effect also makes the Taiwanese avoid elective surgery due to the festive atmosphere and desire to spend time with family. The result was also similar to the one which Dr. Chiu reported . All of The present study makes an important contribution to the existing literature by, firstly, exploring the relationships between sociocultural factors and outpatient surgery using a population-based and nationwide database. The finding of this study shed light on the impact of sociocultural factors on healthcare behavior in Taiwan. The results demonstrate that cultural beliefs and taboos surrounding specific lunar months can significantly influence outpatient surgery rates, with a reduction in cataract surgeries during the seventh and twelfth lunar months. Interestingly, this effect was observed across both genders and in both urban and rural areas, highlighting the widespread influence of cultural beliefs on healthcare utilization in Taiwan. The gender-specific difference in surgical numbers during the seventh lunar month is particularly noteworthy, suggesting that certain cultural beliefs may be more ingrained in certain gender groups.The findings in our study are consistent with other research that indicates that cultural beliefs can have a significant association on medical decision making. To address these issues, healthcare providers can take several steps. One approach is to provide patient education, which can help increase awareness of the risks and benefits of various medical procedures and medications. This can also help patients understand the importance of adhering to their medical treatments and following recommended health behaviors. Moreover, building trust and understanding with patients and their families is also essential. This can involve taking the time to listen to their concerns, respecting their beliefs and cultural practices, and providing individualized care that takes into account their unique cultural backgrounds. By doing so, healthcare providers can better serve the needs of their patients and promote positive adherence and health outcomes, even during culturally sensitive times such as the lunar ghost month or Chinese New Year.The strength of this study is that we used a population-based and nationwide database, which provides a large and diverse sample of medical-seeking behavior in Taiwan. This allows for a more accurate reflection of the impact of cultural beliefs on medical decision making during particular Chinese lunar festivals and events. However, there are also some limitations to this study that need to be considered. Firstly, the data were obtained retrospectively. This can limit the scope of the analysis and make it difficult to draw definitive conclusions about the relationship between cultural beliefs and medical decision making during ghost months. Additionally, the data we collected lacked socioeconomic status and the level of knowledge of the participants. These factors could also play a role in medical decision making and may influence the observed results. Therefore, it is important to conduct further analysis to investigate the potential impact of these factors and to explore whether the observed reduction in surgeries during different lunar months is a true reflection of the impact of cultural beliefs. An advanced questionnaire for citizens and medical providers might be needed in the future. Further studies could also explore the potential impact of this reduction on surgical complication rates and patient outcomes.The belief that the lunar ghost month is inauspicious for major surgical procedures, including cataract surgery, is held among Taiwanese people. As a result, many Taiwanese may avoid elective surgery during this month. In the twelfth lunar month, the number of cataract surgeries also decreased. It might be related to the coming of the Chinese New Year. During this period, individuals tend to delay or avoid seeking medical treatments due to traditional customs and practices that are considered necessary, as well as the desire to spend time with family.The findings in this study emphasized the importance of cultural beliefs in medical decision making in Taiwan; therefore, it may be beneficial for the authorities to consider these factors when developing medical policies and allocating resources.


Circadian clocks are evolutionarily adaptive internal clocks that regulate cycles of activity, behavior, and physiological processes. In this study, we used the circadian (24 h) and circannual (across the year) rhythms of behavior of 13 zoo-housed giant pandas to understand their needs and assess welfare. We found that they show changes in the pattern and intensity of behavior cycles based on their life stage and sex. Their circadian activity patterns showed three peaks, like wild giant pandas, including a night-time peak. We found specific cycles of feeding anticipatory activity, sexual-related behavior, and stereotypical/abnormal behavior, which align with the timing of migration in wild giant pandas, and we therefore suggest that this may be how thwarted migration manifests itself in captivity. We also determined the cycles of maternal behaviors, including nursing, and proximity for a mother and cub, providing context to the development of a circadian rhythm in a cub and information on the way a mammalian mother’s circadian rhythm is disrupted during nursing. Overall, our study provides a holistic, evidence-based method that can be applied across captive environments so that staff can better understand the needs of their species and appropriately provide for them, promoting positive welfare and increasing the likelihood of successful breeding and conservation.Ailuropoda melanoleuca), across life stages and between sexes, each month for one year using live camera footage from six zoos across the world. Our results indicate that life stage was associated with changes in overall activity, feeding, locomotion, and pacing, and that sex influenced scent anointing and anogenital rubbing. Overall, the circadian rhythms showed three peaks of activity, including a nocturnal peak, as seen in wild giant pandas. We also found associations between sexual-related, stereotypical/abnormal, and feeding behavior, which are possibly linked to the timing of migration of wild pandas, and elucidated the relationship between a mother and cub, finding that they concentrate maternal behaviors to mainly after closing hours. Understanding these cycle patterns can aid animal care staff in predicting changing needs throughout the day, year, and life cycle and preemptively provide for those needs to best avoid welfare concerns.Circadian and circannual cycles of behavior regulate many aspects of welfare including metabolism, breeding, and behavioral interactions. In this study, we aim to demonstrate how systematically determining circadian and circannual cycles can provide insight into animals’ needs and be part of an evidence-based approach to welfare assessment. We measured and analyzed the observational behavioral data of 13 zoo-housed giant pandas ( Circadian rhythms have been recognized across the animal kingdom from birds, reptiles, mammals, amphibians, fishes, and arthropods, including insects ,2. The wAnimals exhibit life history trade-offs expressed through physiological and behavioral trade-offs to maximize energy and fitness . EnergetThe optimal foraging theory suggests that animals will choose the type of food, how much time is spent foraging and in which patches, and the speed at which to forage to maximize energy intake and minimize energy expenditure . HoweverAging increases the possibility of desynchrony because the circadian system ages, causing the decoupling of internal cell and/or tissue clocks and, consequently, overt rhythm changes ,24. HoweBreeding is a behavior that zoos monitor closely to improve conservation efforts; however, successful breeding has been notoriously difficult in some species. In addition, the ability to perform natural sexual behaviors is necessary for animals to feel sexually gratified, contributing to positive affective states ,26. SincIn captivity, sleep is not often monitored . Though Zugunruhe, from German, which translates to “migratory restlessness”. Captive migratory birds will display increased levels of activity and nocturnal migratory restlessness during periods that coincide with natural migratory behavior [Migration is a seasonal event that has been widely studied in wild and captive bird species. In migratory birds, migration is triggered by photoperiods of specific length depending on the season . In prepbehavior . The frebehavior . Therefobehavior . InvestiTwo of the main goals of reputable zoos are to promote positive welfare of their animals and to conserve species. We aim to investigate behaviors using a holistic approach that could provide insight into the animal’s needs and potential welfare states or provide information on the cycles of behavior that can inform husbandry practices. To demonstrate this holistic approach and to investigate the effects of life stage and sex on captive animal behavior, we investigate the circadian and circannual cycles of captive giant pandas, including a mother and cub pair as a case study. Giant pandas are seasonal breeders that mate between March and April . Giant pIn this study, we recorded the circadian cycles for one year for male and female captive giant pandas across life stages. We investigated the cycles of general activity and several more specific active behaviors including stereotypical/abnormal behaviors, sexual-related behaviors, and maternal behaviors. These cycles were then compared to each other to infer possible synergistic dynamics between them and to determine possible associations with migration. We hypothesize that life stage and sex have effects on the circadian cycles. Our study cannot determine causality, but providing a holistic view of giant panda behavior can give new insights on the needs of giant pandas and possibly reveal the husbandry and environmental factors that may promote the positive welfare states that zoos want to see in their animals.We received ethical approval for this study from the University of Stirling Animal Welfare Ethics Review Body . This study also received endorsement from the Association of Zoos and Aquariums, Giant Panda Species Survival Plan . In addition, we submitted research applications to all zoos involved and received approval from the participating zoos’ administrations. We also sent a voluntary questionnaire to keepers asking information on (1) panda identities, (2) cameras, (3) enclosure design, (4) artificial lighting, (5) feeding husbandry, and (6) mating behavior. Four zoos provided some or all of the requested information. The identifying data for the zoos and pandas are anonymized.The inclusion criterion for a giant panda was whether the panda was in a zoo that had a publicly accessible web camera or a surveillance system that we could be allowed to access. We selected 13 giant pandas  from six zoos . We idenBehavioral observations were completed using the ZooMonitor application . The ethData were collected through web cameras from December 2020 to November 2021 for all pandas except for the mother and cub. The mother was observed from December 2020 to March 2022, and her cub was observed from March 2021 to March 2022. The cub was aged 6 months when his observations began, providing an opportunity for a case study of how circadian rhythms develop in a cub. Focal sampling was completed for each giant panda using one 10 min sessions with 30 s intervals in each hour to gain an estimate of the behavior in that hour. Each month, data collection began on the 10th day and continued through the end of the month until one daylight or one 24 h cycle was recorded (dependent on the night vision of the camera) for each panda. Observations were performed in real time. Observers were assigned a maximum of 5 consecutive hours of observations, completing a maximum of three 10 min sessions with a minimum of 30 min rest each hour. Observers would determine which pandas needed a session completed in the hour and scan the cameras until they found a panda in view and would complete the 10 min session for the panda in view. Observers were trained to observe all pandas except for the mother and cub, which only the lead investigator observed. In addition, only the lead investigator had access to cameras at Zoo D, and therefore, these pandas were also only observed by the lead investigator. Between all 13 pandas, a total of 2592 ten-minute sessions (432 h) were completed and used for analysis. A graphical representation of the sampling method can be seen in Vocalizations were not recorded, as some cameras did not have audio. Whether the panda was out-of-sight was also recorded, and a session was only saved if the panda was in sight for 60% of intervals  to provide representative data for analysis. Sessions with more than 8/20 out-of-sight intervals were deleted and reperformed.In total, 13 observers assisted in data collection throughout the data collection period. To produce data that would be used for analysis, observers had to pass reliability testing. Since testing reliability purely from live observations often results in many ethogram behaviors not being evaluated , we desiOur predictor variables were life stage , sex , hour of day, and season. Definitions of the behaviors we recorded are given in We also investigated the rhythms of maternal behaviors and proximity for the mother and cub. We determined the rhythms of nursing behavior and non-nursing maternal behaviors , a model for zero inflation, and a dispersion model. The conditional mean and dispersion models analyze positive values using log links. The zero-inflated model describes the probability of observing a true/structural zero that is not generated by the conditional model. The values within the zero-inflated model are constrained between 0 and 1 by applying a logit link [Within our data, each of our response variables had a very high percentage of zeros (between 45 and 98%). Our data have both true/structural and false/sample zeros, but mainly zero inflation due to true/structural zeros, which results in overdispersion . TherefoglmmTMB . In glmmgit link ,55,56. TFor each behavior in the ZINB mixed model, the zero-inflated model was the same as the conditional model. The categorical variables of season, life stage, and sex were coded within the model using contrast sums. Therefore, each level of the variable was compared against a grand mean within the model, which was the mean of the response variable means at each level of the categorical variable. In addition, Gandia et al.  determinIn addition to the models for all individuals and the selected behaviors, we also conducted ZINB mixed models for female vs. maternal female activity. This model only had hour, season, and sex as predictor variables, with sex having the activity levels of a female or maternal female panda. The season was coded using contrast sums, while sex was coded using the standard dummy coding, where the female level served as a control. For the mother and cub pair, we also modeled nursing, maternal behaviors  were conducted on the season, sex, and life stage variables using the R package emmeans  to deterTo extrapolate more information on mother and cub behavioral cycles throughout the year, the synchronization between mother and cub, and how animals synchronize sexual-related behaviors . The activity among all pandas was also lower in the Summer compared to the Winter . For resting/sleeping, the count model reveals a slight decrease in rest/sleep in the Spring compared to the grand mean for all seasons. Within the zero-inflated model, all the coefficients are significant except for either sex , the sub-adults , and the adults , and this can also be seen in his circadian and circannual cycles of feeding in Feeding accounts for 70.6% of active behavior overall and, consequently, has similar circadian and circannual rhythmicity to overall activity b. The coFor drinking, the count model and pairwise comparisons produced no significant coefficients or differences. However, the zero-inflated model indicates that it was more likely for drinking to be at the zero level during the Summer and less likely during the Spring. The circadian cycle of drinking seems to show the largest peak among all individuals in the afternoon c.p = 0.02), and can be seen in For locomotion, the count model indicates an increase in locomotion in the Winter and a decrease in the Summer compared to the grand mean of all seasons. In addition to the increased levels of locomotion in the Winter, the zero-inflated model also indicates that locomotion was more likely to be at zero levels in the Winter. These two results together may suggest that pandas have more intense but less frequent bouts of locomotion in the Winter. These results for the seasonal variation in locomotion are further supported by the pairwise comparison, showing significantly more locomotion in the Winter compared to the Summer . Also, despite being locomotor pacing, the circadian and circannual rhythms of pacing did not match those of locomotion  and Winter . Although no results for life stage were significant for bipedal standing, we displayed the life stages for comparison with pacing, as this behavior was often performed in conjunction with pacing. Bipedal standing also displays a similar early morning peak to pacing and increases in the Spring , Spring , and Winter . This decreased level of anogenital rubbing in the Summer can be seen in Anogenital rubbing was modeled with only sex, season, and hour, because adding age overparameterized the model. The count model suggests that anogenital rubbing significantly increases in the Spring and decreases in the Summer compared to the grand mean. The zero-inflated model also indicates that during the Summer, anogenital rubbing was less likely to be at the zero level, or rather, the pandas were more likely to show some level of anogenital rubbing. This result, combined with the decrease in the Summer seen in the count model, may suggest that anogenital rubbing may occur more consistently in the Summer, but at low levels. The zero-inflated model also indicates that during Autumn, the pandas were more likely to have true zeros for anogenital rubbing. In addition, the females were more likely to have true zeros for anogenital rubbing, while the males were less likely to have true zeros. The post hoc pairwise comparisons show that there was significantly less anogenital rubbing in the Summer compared to Autumn . The circadian and circannual rhythms also show the maternal female displaying consistently higher average activity levels than the other females, with some areas of no overlap between 95% confidence intervals  and Spring 22  (see p = 0.029), Spring 21 , Winter 21–22 , and Spring 22 . They were also proximate significantly less in Summer 21 compared to Winter 20–21 , Spring 21 , Winter 21–22 , and Spring 22 . The model for distant proximity displayed a model convergence warning, which indicated that the best fitting model was likely not found, and therefore, the AIC and BIC scores were not produced. However, the pairwise comparisons indicate that the mother and cub spent significantly less time being distant in Spring 22 compared to Spring 21 , Summer 21 , and Autumn 21 . They also spent significantly more time being distant in Spring 21 compared to Winter 21–22 . These results do not support our prediction that the mother and cub would gradually spend more time being distant as more time passed.The circannual rhythm of nursing did not show any changes over time, but it should be noted that the cub was not fully weaned  until 11 months after the observations ended. The pairwise comparisons for the proximity of the mother and cub indicate that they were significantly more in contact in Summer 21 compared to Autumn 21  and cub (13 months of data) using continuous wavelet transform. We found that they displayed similar clear cycle lengths of activity as follows: ~3 h, 5 h, 8 h, 12 h, and 24 h. The power of the cycles (a measure of the consistency of magnitude through time) was similar between the mother and cub for the 3 h, 5 h, and 8 h cycles. However, the cub had a stronger 12 h cycle, and the mother had a stronger 24 h cycle, with the mother showing an increasing magnitude of her 24 h cycle towards the end of the observation period  could be feeding anticipatory activity (FAA). Pandas across all the studied zoos were left with bamboo overnight and would receive fresh bamboo in the mornings when the keepers arrived. Predictable feeding schedules cause animals to display anticipatory behaviors, which may signal stress should their frequency increase in response to the predictable schedule becoming delayed ,80,81. SThis result is similar to that found in the study investigating rhythms of activity in captive pandas at the Wolong Reserve, where the pandas were seen to have two peaks of daytime activity that coincided perfectly with the feeding times . AdditioOur results may indicate a combined effect of anticipation for feeding and breeding opportunities. Zoo staff can use the cycles and paired behaviors to infer the needs that the panda wants to express. Pacing paired with bipedal standing can be an indication of food anticipatory activity, while pacing combined with anogenital rubbing can be a desire for breeding opportunities. Observing full cycles and comparing them all together allows for new associations between behaviors to be made. Though the associations between stereotypical/abnormal behaviors, feeding, and mating cannot be generalized to all species, the method in which these associations are investigated can be generalized. Circadian and circannual rhythms provide a fuller picture of behavior, and investigating them provides new insights into the possible motivations behind behaviors.Previous studies on giant pandas investigated the cycles of maternal activity levels in the wild  and in cOur results do not show a significant difference in the maternal female’s activity compared to other females, which is a similar result to what was found by Mainka and Zhang  in materThe circadian rhythms of new mammalian mothers are often disrupted in response to having an infant who is still developing a circadian rhythm and nursing. Although most mammal newborns, aside from cetaceans, have increased sleep and reduced mobility after birth that are associated with requirements for brain and body development , mothersThe full circadian cycle of mother and cub behaviors, including maternal and nursing behaviors, has not been previously investigated in captive pandas. This was an opportunity to investigate how the circadian rhythm of a cub develops in captivity, how a mother’s circadian rhythm changes or not as a result of having a nursing cub, and how the levels of nursing and other maternal behaviors shift over the first years of a cub’s life. In mammals, circadian rhythms begin to develop slowly before birth, largely emerging in different cell types at stages of cellular differentiation . After bOur results showing that the mother and cub did not have changes in the levels of nursing throughout the course of observation is expected, as the cub was still dependent by the time the observations ended. The keepers began creating independence by gradually housing the mother and cub separately beginning 2 months after the observations ended. Occasional nursing was seen by the keepers until the separation process was completed, and the mother and cub were housed entirely separate 11 months after the study concluded. However, another study on a giant panda’s maternal behavior found a gradual decrease in non-nursing maternal behavior towards her cub up to 150 days after birth . We alsoOur study demonstrates a holistic approach in assessing animal behavior, their needs, and welfare indicators through the use of circadian and circannual rhythms. Circadian and circannual rhythms provide a fuller view of what a healthy, adaptive cycle of behavior is, and since circadian clocks regulate internal physiological clocks, the rhythms can also provide insight into the physiological state of the animal. Using this approach to study captive giant panda behavior allowed us to understand the possible energetic dynamics between behaviors like locomotion, drinking, feeding, and resting. It is pleasing to report that the natural cycle of the three activity peaks in the captive giant pandas are similar to their wild counterparts. These results also demonstrate how this method can be used to determine species’ typical levels of behaviors to validate valences applied to behaviors in relation to welfare. In addition, with this broad view, we were able to highlight some possible links between the timing of migration in the wild and stereotypical/abnormal behavior, sexual-related behaviors, and feeding behaviors in captivity, suggesting that this is how thwarted migration may manifest. We also expanded on the knowledge of how a mother and cub interact in captivity, adding important context to the kinds of maternal behaviors displayed and the times of day that are more likely to show the mother and cub interacting. Exploring sex and life stage in concordance with rhythms adds another layer of context. Investigating all these variables together, including life stage, sex, time of day, and time of year, is more informative than investigating any of them individually, because connecting them allows for new associations and predictable changes in rhythm by sex or life stage to be identified.Circadian clocks are evolutionarily adaptive and are at the basis of biological function in living organisms. This makes circadian rhythms equally relevant in wild individuals as in captive ones, since the rhythms persist in captive environments and regulate many processes affecting welfare. We must be conscious of circadian rhythms as a way to educate ourselves on the evolutionary needs of an animal. This method can be modified in accordance with each zoos’ questions to investigate the welfare states of animals. The insight on animal behavior that is gained from these kinds of analyses can be used by zoos to modify their practices of care in accordance with the biological needs of a species, and can also allow them to predict what resources or special care might be needed across the day, year, and lifespan of the animals.