Antonio Cancela

María Antonia Quintero

Teresa Gómez-López

Alejandro García-García

Reina Quintero

María Teresa Gómez-López

Alejandro -3562-875x]

García-García

Standardizing Process-Data Exploitation by Means of a Process-Instance Metamodel

Keywords: Process-Instance Metamodel, Data Model, Model Mapping, Domain Knowledge, Business-Process Data Exploitation Companies Cloud & APIs Relational Databases Process Mining Data Production Data Consumption Business Process Instance Metamodel Process Querying Reasoning Data Warehouses

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Companies today produce a great amount of data in a daily basis that accurately reflects their business processes. This data holds special interest for the study and optimization of these business processes. However, increasingly, the data comes from heterogeneous sources with different formats and structures (relational databases, NoSQL, APIs, data warehouses...). This causes the analysis and exploitation of data to become highly time-consuming, since many solutions are ad-hoc solutions, and, as a consequence, they have to be adapted depending on the techniques to be applied. This data-preparation process constitutes the most significant barrier to be improved and one of the highest time-consuming tasks in data-analysis projects [START_REF] Stodder | Improving data preparation for business analytics. applying technologies and methods for establishing trusted data assets for more productive users[END_REF].

In this paper, we propose the use of a Business-Process Instance Metamodel as an intermediate layer to specify the relation between the domain-specific data produced and its meaning in a business process, thereby facilitating how it can be exploited by business analysis techniques. Our research goal is the simplification of the data analysis by making independent the structures of data production from data consumption. The approach is based on the definition of mappings between data sources and the business process concepts specified in the Business-Process Instance Metamodel. The benefits obtained by using an intermediate metamodel include the reduction of the analysis time and the exploitation of data in a more appropriate way [START_REF] Mannhardt | Guided process discovery -A pattern-based approach[END_REF]. In fact, the use of the intermediate metamodel is a benefit itself, since it provides a standard way to access business-process data and also improves the interoperability among organizations.

The paper is organized as follows: Firstly, Section 2 gives a general overview of the approach and introduces how the proposed Business Instance Metamodel may be employed in different contexts. Secondly, Section 3 describes a case study that has been used to test the approach. Thirdly, the metamodel is detailed in Section 4. Section 5 presents the tool implemented as a proof of concept. The tool helps to define the matching between an Oracle T M database and the Process Instance Metamodel. Section 6 then surveys other existing approaches that exploit data in different contexts. Finally, conclusions are drawn and further work is outlined in Section 7.

Approach overview and contributions

Business process data exploitation depends highly on the technology that supports the business data storage as well as how the data is structured. As a consequence, no standard approach exists that can exploit any type of source, and it is therefore necessary to develop ad-hoc data analysis mechanisms adapted to both data technology and model. Thus, for example, the necessary data preparation to generate an event log to be employed by a process-mining tool is totally different depending on whether data is stored in a relational database or whether it comes from a cloud data source or a data warehouse. Moreover, this generation process also depends on the specific data model.

In order to render data exploitation as technology-agnostic regarding its data structure [START_REF] Pérez-Álvarez | Verifying the manipulation of data objects according to business process and data models[END_REF], our approach is inspired by the guidelines provided by Model-Driven Architecture in such a way that we propose a Business Process Instance Metamodel that allows us to separate produced data structure from data analysis solutions. In other words, the Business-Process Instance Metamodel can be seen as an intermediate artifact that allows applications that produce business process data to become independent from those applications that consume such data [START_REF] Gómez-López | An architecture for querying business process, business process instances, and business data models[END_REF]. Figure 1 depicts how the process instance metamodel acts as an interface between data producers and consumers.

The following subsections describe how the metamodel proposed in the paper could be used in different contexts under the previous viewpoints.

Data production viewpoint

This viewpoint represents those contexts in which business-process data is produced. This data is mapped into the metamodel in order to be analysed. The Regarding the context of cloud systems and APIs, it should be borne in mind that companies use more and more cloud data sources which rely on complex structures such as JSON, whose objects might have different properties. This data usually complements the specific company data with data from payments, geolocation, etc. Furthermore, APIs can be used to cross-reference information (such as weather and macroeconomics) and cloud systems usually perform some computation over data, which results in new data sources.

Data warehouse based applications are an especially important context of use, above all when the business process data produced is used as input for processmining and process-discovery techniques, since data warehouses commonly store historical information of the companies as well as many details regarding the timing of that information. Note that process-mining techniques need historical information in order to rebuild a consistent process model.

Finally, a common context of use from the data production viewpoint is related to applications that use relational databases. In fact, the case study introduced in this paper is based on a relational database. Relational databases also provide one of the most widely used scenarios for process querying, as detailed in Section 6.

Data consumption viewpoint

This viewpoint represents those contexts in which data obtained from business processes is exploited. The right-hand side of Figure 1 depicts three different contexts of use related to data exploitation: reasoning by using defined ontologies; process queries for the creation of dashboards that improve decision-making; and event log generation for process mining.

In the reasoning context of use, applications use semantization techniques, which are based on an ontology as a formal specification. Many business process semantization approaches link concepts from domain ontologies with business process elements that are grounded in a business process ontology [START_REF] Kluza | Opportunities for business process semantization in open-source process execution environments[END_REF]. Thus, reasoning is used to derive facts from the ontology, which are not expressed explicitly. The elements of this business process ontology can be mapped to the concepts defined in our metamodel, since ontologies and metamodels are closely related [START_REF] Parreiras | Marrying Ontology and Model-Driven Engineering[END_REF].

Process queries improve decision-making, for example, by creating dashboards to exploit the business process data [START_REF] Polyvyanyy | Process querying: Enabling business intelligence through query-based process analytics[END_REF]. As far as our metamodel covers information related to process definitions, process instances, activities and activity instances and their attributes, we can ask for durations, sequences of activities, frequencies of executions, and can identify bottleneck activities, study deviated instances of activities/processes, etc. As a consequence, this information can be used to infer Key Performance Indicators which facilitate the monitoring of the process [START_REF] Pérez-Álvarez | Tactical businessprocess-decision support based on KPIs monitoring and validation[END_REF].

Finally, in the context of event logs for process-mining techniques, applications may not be able to produce event logs or may fail to produce them in the correct format [START_REF] Van Der Aalst | Process mining: The missing link[END_REF]. Obtaining logs from the instances of our metamodel implies listing the activity instances ordered in terms of execution time, grouping them by process instance, and producing files with XES-formatted data. Note that the process to perform this transformation must be adapted to the data source in order to obtain the correct data output for processing. Moreover, it must be considered that the company systems work with various data sources at the same time. From the consumer viewpoint, all these details must be transparent by means of an appropriate transformation.

Case Study

This section presents the case study carried out to test the validity of the proposal. Data has been obtained from the execution of a business process within a prominent aerospace company. Although the company has no Business Process Management System, it does have a proprietary system that is supported by a relational database. The core business of the company consists of the assembly of aircraft and their modules. An aircraft undergoes a huge process of engineering, components designing, components construction that must be followed to assemble the final product to be ready to fly. When a new aircraft is about to be released, it must be tested several times. Figure 2 depicts the testing process of the aircraft modules.

When the aircraft testing process starts, the New aircraft order arrives activity begins, and, as a consequence, its data is introduced in the AIRCRAFT table (Figure 3). Bear in mind that an aircraft passes through different stations, and that in each station, the aircraft modules must pass a set of tests that are composed of different sections. Thereby the execution of each test brings about the execution of every section in that test.

The Configuration of the test sections that the aircraft must pass activity consists of scheduling the different test sections that must be executed on the Every time a test is launched, a row is inserted in the TEST EXECUTION table and another row is inserted in TEST SECTION EXECUTIONS (one for each test section executed). Furthermore, if the test fails, usually due to some kind of incidence, the Incidence Registration activity starts and the Troubleshooting subprocess is triggered. As a consequence: first, the original row is modified in order to register both the moment when the test failed and the status of the test after being executed; and second, a new row is inserted in the TEST INCIDENCES table. Note that if an incidence appears during the execution of a section, it must be solved successfully before the airplane is released. As a consequence, the full test needs to be repeated, regardless of which section the error appeared, since the success of some parts of a test may depend on other parts of the test. Thus, when the Troubleshooting subprocess finishes, then the whole test is relaunched (Relaunch test activity).

Due to the lack of a Business Process Management System, every test execution is stored in detail in the database, whereby information related to aircraft, tests, stations, etc. is held. Thus, each time a new test is launched, the data involved is stored, such as timestamps related to every action, the status of the test, when the test has finished, and which sections were executed. The data model which supports this process is composed of the following tables (Figure 3):

-AIRCRAFT: This stores information about the tested aircraft. As a consequence, a row is inserted in this table each time an airplane is going to be tested. The table stores: the type of the airplane, the model of the airplane, the name, the start date, and the end date scheduled.

-TESTS: This stores information about the collection of tests defined in the system: the name of the test, the creation date, and its type. -TEST SECTIONS: This stores the sections of each test that each airplane should pass and the order in which the sections should be executed. The table stores the timestamp when the test section execution started, the timestamp when the test section execution ended, and the final status. -TEST INCIDENCES: This stores information about the incidences produced during test executions. As a consequence, a row is inserted in this table when an error appears while running a test. The table stores the time when the incidence appeared, the incidence type, the status of the incidence, and the error that caused the incidence.

Process Instance Metamodel

The Business Process Instance Metamodel is detailed in Figure 4. The metamodel has been specified with EMF [START_REF] Steinberg | EMF: Eclipse Modeling Framework 2.0[END_REF]. Note that it is a very simple model which is mainly centred on the most basic entities related to business process instances together with their attributes. A previous extension of this metamodel was published in [START_REF] Gómez-López | An architecture for querying business process, business process instances, and business data models[END_REF]. The root of the metamodel is the ProcessEngine metaclass and represents the BPMS or software application that is in charge of process execution. The process engine can be in charge of several processes. The ProcessDefinition metaclass represents the formal definition of the process, that is, what we call the Business Process Model. The attributes are:

id. Key identifier of the process.

name. Name of the process model.

description. Description of the process model.

suspended. This attribute represents whether a process is suspended (temporarily disabled). While it is suspended, the process is not instantiated.

A business process is composed of different activities and the Activity metaclass models these activities. The attributes are:

id. Key identifier of the activity.

name. Name of the activity.

description. Description of the activity.

One business process can be executed many times and the ProcessInstance metaclass models these executions or instances. The attributes are:

id. Key identifier of the process instance.

ended. A flag (Boolean) indicating whether the instance is still running.

suspended. A flag (Boolean) indicating whether the instance is suspended.

-startUser. The user who started the instance process.

duration. Time spent on process execution. This information is recovered when the process has ended. -startTime. This represents when the instance process started.

-endTime. This represents when the instance process ended.

Finally, the ActivityInstance metaclass represents the execution of an activity and is related to the Activity metaclass (note that an activity may be executed many times) and to the ProcessInstance metaclass (an activity may be executed in the context of different business processes). The attributes are:

id. Key identifier of the activity instance.

-startTime. This represents when the instance activity started.

-endTime. This represents when the instance activity ended.

duration. Time spent on activity execution. This information is recovered when the activity ends. cancelled. A flag (Boolean) indicating whether the instance is cancelled.

assignee. The user assigned to the execution of the activity.

Note that this metamodel allows us to exploit business data in different contexts, independently of the storage technology and how the information is structured. We only need to define mappings from the concrete technology to the Process Instance Metamodel. Therefore, the information stored as instances of the Business Process Instance Metamodel may be used to generate event log traces (both in XES or MXML format), to be queried for decision-making or to be semantized thereby enabling the application of reasoning techniques.

Mapping the metamodel and the case study models

This section explains how the Process Instance Metamodel is used, from the data production viewpoint, in the context of the case study introduced in Section 3.

The Process Definition metaclass is related to the Testing Aircraft Process shown in Figure 2. Each instance of that process is mapped into the Process Instance metaclass (see Figure 5). As a consequence, when a new row is inserted into the TEST EXECUTIONS table, then an instance of the Process Instance Since there are different activities, such as the Launch next test or the Incidence registration activities, there are mappings between the Activity Instance metaclass and different tables (see Figure 5). Thus, an instance of the Activity Instance metaclass is created each time a new row is inserted into the TEST SECTION EXECUTIONS, TEST INCIDENCES, or TEST EXECUTIONS tables. The expected startDate of an assembly process of an airplane is stored in the AIRCRAFT table. However, the real start time is represented by the oldest startTime of the TEST EXECUTION related to a specific idAircraft that indicates the true beginning of the process.

Finally note that, although in this case study every mapping is related to the insertion of a row into a table, this is not the only possible scenario. The mappings of the Activity Instance metaclass could also be related to editions of rows. Thus, for example, the incidenceType field could be mapped to different activities if the various types of incidences lead to different subprocess executions.

Proof of Concept Implementation

In order to support our proposal, a proof-of-concept has been implemented to illustrate the mapping process between the business data repository and our Process Instance Metamodel. One of the main benefits of our proposal is that the mapping itself is that which remains after performing the matching between data repositories and the metamodel, instead of the mapped data, as in other approaches [START_REF] Buijs | Mapping data sources to XES in a generic way[END_REF]. Thus, every new item of data registered in the repository is automatically available in the Process Instance Metamodel, and it is able to perform mapping mapping Fig. 5. Mappings between metamodel and produced data business process analysis not just after the process execution, but also whilst the execution is happening, which is key in some cases. This provides agility and the opportunity of making decisions during the business process instance. Another considerable benefit of this approach, since it is not tied to any specific data consumption context (process mining, process querying, reasoning over processes...), is the ability to exploit the business process data simultaneously in different contexts. We could use it to generate event logs while visualizing statistic data on a dashboard, as is showed in the demo video recorded using the proof-of-concept tool. This provides versatility to the way business process data can be used by the companies without the necessity of performing specific ad-hoc applications or data transformations for each context or goal. The proof of concept has been developed as a web application and implements a simple dashboard where we can compare visually different instances, cross-check statistics information related to our instances, and watch the evolution of our process data over time. Furthermore, a video demo shows how the tool is able to automatically analyse the structure of the data repository and how the mapping process can be executed in an easy way. Figure 6 shows a screenshot that captures the mapping definition process. The proof-of-concept has been developed as a result of collaboration with a company whose data could never be publicly available. However, the software is available for application to other cases. Moreover, a video demo using the tool has been recorded to facilitate the use of the tool. For any further details regarding the tool, check the website http://www.idea.us.es/portfolio-item/process-data-matching-tool/.

Related Work

We will limit the scope of this section to the approaches related to business processes whose focus is on the exploitation of data generated during process execution. The approaches can be classified into: approaches whose goal is the semantization of process data in order to use ontology-based reasoning; approaches whose goal involves the querying of process data to aid in decision-making in business process scenarios; and approaches whose goal is the creation of exe-Fig. 6. Developed tool as proof of concept cution traces that are used as input for process discovery algorithms. Bear in mind that these different scenarios consume data in different formats, and certain conversion and formatting tasks can be tedious and complex since data can be stored in heterogeneous repositories [START_REF] Buijs | Mapping data sources to XES in a generic way[END_REF]. The following subsections give a general overview of the state-of-the-art of the aforementioned contexts.

Approaches that consume data for reasoning

This group introduces the incorporation of data ontology in order to support functionalities of a more intelligent nature, such as process reasoning. In general, these approaches augment existing processes with semantic annotations, so that formal reasoning techniques can be applied. There are several techniques of semantization of Business Processes [START_REF] Kluza | Overview of Selected Business Process Semantization Techniques[END_REF]:

-The SUPER project [START_REF] Wetzstein | Semantic business process management: A lifecycle based requirements analysis[END_REF] formally represents business process concepts by means of a stack of five ontologies and provides a modelling environment for the enrichment of existing processes with semantic annotations. -The SAP AG system [START_REF] Born | User-friendly semantic annotation in business process modeling[END_REF] integrates semantic descriptions and business process artifacts by linking concepts from an ontology and elements of business process models. -The Prosecco project [START_REF] Nalepa | Unifying business concepts for smes with prosecco ontology[END_REF] provides a unified dictionary of business concepts to help with the systems integration and takes into account semantic dependencies between business process models and rule models. -Finally, there is also a group of techniques that could be used for semantization of business processes that are not process specific, for example, since many business process execution environments use REST interfaces, certain techniques for semantization of REST interfaces could be used. However, these kinds of techniques remain out of the scope of this study.

The approach that is most closely related to ours is the SAP AG system in the sense that the domain ontology and the business process model are integrated by means of links; however, that system is focused on semantic sources.

Approaches that consume data for querying

The approaches in this group query process data to help in decision-making in business process scenarios [START_REF] Polyvyanyy | Process querying: Enabling business intelligence through query-based process analytics[END_REF]. There are many different approaches to query process data. According to [START_REF] Polyvyanyy | Business Process Querying[END_REF], these approaches can be classified depending on the type of behaviour models they can take as input:

-Methods that operate over event logs. This group includes approaches such as CRG [START_REF] Ly | Design and verification of instantiable compliance rule graphs in process-aware information systems[END_REF], eCRG [START_REF] Knuplesch | A visual language for modeling multiple perspectives of business process compliance rules[END_REF], DAPOQ-Lang [START_REF] De Murillas | Everything you always wanted to know about your process, but did not know how to ask[END_REF], FPSPARQL [START_REF] Beheshti | A query language for analyzing business processes execution[END_REF], and PIQL [START_REF] Pérez-Álvarez | Process instance query language to include process performance indicators in DMN[END_REF]. The approach most closely related to ours is DAPOQ-Lang because it is built on top of the metamodel proposed in [START_REF] López De Murillas | Connecting databases with process mining: a meta model and toolset[END_REF]. The main difference is that their metamodel subsumes two different viewpoints, (process, and data), while in our approach the viewpoints are defined with different metamodels, in such a way that we have applied the principle of the separation of concerns. -Methods that operate over process model specifications. This group includes a set of approaches that were originally conceived for querying conceptual models, and, as a consequence, they are also useful for querying process models, and another set of approaches that were originally conceived for querying process model collections. The first subgroup includes approaches such as DMQL [START_REF] Delfmann | The generic model query language GMQL. conceptual specification, implementation, and runtime evaluation[END_REF], GMQL [START_REF] Delfmann | Supporting information systems analysis through conceptual model query. the diagramed model query language (DMQL)[END_REF], and VMQL [START_REF] Strrle | VMQL: A visual language for ad-hoc model querying[END_REF]. The second subgroup includes approaches such as BPMN-Q [START_REF] Awad | BPMN-Q: a language to query business processes[END_REF], BPMN VQL [START_REF] Di Francescomarino | Crosscutting concern documentation by visual query of business processes[END_REF], BPSL [START_REF] Liu | A static compliance-checking framework for business process models[END_REF], CRL [START_REF] Elgammal | Formalizing and applying compliance patterns for business process compliance[END_REF], Descriptive PQL [START_REF] Kammerer | PQL. a descriptive language for querying, abstracting and changing process models[END_REF], IPM-PQL [START_REF] Choi | An XML-based process repository and process query language for integrated process management[END_REF], and PPSL [START_REF] Foerster | Activity diagram patterns for modeling quality constraints in business processes[END_REF]. The approaches most closely related to ours are DMQL and GMQL in the sense that they define a generic metamodel to cover all types of modelling languages. This metamodel can be seen as a way to decouple query languages from modelling languages. -Methods that operate over behaviours encoded in process models.

This group includes approaches such as APQL [START_REF] Ter Hofstede | APQL: A process-model query language[END_REF], BQL [START_REF] Jin | Querying business process models based on semantics[END_REF], QuBPAL [START_REF] Smith | Ontology-based querying of composite services[END_REF], and PQL [START_REF] Polyvyanyy | Process querying in Apromore[END_REF]. All of these approaches are based on the definition of semantic relations between tasks. The most closely related to our approach is that of APQL, in the sense that the proposed language is independent of the notation used to specify process models. -Methods that operate over collections that may include process models and/or event logs. This group includes approaches such as BPQL [START_REF] Momotko | Process query language: A way to make workflow processes more flexible[END_REF] and NP-QL [START_REF] Beeri | Querying business processes[END_REF]. This group is the least related to our approach.

Approaches that consume data for the creation of execution traces

There are several approaches that consume data to create execution traces. Thus, in [START_REF] Buijs | Mapping data sources to XES in a generic way[END_REF], a conversion from a data source in table format to an event log is proposed. The approach is tested by means of two case studies: an SAP system, and a set of CSV files that are the result of exporting a database.

In [START_REF] Calvanese | Ontologydriven extraction of event logs from relational databases[END_REF], a framework to extract XES event log information from legacy relational databases is proposed. The extraction is made by defining two ontologies, one that represents the domain of interest and another one that represents event logs. The domain ontology is linked to the legacy data by using the ontologybased data access paradigm (OBDA), and the concepts defined in the event log ontology are mapped into the concepts defined in the domain ontology by means of annotations.

In [START_REF] Van Der Aalst | Process discovery from event data: Relating models and logs through abstractions[END_REF], a framework to unify existing approaches of process discovery from event logs is introduced. The framework is based on event log and process model abstractions, and, as a consequence, it only includes concepts from event log and process viewpoints.

In [START_REF] López De Murillas | Connecting databases with process mining: a meta model and toolset[END_REF], a metamodel is proposed to query the data from different sources in a standardized way. Thus, the metamodel allows the decoupling of the application of the data analysis techniques. The proposed metamodel includes concepts related to two different viewpoints: process and data. Furthermore, in order to be compatible with the XES metamodel, the proposed metamodel also includes events and cases. Mappings from data sources of three different scenarios (database redo logs, in-table version storage, and SAP-style change tables) to the proposed metamodel are formalized.

Note that all these approaches share at least one of the following two weak points covered by our approach: 1) different data sources are considered, but relational databases and/or tabular formats are taken for granted [7] [26]; and 2) the focus is on the results (event logs) instead of on the means (relations between stored data and events data), which forces the process of mapping to be repeated each time a new log needs to be generated [START_REF] Buijs | Mapping data sources to XES in a generic way[END_REF] [8] [START_REF] Van Der Aalst | Process discovery from event data: Relating models and logs through abstractions[END_REF].

Conclusions and further work

Due to the existence of multiple techniques based on Business Process Analysis, this paper introduces the necessity of the utilization of a Business Process Instance Metamodel as a bridge between data sources and data exploitation techniques.

As we have seen, this metamodel provides the first step towards isolating the process data produced and the objective of its analysis. This is especially relevant in scenarios where different types of business process data exploitation are going to be applied and/or scenarios where different data sources with various formats are working together. Thereby, this paper shows how the use of an intermediate metamodel can help to standardize the exploitation of business process data by defining a common infrastructure that may be used in various contexts of business process analytics.

In terms of further work, how to query the metamodel in order to extract the required information in the correct format constitutes the next challenge to tackle. This challenge brings about the extension of the metamodel to encapsulate other existing proposals of consumers and producers, while it maintains the abstraction level to ensure adaptability to any business regardless of its sector or domain knowledge.

Finally, we consider it interesting to enrich the way of defining the matching, by making the tool more flexible and by allowing the building of processes of a more complex nature and the exploitation of more complex data sources.

Fig. 1 .

 1 Fig. 1. Approach overview

Fig. 4 .

 4 Fig. 4. Process Instance Metamodel

  -TEST EXECUTIONS: This table stores information about a test execution. Thus, a row is inserted in this table each time a test is launched. The table Relational Model of the Aircraft Assembly Process stores: the station in which the test was executed, the time when the test execution started, the time when the test execution ended, and the test status after finishing. -TEST SECTION EXECUTIONS: This stores information about the execution of a test section. Note that each test is split into different sections that are in charge of preparing the execution or checking certain variables.

	AIRCRAFT
	TEST_SECTIONS
	Fig. 3.

Acknowledgements

This work has been partially funded by the Ministry of Science and Technology of Spain by the Project ECLIPSE (RTI2018-094283-B-C33 and TIN2016-75394-R) and the European Regional Development Fund (ERDF/FEDER).


Paolo Ceravolo

Maurice Van Keulen

María Teresa Gómez-López

Preface

The rapid growth at which organizations and businesses process data, managed via information systems, has made available a big variety of information that consequently has created a high demand for making data analytics more effective and valuable. Today, these new data analyzing techniques have to cope with the continuous advancements in the digital transformation course. Blockchain infrastructures bring trusted transactions to interorganizational procedures. The growing maturity level of Artificial Intelligence solutions conveys the integration of various analyzing techniques and cultures. IoT technologies bring traceability to potentially any human-in-the-loop process. The eighth and ninth editions of the International Symposium on Data-driven Process Discovery and Analysis (SIMPDA 2018, 2019) were conceived to offer a forum where researchers from different communities could share their insights in this hot new field. As a symposium, SIMPDA fosters exchanges among academic researchers, industry experts, and a wider audience interested in process discovery and analysis.

Submissions cover theoretical issues related to processing representation, discovery, and analysis, or provide practical and operational examples of their application. To improve the quality of the contributions, the symposium is structured towards fostering discussion and stimulating improvements. Papers are pre-circulated to the authors, who are expected to read them and make ready comments and suggestions. After the event, authors have the opportunity to improve their work by extending the presented results. For this reason, authors of accepted papers were invited to submit extended articles to this post-symposium volume. We received 25 submissions and 6 papers were accepted for publication.

The current selection of papers underlines the most relevant challenges that were identified, and proposes novel solutions for facing these challenges.

In the first paper, "Designing Process-Centric Blockchain-based Architectures: A Case Study in e-voting as a Service," Emanuele Bellini et al. study a solution to put into operation Business Process Management on a Blockchain-based infrastructure to develop a diverse set of execution and monitoring systems on Blockchain, and define appropriate methods for evolution and adaptation.

The second paper, by Berti and Van der Aalst, is titled "Extracting Multiple Viewpoint Models from Relational Databases," and presents an advanced methodology for coping with discovering multiple viewpoints in relational databases collecting event log data.

The third paper by Cancela et al., "Standardizing Process-Data Exploitation by means of a Process-Instance Metamodel," proposes the use of a Business-Process Instance Metamodel as an interface between the applications that produce the data and those which consume the data making their data structures independent and, by consequence, their set up less expensive.

The fourth paper by Hinkka et al., "Exploiting Event Log Event Attributes in RNN Based on Prediction," discusses a method for giving a trade-off between prediction accuracy and training time in RNN predictions over business process cases. This trade-off is achieved by enriching the vectors imputing the RNN using the groups obtained by clustering techniques. This experimental analysis shows that having event attribute clusters encoded into the input vectors outperforms having the actual attribute values in the input vector.

The fifth paper by Martinez-Gil et al., "General Model for Tracking Manufacturing Products Using Graph Databases," presents a case study on product manufacturing where a graph database is exploited to reduce response times in tacking the process execution.

The sixth paper by Rafei et al., "Supporting Confidentiality in Process Mining Using Abstraction and Encryption," presents an approach for supporting data encryption in Process Mining. Using abstraction, the authors hide confidential information in a controlled manner while ensuring that the desired Process Mining results can still be obtained.

We gratefully acknowledge the research community that gathered around the problems related to process data analysis. We would also like to express our deep appreciation for the referees' hard work and dedication. Above all, thanks are due to the authors for submitting the best results of their work to SIMPDA.

We are very grateful to the Università degli Studi di Milano and IFIP for their organizational support.

March 2020

Paolo Ceravolo Maurice van Keulen María Teresa Gómez-López vi Preface


Eric Hermand
email: eric.hermand17@gmail.com

François J Lhuissier

Nicolas Voituron

Jean-Paul Richalet
email: richalet@univ-paris13.fr

Ventilatory oscillations at exercise in

Keywords: ventilatory oscillations, periodic breathing, hypoxia, exercise, gain, delays, O2, CO2, chemoreflex, modeling

come

Introduction

Recent observations showed the existence of ventilatory oscillations in hypoxia during exercise (Hermand et al., 2015a(Hermand et al., , 2015b;;[START_REF] Latshang | Acclimatization improves submaximal exercise economy at 5533 m[END_REF]. This instability of the ventilatory control system was related, at exercise, to cardiac output, minute ventilation, ventilatory response to hypoxia and to hypercapnia (Hermand et al., 2015a(Hermand et al., , 2015b)). A subtle interplay between CO 2 and O 2 sensing seemed to play a major role in the underlying mechanisms. However, considering the complexity of the system, we thought that developing a model of ventilatory control in these specific conditions of hypoxia and exercise would allow us to unravel the factors involved in this instability.

The first attempt of modeling the ventilatory control system was developed by Grodins, and was based on mass balance equation for O 2 and CO 2 [START_REF] Grodins | Mathematical analysis and digital simulation of the respiratory control system[END_REF]. Many of the next developed models followed this approach. Whereas most of them were focused on steady state breathing under hypoxia and/or hypercapnia, only a few covered the complex topic of stability of ventilation control.

Longobardo [START_REF] Longobardo | Sleep apnea considered as a control system instability[END_REF] and [START_REF] Khoo | Factors inducing periodic breathing in humans: a general model[END_REF] developed models describing the mechanisms of ventilatory oscillations in sleep apnea syndrome (SAS) and chronic heart failure (CHF). Models became more complex with the addition of numerous cardiorespiratory and neural inputs, and the technological and computing progress [START_REF] Fan | PNEUMA -a comprehensive cardiorespiratory model[END_REF]. These simulations have brought valuable clinical insights in our understanding of breathing disorders in SAS and CHF patients, both in their intrinsic mechanisms and in the potential treatments by O 2 or CO 2 inhalation [START_REF] Cherniack | Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders[END_REF].

However, to our knowledge, no dynamic model involving both hypoxia and exercise has been built yet. This double concomitant stress destabilizes the ventilatory control system, enhances the overall loop gain of the system, leading to the genesis of ventilatory oscillations. This phenomenon, not characterized until very recently, is not included in nor explained by any of the existing models.

Therefore, in order to deepen our understanding of mechanisms and parameters influencing the ventilatory system stability under these specific physiological and environmental stimuli, our objective was to develop a new mathematical model including most of the processes involved in ventilatory control, and to identify the physiological factors that could account for our recent observations (Hermand et al., 2015a(Hermand et al., , 2015b)). However, as a rule in modeling physiological processes, we aimed to find the simplest model that could account for the physiological observations [START_REF] Richalet | Pratique de l'identification[END_REF].

Methods

Model description

Our model of ventilation control can be described as a pulmonary gas exchange system and chemoreflex / regulation centers, connected by the cardiovascular system, which transports blood gas information (Fig. 1) [START_REF] Duffin | Role of acid-base balance in the chemoreflex control of breathing[END_REF][START_REF] Grodins | Mathematical analysis and digital simulation of the respiratory control system[END_REF][START_REF] Wolf | A mathematical model of human respiration at altitude[END_REF]. The cardiovascular and ventilatory systems are functioning tightly together and are dependent upon each other in a complex and time-related way. In existing models, the emergence of oscillations in SAS and CHF is conditioned by two main factors: a longer circulation time from lung to peripheral and central chemoreceptors, and a higher chemosensitivity to O 2 and CO 2 . Those parameters will be included into our model, and their assigned values will vary accordingly to: 1. a metabolic stress, exercise, which will impact O 2 consumption ( O 2 ), CO 2 production ( CO 2 ) and cardiac output ( c) in a different way than in sleep apneas or heart failure; 2. an environmental stress, hypoxia, with an inhaled fraction of O 2 (FIO 2 ) varying from a simulated sea level (FIO 2 = 0.21) to a 4800 m altitude (FIO 2 = 0.115). The respiratory control center is then stimulated to adjust E according to P a O 2 and P a CO 2 set points.

Protocol design

In accordance with our previous work (Hermand et al., 2015b), our model consists in two successive phases built to simulate similar protocol conditions: rest and mild exercise, either in normoxia or hypoxia, the latter obtained by breathing a hypoxic gas mixture, arterial blood CO 2 pressure (P a CO 2 ) being free to vary (poikilocapnia).

To remain close to physiological behavior, time constants are applied to the basal cardiorespiratory parameters ( c, O 2 , and ventilation E) in the transitions from normoxia to hypoxia and from rest to exercise. We obtained realistic values of these time constants by identifying our experimental data with a simple first order system (Fig. 2).

Mass balance equations

Mass balance equations are defined for each state variable, per unit of time.

Model inputs are O 2 fraction in the inspired air (FIO 2 ), O 2 consumption rate ( O 2 ), cardiac output ( c), ventilatory equivalent for O 2 (EVO 2 ), respiratory quotient (QR), alveolar/total ventilation ratio (rVAVE), circulation time from lungs to central and peripheral chemoreceptors (see section 2.1.4), gains of ventilatory responses to O 2 and CO 2 (see section 2.1.5). Model outputs are minute ventilation ( E), arterial O 2 pressure and saturation (P a O 2 and S a O 2 ) and arterial CO 2 pressure (P a CO 2 ).

Intrapulmonary and cardiac shunts are negligible at rest and during mild exercise.

Ventilatory control system

Two distinct components are included in total ventilation ( E), in addition to a basal ventilation ( Eb) determined by the central command: the ventilatory response from peripheral chemoreceptors ( Ep) and the ventilatory response from central chemoreceptors ( Ec), when activated by hypoxia and/or hypercapnia.

In case of disturbances in the ventilatory system, the central and peripheral components will act as negative feedback mechanisms to bring back the system to equilibrium, represented by P a CO 2 and P a O 2 set points.

Ventilatory response to hypoxia at rest shows a biphasic response: first, a rise of ventilation due to the activation of peripheral chemoreceptors by the decrease of arterial O 2 pressure; then a progressive decline, called hypoxic ventilatory depression (HVD), after several minutes [START_REF] Khamnei | Hypoxic depression of ventilation in humans: alternative models for the chemoreflexes[END_REF], mainly due to prolonged neural hypoxia and central CO 2 washout caused by an increase of cerebral blood flow [START_REF] Ursino | An integrated model of the human ventilatory control system: the response to hypoxia[END_REF]. Most models integrate HVD. However, during mild exercise, HVD is largely blunted [START_REF] Ward | Ventilatory response to sustained hypoxia during exercise[END_REF] and our experimental data confirm that ventilation remains steady during the entire exercise phase. Therefore, HVD mechanism was not included in our model.

Cardiovascular control: cardiac output, cerebral blood flow and circulation delay

Data from the literature and from our own experimental observations indicate that cardiac output is increased twofold during mild exercise (30% of maximal aerobic power), compared to rest (Hermand et al., 2015a(Hermand et al., , 2015b)).

In order to facilitate the simulation process and the understanding of the influence of cardiac and cerebral blood flow, depending on several parameters such as blood velocities and vessel diameters in the successive arteries, we computed two circulation delays from lungs to peripheral chemoreceptors (DeltaTp) and from lungs to central chemoreceptors (DeltaTc) respectively. We assume that circulation delays are reduced when passing from rest to exercise and from normoxia to hypoxia.

At the central level, the delay between an instantaneous change of O 2 and CO 2 pressure in the lungs and the corresponding ventilatory response can be split into a circulatory delay and a tissue delay including the diffusion into the tissue (kinetic of H + ions crossing the blood-brain barrier) and a neural delay from the chemoreceptors to integration centers and down to ventilatory muscles. Tissue delay is considered negligible at peripheral chemoreceptors, whereas a significant tissue delay (DeltaTct) will be added to the central circulation delay [START_REF] Ogoh | Cerebral blood flow during exercise: mechanisms of regulation[END_REF]. Therefore, the delay between changes in O 2 and CO 2 pressures in the lungs and the ventilatory response via central chemoreceptors is the sum

Peripheral and central chemoreflex: O 2 and CO 2 gains

The mechanisms of central and peripheral chemoreceptor activation [START_REF] Grodins | Mathematical analysis and digital simulation of the respiratory control system[END_REF][START_REF] Richalet | Pratique de l'identification[END_REF] are represented by relations between gas pressure changes and ventilation, with a pure delay, involving O 2 and CO 2 set points and gains.

pH is generally well regulated by the organism at rest and at low intensity exercise, and therefore no acidosis is observed in the present condition [START_REF] Sun | Carbon dioxide pressure-concentration relationship in arterial and mixed venous blood during exercise[END_REF], and therefore there is no change of peripheral chemoreceptor activity due to a change in blood pH.

The interaction between O 2 and CO 2 stimuli at the level of the peripheral or central chemoreceptors has been introduced in the model to evaluate its possible implication in the generation of instability [START_REF] Blain | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2: Peripheral-central chemoreceptor interdependence[END_REF][START_REF] Duffin | The role of the central chemoreceptors: a modeling perspective[END_REF][START_REF] Smith | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2 : role of carotid body CO2[END_REF]. Recent works from the Dempsey group [START_REF] Blain | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2: Peripheral-central chemoreceptor interdependence[END_REF][START_REF] Smith | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2 : role of carotid body CO2[END_REF] confirmed and quantified, in a mammal model, the interaction between peripheral and central chemoreceptors, and between CO 2 and O 2 : the nucleus tractus solitarius (NTS) receives afferences from the peripheral chemoreceptors and sends projections into the central respiratory command and, potentially, the central chemoreceptors [START_REF] Smith | Brainstem respiratory networks: building blocks and microcircuits[END_REF]. This led us to design and test three models of combined effects of O 2 and CO 2 (fig. 3): 1) Additive model. additive effects of central response to CO 2 and peripheral responses to O 2 and CO 2 . The latter (GCO 2P ) is defined as a ratio (pcratio) of the peripheral/central gain to CO 2 (GCO 2C ) [START_REF] Wolf | A mathematical model of human respiration at altitude[END_REF]; 2) Peripheral interactive model: effect of P a CO 2 at the peripheral level. The peripheral gain to O 2 is positively modulated by a coefficient (contribCO 2p ) multiplied by the difference between P a CO 2 and P a CO 2C . 3) Central interactive model: interaction between central CO 2 sensing and peripheral input (O 2 + CO 2 ) at the central level. In addition to peripheral action on central respiratory command, central gain to CO 2 is augmented by peripheral afferences (gain to O 2 and CO 2 ) modulated by the coefficient 'interac' [START_REF] Blain | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2: Peripheral-central chemoreceptor interdependence[END_REF][START_REF] Smith | Peripheral chemoreceptors determine the respiratory sensitivity of central chemoreceptors to CO2 : role of carotid body CO2[END_REF].

Central CO 2 gain is obtained from a modified Read's rebreathing test [START_REF] Read | A clinical method for assessing the ventilatory response to carbon dioxide[END_REF]. This test also gives a value of alveolar CO 2 pressure threshold (P a CO 2Cth ) under which CO 2 gain is null. Similarly, peripheral ventilatory response to CO2, linear above a peripheral P a CO 2 threshold (P a CO 2Pth ), is defined as the product of peripheral CO2 gain by the difference between P a CO2 and P a CO2 set point (P a CO 2C ) [START_REF] Casey | The effect of exercise on the central-chemoreceptor threshold in man[END_REF]. Exercise does not modify the ventilatory response to CO 2 [START_REF] Hulsbosch | Effects of positive and negative exercise on ventilatory CO2 sensitivity[END_REF]: therefore, we used the same value for exercise and rest conditions.

Peripheral O 2 gain is obtained at rest and exercise from standard tests previously described [START_REF] Lhuissier | Ventilatory and cardiac responses to hypoxia at submaximal exercise are independent of altitude and exercise intensity[END_REF]. The O 2 stimulus for peripheral chemoreceptors is tissue PO 2 , derived from arterial PO 2 , with a hyperbolic response [START_REF] Weil | Hypoxic ventilatory drive in normal man[END_REF]. However, combining this hyperbolic response and the sigmoid shape of oxyhemoglobin dissociation curve (approximated by the Hill constant NH and P50), an empirical linear relationship appears between ventilatory response to hypoxia and arterial O 2 saturation [START_REF] Steinacker | Hypoxic ventilatory response during rest and exercise after a Himalayan expedition[END_REF]. Ec is the product of CO 2 gain by the difference between P a CO 2 and the P a CO 2 set point (P a CO 2C ). Depending on the model used, Ep is the result of the respective contribution of peripheral O 2 and CO 2 gains. See appendix for equations.

Lungs: dead space, mechanoreceptors, respiratory quotient, alveolar-capillary difference in O 2 /CO 2 , O 2 alveolar-arterial diffusion

As values of alveolar blood gases are determined by alveolar ventilation while the chemosensory loops act on total ventilation, it seems important to take into account the dead space by introducing the alveolar/total ventilation ratio (rVAVE). This ratio is slightly augmented by moderate exercise [START_REF] Wasserman | Interaction of physiological mechanisms during exercise[END_REF]. During moderate exercise in hypoxia, respiratory quotient (QR) is slightly higher than at rest [START_REF] De Lattre | Respiratory quotient during moderate muscular exercise in hypoxia and normoxia[END_REF]. The activity of pulmonary mechanoreceptors is not modified by mild exercise [START_REF] Fenik | Mechanoreceptor system of the respiratory center and its contribution to respiratory control[END_REF]) and therefore will not be included in the present model. The alveolarcapillary difference in O 2 (DAaO 2 ) increases with cardiac output from rest to exercise, and with hypoxia [START_REF] Woorons | Moderate exercise in hypoxia induces a greater arterial desaturation in trained than untrained men[END_REF]. This variation in DAaO 2 is modulated by a coefficient (DlimO 2 ) of O 2 diffusion limitation of O 2 . On the other hand, the alveolar-capillary difference in CO 2 (DAaCO 2 ) is considered constant in all conditions (see appendix).

Alveolar space

Pulmonary alveolar space can be considered as a "mixing box" where O 2 and CO 2 are not instantly homogenous when ventilation changes. Alveolar CO 2 pressure (P A CO 2 ) is determined by the equation relating E, QR, O 2 and rVAVE (see appendix). When submitted to various environmental or metabolic stresses, the value of P A CO 2 is not immediately modified by variations of the parameters cited above. A new equilibrium is reached through a first-order equation involving the level of E and the volume of the mixing box (TLC, total lung capacity), from which a time constant TaupCO 2 is computed (see appendix).

Parameter assignment

All values were obtained from previous research protocols (Hermand et al., 2015a(Hermand et al., , 2015b) ) or from the literature [START_REF] Duffin | The role of the central chemoreceptors: a modeling perspective[END_REF][START_REF] Pianosi | Change in the peripheral CO2 chemoreflex from rest to exercise[END_REF][START_REF] Saunders | A breathing model of the respiratory system; the controlled system[END_REF][START_REF] Wolf | A mathematical model of human respiration at altitude[END_REF][START_REF] Zapata | Shifting from hypoxia to hyperoxia to assess the peripheral chemosensory drive of ventilation[END_REF]. The time constants for the main cardiorespiratory parameters ( O 2 , c) were obtained by an identification algorithm from our own data, and in accordance with those found in literature: values are ranged from 10 seconds for FIO 2 to 15 seconds for O 2 and cardiac output. [START_REF] Macfarlane | Dynamics of the ventilatory response in man to step changes of endtidal carbon dioxide and of hypoxia during exercise[END_REF][START_REF] Pedersen | Identification of fast and slow ventilatory responses to carbon dioxide under hypoxic and hyperoxic conditions in humans[END_REF][START_REF] Thamrin | A mathematical model of the human respiratory system during exercise[END_REF].

Modeling and sensitivity analysis

The equations describing the various models were translated in a MatLab® script and the ventilatory output was calculated as a function of time, using 1-second time steps. The pattern of ventilatory output was analyzed in various conditions, by incrementing from a basal value the different cardiorespiratory and structure parameters (O 2 and CO 2 gains, FIO 2 , delays, P50, TLC, rVAVE, pcratio, contribCO 2P , interac), one by one, in a maximal range of ± 50% around a nominal value or within realistic physiological range. If an oscillatory pattern of ventilation was observed, the period and amplitude of oscillations were computed. Then a sensitivity analysis was performed in order to evaluate the respective influence of each parameter of the model on the period and amplitude of the oscillatory pattern. Although it may not necessarily capture the general behavior in a multidimensional space, a single-parameter analysis allows us assessing the relative contribution of each parameter on the ventilation output.

Multivariate regression analysis

A multivariate regression was performed to establish potential correlations between period and magnitude of ventilatory oscillations on one hand, and model parameters on the other hand: FIO 2 , peripheral chemoresponse to O 2 (GO 2 ), central chemoresponse to CO 2 (GCO 2 ), delays from lungs to peripheral and central chemoreceptors (DeltaTp and DeltaTc, respectively), P50, TLC, rVAVE and interaction parameters (pcratio, contribCO 2P , interac).

Addition of white noise

Finally, in order to verify whether spontaneous variations in the ventilatory command would induce deeper instability in E, we added a white noise to Eb, the profile of which is following a normal distribution weighted by a 0.015 coefficient, in order to remain as close as possible to physiological data [START_REF] Milton | Mathematics as a Laboratory Tool -Dynamics, Delays and Noise[END_REF]. We then performed a paired Student t-test to check if there was a significant difference between the two simulations ("noise-enriched" and "no-noise enriched"). Values of period and amplitude of oscillations were also compared in the two conditions. Values of p<0.05 are considered significant.

Results

No significant ventilatory oscillations were found in resting conditions. The following results will concern only data obtained during exercise in hypoxia.

Sensitivity analysis

The variation of E magnitude and period during exercise in hypoxia, due to physiological, environmental and interaction parameters, are presented in figures 4, 5 and 6.

Period of ventilatory oscillations (Fig. 4)

Sensitivity analysis showed that the main factors influencing E period was the time delay between lungs and peripheral chemoreceptors (DeltaTp): in a range from 2 to 12 seconds, around a 4 s nominal value, period increased from -40% to +123% around its corresponding nominal value. In a lesser extent, the level of hypoxia (FIO 2 ) played a significant role: period steadily increased from -3% at FIO 2 =0.115 to + 16% at FIO 2 = 0.21 (Fig. 7, top). The other parameters induced only minor changes in period, remaining in a [-5%; +5%] range. peripheral O 2 gain (GO 2 ), central CO 2 gain (GCO 2C ), inhaled fraction of O 2 (FIO 2 ), delay of blood convection from lung to carotid bodies (DeltaTp), arterial O 2 partial pressure at S a O 2 = 50% (P50), total lung capacity (TLC) and alveolar / total ventilation ratio (rVAVE). Period is linearly related to DeltaTp and also depends on FIO 2 .

Magnitude of ventilatory oscillations (Fig. 5)

Magnitude of ventilatory oscillations was nearly completely blunted, from 0% to -96.5%, when level of hypoxia decreased from FIO 2 =0.14 to normoxia (Fig. 7). Peripheral and central gains to O 2 (GO 2 ) and CO 2 (GCO 2C ) and increased oscillations from -46% to +35%, and from -32% to +36%, respectively. DeltaTp enhanced oscillations from -95% to +59%. P50 and TLC had a dampening effect on oscillations, by decreasing them from +45% to -54% and from +24% to -31%, respectively.

Finally, a decrease in rVAVE (i.e. an increase in dead space) from 1 to 0.7 increased oscillations from -77% to +75%. The influence of DeltaTcc is mainly due to the tissue component DeltaTct (fig. 8): magnitude of oscillations shows a phasic pattern that can lead to either enhanced or blunted oscillations, depending on the tissue component. peripheral O 2 gain (GO 2 ), central CO 2 gain (GCO 2C ), inhaled fraction of O 2 (FIO 2 ), delay of blood convection from lung to carotid bodies (DeltaTp), arterial O 2 partial pressure at S a O 2 = 50% (P50), total lung capacity (TLC) and alveolar / total ventilation ratio (rVAVE). Magnitude mainly increases with GCO 2C , GO 2 (in a nearly linear manner) and DeltaTp, and decreases with P50, rVAVE, TLC and FIO 2 .

Effect of interaction between O 2 and CO 2 at the central and peripheral level (fig. 6)

The effect of contribCO 2P (effect of CO 2 on O 2 gain in peripheral chemoreceptors) and interac (effect of peripheral afferences on central gain to CO 2 ) is very low on period values, in a tight range of 0 to 4.5% (results not shown). In contrast, a significant positive correlation links magnitude of E oscillations to contribCO 2P and interac, from 0 to 134%, and from 0 to 75%, respectively (fig. 6). The parameter pcratio (ratio of peripheral/central response to CO 2 ) does not impact period and magnitude of ventilatory oscillations. The effect of interac and contribCO 2P are additive.

(L.min -1 ) Figure 6. Magnitude of ventilatory oscillations according to interaction parameters: interac (effect of peripheral O 2 /CO 2 gain on central gain to CO 2 : model 3), pcratio (effect of CO 2 on peripheral gain: model 1) and contribCO 2P (effect of CO 2 on peripheral gain to O 2 : model 2). Contributions of pcratio and contribCO 2P are computed at 2 values of interac (0 and 0.1) and show an additive effect of the rise from peripheral activity level.

Multivariate regression analysis

Period of ventilatory oscillations

The multivariate regression analysis significantly linked E period to FIO 2 , GO 2C , DeltaTp, DeltaTc and TLC. A trend was observed for GO 2 (p = 0.053). E period increased when FIO 2 , GCO 2C , DeltaTp and TLC increased (p<0.001, p<0.05 for GCO 2C ) whereas it was shortened when DeltaTc increased (p<0.001, respectively).

Magnitude of ventilatory oscillations

Magnitude of oscillations was enhanced when GO 2 , GCO 2C and DeltaTp increased (p<0.001) but decreased when FIO 2 , DeltaTc, rVAVE, P50 and TLC increased (p<0.001).

Effect of white-noise addition

The addition of a white noise did not alter magnitude or period of oscillations: there was no significant change between non-noise and noise-enriched models (Fig. 9). Varying the noise coefficient, from 0.001 to 0.5, did not modify the E output behavior either.

Figure 9. Effects of added white noise to the central ventilation command, at two levels of FIO 2 . There is no significant difference between "noise-enriched" (dashed lines) and "non-noise enriched" (solid lines) models.

Discussion

To our knowledge, this model is the first attempt to describe the phenomenon of ventilatory oscillations observed in healthy subjects. Our observations underline the key role of c, FIO 2 , GO 2 and GCO 2C in the genesis of such oscillations, their period and amplitude. First, resting conditions, even in hypoxia, did not provoke ventilatory oscillations, whereas a double stimulus hypoxia / exercise promoted the emergence of periodic breathing. Subjects with a higher ventilatory response to hypoxia (GO 2 ) or with a higher ventilatory response to CO 2 (GCO 2C ) showed greater ventilatory oscillations during exercise performed in hypoxia. Moreover, a greater cardiac output c (lower DeltaTp) was significantly correlated to a higher magnitude and a shorter period.

The main difference with existing models lies in the inclusion of exercise-oriented components through a higher cardiac output and a consequent decreased circulation time from lungs to central and peripheral chemoreceptors. The existing studies and models were mostly focused on central and obstructive sleep apneas and heart failure during sleep, and described a phenomenon with a much longer period, associated with an enhanced sensitivity to CO 2 [START_REF] Hall | Cycle length of periodic breathing in patients with and without heart failure[END_REF][START_REF] Javaheri | A mechanism of central sleep apnea in patients with heart failure[END_REF][START_REF] Khoo | Determinants of ventilatory instability and variability[END_REF]. The present work confirms previous studies in healthy subjects in which greater ventilatory oscillations were related to a higher cardiac output (mild exercise) and to hypoxia [START_REF] Garde | Periodic breathing during ascent to extreme altitude quantified by spectral analysis of the respiratory volume signal[END_REF]Hermand et al., 2015b;[START_REF] Latshang | Acclimatization improves submaximal exercise economy at 5533 m[END_REF] (Fig. 7). It is remarkable to notice the proximity of the period between theoretical and physiological data, around 11 seconds (Hermand et al., 2015a). FIO 2 level is also correlated to both period and magnitude of ventilatory oscillations, as observed in our previous studies (from FIO 2 = 0.165).

The O 2 gain has an important impact on the amplitude of oscillations, as subjects with a higher ventilatory response to hypoxia at exercise show a higher magnitude of oscillations, in coherence with our experimental observations (Hermand et al., 2015b). In addition to this intrinsic sensibility to O 2 , the O 2 -CO 2 interaction at the peripheral level enhances the instability in a degree depending on model used (fig. 6). The sensitivity analysis showed that a simple additive CO 2 contribution, via the pcratio coefficient (model 1), brings the least disturbance to ventilatory control system. Then, peripheral afferences to central chemoreceptors (interac contribution, model 3) further augments oscillations. The most unstable situation is created by the peripheral interactive model, in which increased peripheral O 2 gain by a hypercapnic stimulus (contribCO 2P , model 2) severely destabilizes the respiratory command.

Regardless of the studied model, these simulations highlight the major role played by the peripheral chemoreceptors in the genesis of ventilatory oscillations, with and without CO 2 interaction, and is in accordance with the observations of CHF and SAS patients [START_REF] Beecroft | Enhanced chemoresponsiveness in patients with sleep apnoea and end-stage renal disease[END_REF][START_REF] Ponikowski | Peripheral chemoreceptor hypersensitivity: an ominous sign in patients with chronic heart failure[END_REF][START_REF] Trombetta | Obstructive sleep apnea is associated with increased chemoreflex sensitivity in patients with metabolic syndrome[END_REF]. This data provide a new perspective in the current debate about the respective contribution of central and peripheral chemoreceptors in the control of ventilation (Paula-Ribeiro and Rocha, 2016).

The central CO 2 gain is also involved, in a lesser extent, into the genesis of periodic breathing and matches the clinical studies on CHF and SAS patients [START_REF] Beecroft | Enhanced chemoresponsiveness in patients with sleep apnoea and end-stage renal disease[END_REF][START_REF] Trombetta | Obstructive sleep apnea is associated with increased chemoreflex sensitivity in patients with metabolic syndrome[END_REF]. This supports our own findings in which ventilatory response to CO 2 is correlated to the magnitude of ventilatory oscillations in healthy subjects (Hermand et al., 2015b).

If both central and peripheral gains play a role in their appearance, they do not seem to play a major role in the period of the phenomenon. The latter is strongly dependent on DeltaTp, illustrating the role of cardiac output and circulation delay. As evidenced in figure 8, a phase shift between peripheral and central responses to chemical stimuli can lead to either a reinforcement or a blunting of ventilatory oscillations. Depending on the value of this phase shift, our model predicts that the effects of hypoxia and hyperventilation-induced hypocapnia can be either hyperadditive or hypoadditive, which could account for the variability of experimental observations [START_REF] Paula-Ribeiro | The peripheral-central chemoreflex interaction: where do we stand and what is the next step?[END_REF]. This original observation highlights the role of dynamics of central control processes in modulating the determinant effect of peripheral chemoreceptors on ventilatory instability. For any given value of DeltaTct, the period of oscillations remains around 11 seconds, reinforcing the essential role of peripheral chemoreceptors in both magnitude and period (fig. 8). Apart those cited above, one additional parameter comes into play: a greater alveolar / total ventilation ratio decreases the amplitude of oscillatory ventilation, implying that a greater dead space will promote periodic breathing. In heart failure patients, augmented dead space will prevent ventilatory oscillations by an increased PETCO 2, which acts on CO 2 apnea threshold and drastically decreased periodic breathing [START_REF] Patz | Dead space mask eliminates central apnea at altitude[END_REF][START_REF] Xie | Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea[END_REF]. Conversely, in normal subjects, the same increase in PETCO 2 will rise E, hence increasing ventilatory oscillations (Hermand et al., 2015a). This adverse effect is particularly noticeable here.

Finally, spontaneous variations in central ventilatory command did not influence the stability of the ventilation control system (fig. 8). Thus, this added chaotic component, very close to what is observed in real life, is not a determinant factor in the genesis of ventilatory oscillations.

A relation between period of ventilatory oscillations and DeltaTp: a limit value

The significant correlation between period of oscillatory ventilations and DeltaTp (Fig. 4) is illustrated by the equation of linear regression relating those two parameters:

(1) (r² = 0.9979, p<0.001)

In our previous work (Hermand et al., 2015a), we established a similar equation relating E period to the total respiratory cycle (Ttot):

(2) (r² = 0.55, p<0.001)

The tight relationship between E period and Ttot points out a theoretical limit of E oscillations period: when Ttot tends toward zero (breathing frequency tending to infinity), E oscillations period tends to approximately 7 seconds (2). Using the latter value in equation ( 1), we can deduce a similar theoretical lower limit DeltaTp min , when intensity of exercise increases along with O 2 and c, below which the ventilatory oscillations disappear: DeltaTp min ≈ 1.8 seconds. As DeltaTp is the sum of circulation delay from lungs to carotid bodies and of the time required for the neural system to produce a ventilatory response, we can deduce that this irreducible time DeltaTp min of nearly 2 seconds is the intrinsic response time of peripheral chemoreceptors, which is in accordance with the existing literature [START_REF] Black | The responses of carotid body chemoreceptors in the cat to sudden changes of hypercapnic and hypoxic stimuli[END_REF][START_REF] Mcclean | Single breath of CO2 as a clinical test of the peripheral chemoreflex[END_REF][START_REF] Teppema | Dynamics of brain extracellular fluid pH and phrenic nerve activity in cats after end-tidal CO2 forcing[END_REF].

Conclusions and perspectives.

Our model reproducing the control of ventilation in specific metabolic and environmental conditions closely matches with the observed experimental data in various protocols and studies. Furthermore, it demonstrates the crucial role of circulatory delays and gains of chemoreceptors in the homeodynamic behavior of the respiratory control system when exposed to brisk changes in physiological or environmental constraints. As pointed out in previous papers, the magnitude of transport delay and control loop gain plays a major role in many physiological conditions, especially in periodic breathing [START_REF] Batzel | Time delay in physiological systems: analyzing and modeling its impact[END_REF]. The intrinsic neural reactivity of peripheral chemoreceptors to a change in gas pressures is also confirmed and quantified by a new and original approach through the analysis of ventilatory oscillations. We also extrapolate from our model the existence of an intrinsic oscillatory pattern in the control system of ventilation in healthy humans. The interaction between O 2 and CO 2 sensing either at central or peripheral level plays an important but not exclusive role in the genesis of the ventilatory instability. Slight differences in the dynamics of the central vs. peripheral components might be determinant for the stability of the whole system. Further improvements may be carried out both in modeling and experimenting. On the one hand, the effect of an additional input, the inhaled fraction of carbon dioxide on ventilatory oscillations (FICO 2 ) may be added to the model. Indeed, contrary to what is observed in patients suffering from sleep apnea, a higher FICO 2 exacerbates ventilatory oscillations (Hermand et al., 2015a). On the other hand, this model could be tested on other subjects at exercise, such as heart failure patients, in which cardiac function is impaired whereas chemosensitivity to CO 2 is increased.

Figure 1 .

 1 Figure 1. Respiratory control model. Minute ventilation ( E) is the sum of a basal value represented by the central command adapted to the metabolic needs (rest/exercise), modulated by peripheral and central components. The P a O 2 and P a CO 2 gas information is transported to peripheral and central chemoreceptors respectively after a pure time delay of blood convection.The respiratory control center is then stimulated to adjust E according to P a O 2 and P a CO 2 set points.

Figure 2 .

 2 Figure 2. Example of identification of transition from normoxia to hypoxia at exercise for the determination of time constants, between physiological data (S a O 2 exp and E exp , dashed lines) and model (S a O 2 mod and E mod , solid lines).

Figure 3 .

 3 Figure 3. Diagrams of the three different models: additive, peripheral interactive and central interactive. The central respiratory command receives direct or indirect afferences from peripheral (through nucleus tractus solitaries, NTS) and central chemoreceptors (PCR and CCR, respectively), modulated by P a O 2 and P a CO 2 . Details of each model are explained in text.

Figure 4 .

 4 Figure 4. Period of ventilatory oscillations according to several cardiorespiratory variables from their nominal values: peripheral O 2 gain (GO 2 ), central CO 2 gain (GCO 2C ), inhaled fraction of O 2 (FIO 2 ), delay of blood convection from lung to carotid bodies (DeltaTp), arterial O 2 partial pressure at S a O 2 = 50% (P50), total lung capacity (TLC) and alveolar / total ventilation ratio (rVAVE). Period is linearly related to DeltaTp and also depends on FIO 2 .

Figure 5 .

 5 Figure 5. Magnitude of ventilatory oscillations according to several cardiorespiratory variables from their nominal values: peripheral O 2 gain (GO 2 ), central CO 2 gain (GCO 2C ), inhaled fraction of O 2 (FIO 2 ), delay of blood convection from lung to carotid bodies (DeltaTp), arterial O 2 partial pressure at S a O 2 = 50% (P50), total lung capacity (TLC) and alveolar / total ventilation ratio (rVAVE). Magnitude mainly increases with GCO 2C , GO 2 (in a nearly linear manner) and DeltaTp, and decreases with P50, rVAVE, TLC and FIO 2 .

Figure 7 .

 7 Figure 7. Variation of E for two levels of FIO 2 : ventilatory oscillations in the additive model (upper panel) and physiological data from a subject exercising successively in normoxia and hypoxia (lower panel) (physiological data from Hermand et al., 2015b).

Figure 8 .

 8 Figure 8. Variation of period and magnitude of ventilatory oscillations as a function of tissue delay at the central level. The period is not affected by changes in DeltaTct. Magnitude can be almost completely blunted (DeltaTct = 5.5 and 15) or enhanced (DeltaTct = 10.5).

Table 1 .

 1 2 partial pressure (P A CO 2 ) mmHg Arterial O 2 partial pressure (P a CO 2 ) mmHg Nominal values for the variables used in model simulations. In the sensitivity analysis, parameters were assigned values ranging from a minimal (Min) to a maximal (Max).The central component of ventilation, resulting from a variation of arterial CO 2 content, includes a static central gain to CO 2 (GCO 2C ) and a delay DeltaTc (see section 2.1.4), above a central threshold (P a CO 2Cth ): if P a CO 2 (t)> P a CO 2Cth , then else .In the central interactive model, the central gain to CO 2 (GCO 2C ) depends on peripheral gains to O 2 and CO 2 (GO 2 and GCO 2P , respectively), modulated by a constant interac:

	Arterial O 2 saturation (S a O 2 )	nu
	Minute ventilation ( )	L.min -1
	Atmospheric pressure (PB)	mmHg	760		760
	Vapor pressure of water (PH 2 O)	mmHg	47		47
	Arterial O 2 saturation Set point (S a O 2C )	%	98		98
	Arterial CO 2 partial pressure Set point (P a CO 2C )	mmHg	40		40
	Alveolo-arterial O 2 difference (DAaO 2 )	mL/mL	5		5
	Alveolo-arterial CO 2 difference (DAaCO 2 )	mL/mL	1		1
	Cardiac output ( c)	L.s -1	6		10
	O 2 metabolic consumption ( O 2 )	mL.min -1	0.25		0.8
	Hill constant	nu	2.7		2.7
	Respiratory quotient (QR)	nu	0.7		0.8
	Ventilatory equivalent for oxygen (EVO 2 )	nu	30		26
	Arterial CO 2 partial pressure threshold	mmHg	40	35	45	55
	Arterial O 2 partial pressure at S a O 2 = 50% (P50)	mmHg	27	25	28	31
	Inhaled fraction of oxygen (FIO 2 )	nu	0.14	0.11	0.14	0.21
	Central chemoreflex CO 2 gain (GCO 2C )	L.min -1 .mmHg -1 0.05 0.025 0.05 0.075
	Peripheral chemoreflex O 2 gain (GO 2 )	L.min -1 .% -1	10	10	15	20
	Total lung capacity (TLC)	L	9	4	9	14
	Circulatory delay from lung to carotid bodies (DeltaTp)	s	8	2	4	12
	Circulatory delay from lung to brain (DeltaTc)	s	10	3	6	13
	Alveolar / total ventilation ratio (rVAVE)	nu	0.7	0.7	0.85	1
	Coefficient of diffusion limitation of O 2 (DlimO 2 )	mmHg.L -1 . min	0	0	5	10
	Ratio of peripheral/central gain to CO 2 (pcratio)	nu	0.5	0.25	0.5	0.75
	Coefficient of CO 2 contribution to peripheral gain (contribCO 2P )	nu	0	0	0	0.2
	Coefficient of peripheral afferences contributing to central gain to CO 2 (interac)	nu	0	0	0	0.2
	Central tissue delay (DeltaTct)	s	1	0	1	21
	359
	360

and Equations of alveolar and arterial gas pressures: steady state and first order

  At equilibrium, the alveolar partial pressures in O 2 and CO 2 as a function of time are defined as:where P B and P H20 are atmospheric and water vapor pressures, respectively, FIO 2 is the inhaled fraction of O 2 . P B , P H20 , FIO 2 , QR, O 2 and rVAVE are predetermined as shown in table 1.

	P A CO 2 is then described through a first-order relation:
	where apCO 2 and bpCO 2 are defined as follows:	,	and
	,	is the	variable determined by initial conditions of O 2 (t) and
	E(t).

Acknowledgement. We are very grateful to Jacques Richalet for his accurate advice on modeling physiological processes.

Appendix

Basal cardiorespiratory parameters: Eb, O 2 , EVO 2 , c, rVAVE, QR.

O 2 consumption O 2 , cardiac output c, alveolar/total ventilation ratio rVAVE, respiratory quotient QR and ventilatory equivalent for oxygen EVO 2 are set at known physiological values for rest/exercise and normoxia/hypoxia, as indicated in table 1.

The basal value of E for all phases is calculated as follows:

The arterial O 2 pressure P a O 2 and arterial O 2 saturation follow the equation:

where P50 is the arterial O 2 partial pressure at S a O 2 = 50%, and NH is the Hill constant.

The alveolar-arterial difference in O 2 (DAaO 2 ) is determined as:

where DAaO 2 0 is the alveolar-arterial difference in O 2 at rest, DlimO 2 a known coefficient of diffusion, and c rep the cardiac output at rest.

Peripheral chemoreceptors

This linear expression involves the peripheral gain to O 2 (GO 2 ) and to CO 2 (GCO 2P ) and a pure delay DeltaTp from lung to peripheral chemoreceptors (blood convection).

The peripheral gain to CO 2 , above a peripheral threshold P a CO 2Pth is defined as: if P a CO 2 (t)> P a CO 2Pth , then the peripheral contribution from a CO 2 stimulus is the linear term with P a CO 2C as a P a CO 2 set point, else it is null.

In the additive and central interactive models, the peripheral contribution is: with S a CO 2C as a S a CO 2 set point.

In the interactive model, the peripheral contribution is: