## 1 Introduction  
Process mining (PM) is a relatively new discipline that adopts a data-driven approach and a classical model-based process analysis. It is becoming popular because there is a demand for better insight into what happens within an organization. PM is a promising approach to reveal and analyse real processes existing in all companies today. There are three types of PM: process discovery, conformance checking, and process enhancement [1]. With discovery algorithms, one can automatically obtain a (business) process model from routinely recorded data, an event log. This type of PM is the research topic of most interest [2]. The results of process discovery techniques can be further used in conformance checking and enhancement. An a priori process model (retrieved from a log or elaborated \"by hand\") is evaluated by its compliance with the data by conformance checking techniques, and its enhancement can be proposed after an analysis of process performance measures. In this study, we address a problem within process discovery. One of the main issues is constructing a model which would both be simple and reflect actual process behaviour. This often results in the trade-off between quality measures of a model [3]. Ideally, a process model should be understandable and interpretable for both analysts and common users and capture the principal way of process execution (if there is no mandate to find all possible realizations). The problem is most acute when dealing with complex and heterogeneous processes, making it possible to discover a so-called _spaghetti-like_ process model [1].  
Processes in the healthcare sector are highly variable and distributed because they are ad hoc and healthcare information systems are usually not process-aware [4]. That is why healthcare is the most researched application domain of process discovery techniques [2; 5; 6]. Moreover, healthcare organizations need to improve their processes to achieve high-quality care standards in a cost-effective way; therefore, they may benefit from PM solutions. The PM community, in turn, needs to generate a 'unique value proposition', providing actionable tools which are aware of domain-specific peculiarities and aimed at solving real-world problems [7]. For example, process model structuring often requires domain knowledge. So, an automatic interpretation and structure analysis of the model are necessary. While there are endeavours and some success in defining and standardizing interpretability in other modelling fields, complex processes with non-trivial domain interpretation are still challenging.  
Taking into account the complex nature of real-world processes (where healthcare processes are considered as an example), we see multi-aspect problems in the optimization of process model structure and parameters. First, a certain balance between case coverage and interpretability of a process needs to be achieved, considering event logs which are often imperfect. Second, domain-specific (interpretable) states often span multiple events in event logs, causing implicit structures (loops, sub-processes) to be presented in a process model. Third, human interpretation as a frequent target of PM needs to reveal such structures and present them explicitly. In this paper, we propose an approach for model interpretability based on a meta-states concept and present a technology which extends a PM algorithm with semi-automatic support to model optimization for higher complexity control. We demonstrate our solution applicability within the healthcare domain, where processes are best suited for model comprehension enhancement and from which the idea of the concept originates. While we provide a case study example, we believe the approach is adaptable to other domains, and is broadly considered as an extension of the process discovery technique.