The results depict the DRS XIII patients’ movements for the resolution of their pregnancy in the region surrounding Ribeirão Preto. This set of displacements configures patterns of the agents’ behavior, due to the interdependence of the municipalities to fulfill the different demands for delivery-related hospitalizations. Looking at these patients’ movements using the lens of complexity, they can be interpreted as emergent behaviors limited by the regional administrative boundaries and other norms that constitute top-down constraints .
Several patterns of emergent behaviors may be analyzed. More than 25% of the admissions related to childbirth come from patients crossing borders to a different municipality to be hospitalized. The functional region found in the study is broader than the limits established by the ordinances and provisions of the State Department of Health, due to the strong influence of Ribeirão Preto to attract patients. There is a mismatch between this data-derived region and the boundaries established in the legal division of the state. A recent study in Turkey found that 22% of the Ministry of Health region boundaries did not match the regions emerging from patient mobility . The study of patients’ flows to hospitals in an Australian state, in order to determine the hospital service area networks (HSAN) showed that 30% of patients came from outside of the designated HSAN areas . The constraints posed by the political and administrative divisions of geographical regions are barriers to the capacity of self-organization that communities may achieve using their own emergent patterns of use as guidance.
Municipalities that are not fully contiguous compose the catchment area surrounding the hospitals. This may be important because it questions contiguity as one of the presuppositions in any regionalization scheme, and is likewise being observed regarding urban areas as in the proposed zoning along main transit axes in the city of São Paulo  and in the rural/urban mix around small rivers in the Amazon basin , calling for a multi-scale approach .
Patients and practitioners show a preference to refer cases to be hospitalized in Ribeirão Preto due to the higher level of its facilities and staff and the availability of resources. This preference may be perceived in the fact that a significant number of pregnant women go to the hospitals of Ribeirão Preto for low-risk procedures. Another indicator of this preference for Ribeirão Preto in the case of birth-related events is the higher willingness to travel of these patients, showing displacements twice as long as patients who receive care in other municipalities, concurring with what is observed in other contexts [26, 49].
Regulatory mechanisms contribute to these preferential flows by the administrative rule of using the best available hierarchy in terms of service, thus sending the patients to the services of Ribeirão Preto and specifically to the HC-FMRPUSP, reinforcing the centrality of this municipality. These accumulated evidences point to the effect of the preferences of the agents (patients, physicians, regulators) in the direction of the flows.
A general landscape of the flows in the region is dominated by the sufficiency of DRS XIII as a whole (due to Ribeirão Preto’s strong “exporter of services” profile). Fukuoka et al.  using data from 2007 to 2008 showed the sufficiency to resolve pregnancy-related hospitalizations in several cities of the DRS XIII. The present study shows that this municipal sufficiency is contrasted by the fact that none of the three micro-regions achieves enough autonomy, showing the need for further sub-regional consolidation. Alves  proposed the use of the concept and metrics of entropy (disorder) to measure the regulation of the flows of patients needing admissions in other municipalities. The entropy index for origin is low when a maximum of residents of one municipality move to be treated exclusively in one hospital; at the opposite, the index is high when there is a wider variation in points of destination for hospitalization. The aforementioned study found that the change from four to three micro-regions in DRS XIII in 2007 was linked to a greater order (expressed as lower entropy) of the flows that presented improved coherence between places of origin and destination in the new regional design.
The successive and non-fully successful alternatives of regionalization and distribution of services in the territories [14, 43] shed light over the aforementioned wicked problem related to the optimal way of combining the best technical quality with the greatest accessibility for the different types of services that parturients can demand. In a universal health system as is in the Brazilian case, this issue involves combining several partially contradictory approaches: a logistic approach based on the problems generally called “the traveling salesman,” trying to minimize the displacements (and their costs); a technical quality approach, seeking to maximize the deployment of high-quality services under the restrictions of resources in most Brazilian municipalities; and an agents’ preference approach with a focus on patients’ individual preferences, who have the right to choose how and where to have their baby.
The logistic approach [49, 50] shows the contradiction between having very specialized centers, well-equipped and trained, inevitably scarce, and therefore less accessible, versus multiple services widely distributed in the territory, albeit presenting compromised technical quality due to human and equipment insufficiencies. In this aspect, there are studies demonstrating that the clinical results depend on the technical experience of teams and equipment regarding the procedures in question [21, 22, 51, 52]. Studies in contexts as diverse as the regional distribution of angioplasty in Italy , the referral of patients to hospitals in various regionalization layouts in Canada , and rural patients in Tanzania  all show the so-called severity effect. When there is a perception of potentially life-threatening situations, the distance to the treatment site has a lesser effect as a perceived impediment by patients, who prefer to travel in order to achieve better quality treatment. This effect is related to the results of the present study, observing that patients prefer to travel greater distances for the resolution of pregnancy in Ribeirão Preto, even in cases of low risk.
The logistic approach is mediated and modified by the technical quality expected for a given service. The distinction made by Kongnyuy et al.  between Basic Obstetric Care and Comprehensive Obstetric Care can help to find a technical quality parameter. Basic obstetric care includes procedures that provide for safe simple deliveries, while comprehensive obstetric care adds the ability to perform cesarean sections and blood transfusion service. The five major causes of maternal mortality in developing countries (which together account for 99% of maternal mortality in the world) are hemorrhage, septicemia, unsafe abortion, eclampsia, and obstructed labor [57, 58]. Therefore, a good answer to the dilemma of the regional distribution of childbirth services may be that they should be widely distributed as long as they can certify that they provide comprehensive care according to the Kongnyuy et al.  definition. The present study should be used as a basis for an expanded mapping of the hospitals equipped with the abovementioned capacities in order to match the regional flows of needs with the deployment of resources able to respond to those needs.
The topic of agent preferences in selecting the place of resolution of pregnancy has raised global interest, motivating studies in both rich and poor countries for different reasons. In rich countries, these studies are motivated by the humanization movements and the empowerment of women’s decisions regarding childbirth [59,60,61]. On the other hand, in poor countries, the studies are oriented to understand the motivations of pregnant women and their families to define the type and place of care in order to promote deliveries in health centers well equipped for obstetric care [55, 62,63,64].
If considered jointly, the set of abovementioned studies helps to understand the observed dynamics in the present study, in order to use patients’ flows as a guiding element for reorganization of the health system. Using a complexity approach, it proposes several ways to characterize the emergent patterns of these flows. The examination of the flows should be considered as expression of how patients and providers are agents for adaptation of the administrative constraints. At the same time, it is possible to draw consequences from the flows as bottom-up guiding principles for reshaping the health systems constraints and improving the adequacy of availability of services to the population needs .
The complex systems analysis proposed by Vandenbroeck et al.  may be useful to understand the patient flows for the resolution of pregnancy, childbirth, and puerperium as emerging from the convergence of several sub-systems. Using Vandenbroeck terms, we can characterize four “engines” that operate separately, with multiple feedback circuits among them.
A first engine is the demo-epidemiology, the dynamics of populations in their settlements, and the health conditions (each of these factors in itself a complex system). As seen in this study, the demographic and epidemiological conditions of the DRS XIII and the surrounding region are relatively homogeneous and therefore not conducing to irregular flows, as could be the case if there were extremely poor or overpopulated municipalities. The second engine encompasses the facilities’ deployment with its own dynamics, related to technological developments, the economic factors related to investments in health and management models and funding (also in each case, complex systems with their own dynamics). In the case of the region studied, several municipalities have hospitals that are supposedly capable of performing deliveries, but at the same time the technological and evolutionary dynamics of what WHO calls comprehensive obstetric care show that some of them may not have the ability for events that exceed basic obstetric care. This “engine” therefore influences flows towards higher-level hospitals and increases patients’ flows.
The third engine is the political geography of the region, encompassing territories, their political organization, the dynamics of regionalization, and communications (which modulate distances). As already seen, DRS XIII has mechanisms of flow regulation and should promote resource pooling. However, as shown in discussions that came to the public in July 2015 , municipal stakeholders do not accept the possibility of combining resources and contributing to maintain centers outside their own limits that would otherwise allow the sufficiency of the micro-regions. Thus, a focus on distance or the simple provision of transport or the residence in a municipality may reveal little about patients’ willingness to travel for health care as one element in their decisions about the choices offered [26, 67].
Finally, the fourth engine consists of the preferences of the agents, in the present case, the decisions of the pregnant women, families, physicians, and other providers of health services shown to be important due to the influence in patients’ flows that do not appear to have technical justification.
The study suffered from several limitations: the patients’ flow due to procedures related to pregnancy, delivery, or puerperium was assumed whenever the municipality of residence and the municipality of hospitalization were different. This is not always the case, as some of the patients may have moved for other reasons and had not changed their registered residence. A second limitation is due to the fact that even in the most complete versions of the database (2012), there are hospitals that do not show complete data, and the database captures the patients that are hospitalized within DRS XIII; therefore, those patients residing in DRS XIII admitted to hospitals in other regions of the state or in other states are not included. A third limitation has to do with the distances traveled, as the study used the distances from the centroids of municipalities, due to the lack of postal codes on the database. Therefore, true origin-destination distance is not computed, as the municipalities in the studied area measure an average of 360 km2 and an average radius from the centroid of 10.7 km.