Introduction
“Form follows function”; a controversial statement that in last two decades has gained more attention especially in spatial planning context; how are forms the reflection of functions and vice versa. Spatial structure of regions has to be a means of spatial planning to understand the dynamics of population and employment through space and time. Methodologically, it consists of two main approaches, functional and morphological, in investigation of relational and nodal features of centers, respectively. Population spatial structure in metropolitan regions represents settlements configuration and mobility while employment structure investigates the dynamics of money, labor, goods, and information in the region. Generally speaking, the spatial structure of regions has a variety of elements. However, CBD, employment sub-centers, and infrastructures are the most influential parts affecting the location and mobility of population and its employment.
The subject of the spatial structure of metropolitan regions are over studied and a long history and rich literature are formed in local, regional, national, and even international levels. However, as this concept is highly context dependent, in various geographies may have different meanings and mechanisms. This study has investigated the issue in the Iranian context. The spatial structure of metropolitan regions may have different patterns, while monocentricity and polycentricity are the most common phenomena that can explain the whole situation. Metropolitan region spatial structure is a fuzzy concept from mono-centric to completely polycentric. In the literature, this structure is mainly affected by triple factors; CBD, subcenters, and transportation infrastructures. As spatial planning is an interdisciplinary subject, most theories and methodologies are taken from different fields, so most of the models used in this paper are economically based subjects combined with spatial aspects.
The aim of this study is to analyze the distribution of the population in Tehran Metropolitan Region (TMR) by a morphological approach. Thus, three main questions can be addressed; what is the relationship between population distribution and distance to CBD? How much population density in TMR is affected by transportation network? And, what are TMR sub-centers and is there any relation between them and population density? 
Methodology
The morphological approach is applied in this study that refers to the plurality of centers in a given territory. As the main objective is to assess the influence of some factors on population distribution, we used various types of regression functions. Required data for the proposed methods are acquired from the Statistical Center of Iran (SCI) and corrected by the authors. To evaluate the relationship between CBD and population density, different forms of monocentric functions adopted that the most useful and commonly used forms are linear, gravitational, exponential and logarithmic. In terms of transportation networks (highway and freeways), several forms of univariate regression functions are used to assess the relationship between population density and distance to the nearest network. The third part of this study is evaluation of the influence of subcenters on population density that is more challengeable because of the majority of the methods proposed in subcenters identification; most of them have a kind of arbitrary state. However, we used a combination of adopted models including threshold method, density and proportional based method, parametric model, GWR, and ESDA. Then, in a multivariate nonlinear function, we investigated relation between population density and distance to nearest subcenters. In the end, a linear integrated model is used to assess the population density changes based on distance to CBD, transportation network and subcenters simultaneously. In all cases used OLS technique is applied to estimate variables.
 
Results and discussion
Tehran Metropolitan Region (TMR) is the most important and populated region in Iran. TMR almost encompass all Tehran Province, but by the parliamentary approval (2010), it divided into two separate provinces, Tehran and Alborz. Tehran City is considered as the center the Tehran province and Karaj is the center of Alborz. Tehran city has been the capital of Iran from 1776 up to now and the population is increased from 15000 to 8154051 inhabitants in 2011. In this period, Tehran has become a great metropolitan region by 18000 square kilometers area and a population of 14 million, according to the last census (2011). TMR includes 14 counties (Shahrestan), 54 cities and 87 rural districts (Dehestan), in total 141 administrative sections. Population decentralization was started in 1976-86, that is mainly due to Islamic Revolution in the 1979. It should be noted that the increased rate of population doesn’t mean the decentralization of population from Tehran city, even though these inhabitants are attracted from other parts of the country.
The results of a monocentric model to assess the relationship between population density and CBD is not significant (R²=0.1). This means that CBD cannot explain the population density variation. However, OLS results of road-based models show no considerable significant relationship but it is more powerful than CBD variable. A large number of subcenters identification methods are applied in TMR to find appropriate and applicable methods. The results found six subcenters including Karaj, Eslamshahr, Baghershahr, Nasimshahr, Varamin, and Rey. In the next step, OLS results of regression model demonstrated a high value of GOF (goodness of fit (R²=0.5)) that confirmed the hypothesis of the research about slight polycentricity of TMR population distribution. Finally, the results of the integrated model to test the comparative importance of triple variables (CBD, subcenter and transportation network) on population density, surprisingly demonstrated that road is the most important factor, subcenter and CBD are in the lower level of significance, by -5.65, -1.18 and 0.45 t-value, respectively.
 
Conclusion
This research aimed to describe and analyze the population spatial structure of TMR. The results showed the effects of transportation networks, subcenters, and CBD on population distribution over TMR territory by different levels of significance. Therefore, the empirical evidence obtained from TMR allows us to state that the monocentric model cannot explain the dynamics of TMR population distribution. Although it does not mean that TMR is significantly polycentric, a degree of polycentricity could be considered in this case.