In modern wireless networks especially in Machine-to-Machine (M2M) systems and in the Internet of Things (IoT) there is a high densities of users and spatial reuse has become an absolute necessity for telecommunication entities. This paper studies the maximum throughput of Carrier Sense Multiple Access (CSMA) in scenarios with spatial reuse. Instead of running extensive simulation with complex tools which would be somewhat time consuming, we evaluate the spatial throughput of a CSMA network using a simple model which produces closed formulas and give nearly instantaneous values. This simple model allows us to optimize the network easily and study the influence of the main network parameters. The nodes will be deployed as a Poisson Point Process (PPP) of a one or two dimensional space. To model the effect of (CSMA), we give random marks to our nodes and to elect transmitting nodes in the PPP we choose those with the smallest marks in their neighborhood. To describe the signal propagation, we use a signal with power-law decay and we add a random Rayleigh fading. To decide whether or not a transmission is successful, we adopt the Signal-over-Interference Ratio (SIR) model in which a packet is correctly received if its transmission power divided by the interference power is above a capture threshold. We assume that each node in our PPP has a random receiver at a typical distance from the transmitter i.e. the average distance between a node and its closest neighbor. We also assume that all the network nodes always have a pending packet. With all these assumptions, we analytically study the density of throughput of successful transmissions and we show that it can be optimized with regard to the carrier-sense threshold.