The role of the cardiovascular system is is to deliver oxygen and nutrients via arteries to the tissues of the body and to remove their waste products through the venous system. Due to certain pathological processes, arteries can be damaged resulting in a reduction of well oxygenated nutrient rich blood delivered to the tissues. Chronic hypoperfusion to the brain has been related to Alzeimer„s disease (AD). AD primarily affects people over 55 years of age, with an average duration of 7-10 years, resulting in death. Currently there are 600 million people in the world aged 60 years and over. This figure is expected to double by 2025 and to reach 2 billions by 2050. Finding a cure for a neurodegenerative disease such as AD would herald a major breakthrough in medical care. Currently AD is being widely investigated, but in order to find a cure, the complete pathophysiology of AD needs to be understood. Physilogical modelling could play a significant role to further develop that understanding. The underlying cause for AD is debated although several genetic loci have been identified for AD. Scientists have also demonstrated a strong connection with cerebral hypoperfusion. This results in tissue oxygen and nutrition deprivation which is a possible causative factor in the development of AD. In this thesis a Simulation model (SM) has been built to produce an arterial tree which resembles a natureal arterial tree. The SM model is based on Schreiner et al´s Constrained Constructive Optimization (CCO) method. The SM model produces a binary tree by choosing a random point in a defined area, and connects it to an exising tree structure, each time forming a new bifurcation. This bifurcation is optimized using the target function total minimum volume of the tree. The main difference between the CCO and SM method is the handling of the constrained areas in which the binary trees are grown within. The CCO method inceases the constrained area each time a segment is added to the tree structure, resulting in rescaling of the total tree each time. The SM tree utilizes a unit circle for the tree to grow in and uses a scaling factor to retrieve the real values of the tree segments as needed. Two trees were produced using the SM method, containing 250 (T250) and 2000 (T2000) terminals respectively. The segment Radii and length of the T2000 terminal tree was extracted and reorganized to fit the data structure of a zero-dimensional model developed by Alzaidi. This model was used to produce pressure and flow rate results for the T2000 tree. The relative perfusion of the infiltrated area in the T2000 tree was also calculated. This thesis shows a close resemblance between the SM tree and a true arterial tree, both visually and geometrically. The morphometric distribution of radii and length showed a good correlation between the SM tree and previous experimental research. The real values of radii and length found in the T2000 SM tree were found to be of larger radii and shorter length compared to previously reported values in the literature. However the results from the T250 SM tree showed excellent correlation with previous experimental results. The physiological parameters of pressure changes in the SM T2000 tree strongly mimic known in vivo physiological parameters from the human circulation. The flow rate in the tree was larger than expected, but can easily be rectified by changing the initial parameters of the SM program. The perfusion distribution diagram demonstrates a well known in vivo occurrence known as watershed zones which has recently been shown to be strongly associated with pathophysiological changes found on autopsies of brains from Alzheimer‟s patients.