The placenta performs many physiological functions critical for development. Insufficient placental perfusion, due to improper vascular remodelling, has been linked to many pregnancy-related diseases. To study longitudinal in vivo placental perfusion, we have implemented a pixel-wise time-intensity curve (TIC) analysis of contrast-enhanced ultrasound (CEUS) images. CEUS images were acquired of pregnant Sprague Dawley rats after bolus injections of gas-filled microbubble contrast agents. Conventionally, perfusion can be quantified using a TIC of contrast enhancement in an averaged region of interest. However, the placenta has a complex structure and flow profile, which is insufficiently described using the conventional technique. In this work, we apply curve fitting in each pixel of the CEUS image series in order to quantify haemodynamic parameters in the placenta and surrounding tissue. The methods quantified an increase in mean placental blood volume and relative blood flow from gestational day (GD) 14 to GD18, while the mean transit time of the microbubbles decreased, demonstrating an overall rise in placental perfusion during gestation. The variance of all three parameters increased during gestation, showing that regional differences in perfusion are observable using the pixel-wise TIC approach. Additionally, the high-resolution parametric images show distinct regions of high blood flow developing during late gestation. The developed methods could be applied to assess placental vascular remodelling during the treatment of the pathologies of pregnancy.