The reliability of intra-body wireless communication systems is very important in medical applications to ensure the data transmission between implanted devices. In this paper, we present newly developed measurements to investigate the effect of blood vessels on the data packet reception through the fat tissue. We use an IEEE 802.15.4-based WBAN prototype to measure the packet reception rate (PRR) through a tissue-equivalent phantom model. The blood vessels are modelled using copper rods. We measure the PRR at the frequency 2.45 GHz for several power levels. The results revealed that the presence of blood vessels aligned with the fat channel has tiny influence on the PRR when measured over the range -25 dBm to 0 dBm power level and for different blood vessels positions. Our investigations show 97% successful PRR through a 10 cm length fat channel in presence of the blood vessels.