Is it possible to have anxiety/panic attacks, without an increased heart rate? so the heart rate remains the same as when resting, during the attacks?

Anxiety: Panic disorder is an illness that causes the sufferer to have unprovoked panic attacks and to fear further panic attacks. Most panic attacks are accompanied by increased heart rate. It is always possible that your heart rate doesn't go up during a panic attack, but this would be slightly less common. Talk to your doc about proper treatment!