Travelling to altitude can have several effects on your heart. The lower oxygen in the air and exercise you are doing can make your heart beat faster. This is not normally a problem but if you have a heart condition (eg angina) it can put extra strain on your heart. Your blood pressure may go up a small amount at altitude, but this effect is not normally noticed.
One of the effects of altitude is for you to produce more red blood cells (so you can carry more oxygen). This can sometimes lead to the blood thickening, making the circulation sluggish. With this in mind, you should make sure you drink plenty. If you have a known heart problem (such as an irregular heart beat, high blood pressure, a heart attack or angina) or have had surgery on your heart you should talk to your doctor to make sure that what you are planning is not going to put undue strain on your heart. If you take medicines, make sure you take plenty with you.
If you are healthy then travel to altitude will not put any more strain on your heart than rigorous exercise at sea level.
People with inherited sickle cell problems are at risk and should going to altitude.
Walk slowly, don't race.
Take plenty of rests.
Drink plenty of fluids.
If you have any problems, stay at that altitude, don't go higher.
If problems persist then descend
Get as fit as possible.
Try the level of exercise out at home before you try it at altitude.
Make sure you have all your medications / prescriptions.
On a Medex trip, my BP was recorded at 168/118 one day. The group doctor said this was common on ascending but usually sorted itself out as you acclimatise. He advised that my rest day was to be taken very easily, even though I felt fine.