For TAA - thoracic aorta aneursym, when the size is less than 4 cm, the 5 year incidence of rupture is close to 0 percent. When it grows to 4 - 5.9 cm, the 5 year incidence of rupture rises to 16%. The incidence goes up to 31% when the TAA grows beyond 6 cm. In diameter.
Yours is already 4.5 cm, despite of etiology and location you'll need bi-annual scan, CT or MRI, because the aneurysm grows. The good news is thoracic aorta grows slowly, 1 mm/yr for ascending, 3 mm/yr for descending.
If you follow up with your cardiologist, he/she will set a line, when the TAA grows to the line, I'm sure your Dr. will discuss with you about treatment or surgery.