Laser Driven Plasma Accelerators (LDPA) can generate both characteristic and Bremsstrahlung x-rays in ultrashort bunches. Because of the high intensity of the laser pulses, these laser-induced x-ray sources can achieve peak dose rates compatible with the FLASH regime. At the Laser Laboratory for Acceleration and Applications (L2A2/USC), a setup for the irradiation of in vitro cell cultures with a laser-driven x-ray source has been developed. The suitability of this source for studying the influence of Ultra High Dose Rates (UHDR) on DNA damage has been proven through the irradiation of in vitro cell cultures.