There is provided an electrically heated aerosol-generating device (100) for use with a consumable cartridge (200) comprising a storage portion (202) containing an aerosol-forming substrate and having a fluid permeable internal surface surrounding an open-ended passage (208) extending through the cartridge. The device includes a housing (102) having a cavity (108) for receiving the cartridge, and a heater assembly (300) positioned in the cavity comprising an elongate support member (302) connected to the housing and arranged to extend into the open-ended passage of a cartridge inserted in the cavity, and a plurality of electric heaters (400) fixed to and spaced along the length of the elongate support member.. The device also includes a power supply (104) connected to the heater assembly and electric circuitry (106) configured to measure one or more electrical parameters of the electric heaters and to calculate an estimated remaining amount, or an estimated distribution, of aerosol forming substrate in the cartridge, based on the measured electrical parameters. A consumable cartridge (200) for use with the device, an electrically heated aerosol-generating system (10), and a kit for an electrically heated aerosol-generating system are also provided.
