Hi,
In the due course of time, I have witnessed that, compared to the use of picolasers, such as Picosure and others for tattoo removal, very good or even better results can be obtained with the application of a high quality Q-Switch Nd YAG Laser, using the 1064 nm and the 532 nm probes. I have been using the one from Alma Lasers, namely the Q-Switch Nd YAG Laser on Harmony XL Pro and I have never seen any such problem arising as residual stubborn black ink. By the way, black is the color that disappears the fastest. Next, the average number of treatment sessions for tattoo removal is normally between 7-10 but with this technology this number is even decreasing to between 3-7 as per my personal experience.
Therefore, I believe you won't need so many sessions as you did with Picosure.
Please look for a doctor who is a laser expert doing the job. In case of unexpected resistance to treatment, he/she could also consider to combine the Q-Switch Nd YAG laser treatment with iPixel Er:YAG or Pixel CO2 fractional laser treatment (in alternate sessions) in order to make the tattoo disappear faster.
Proper application of post-treatment medico-aesthetic products is a must for protection from infection (application of a sterile dressing medicated with an antibiotic cream followed by a corticosteroid cream for a short time period until the immediate after effects on the skin are over), moisturization for rapid evacuation/elimination of ink pigment micro-particles (regular application of a hyaluronic acid moisturiser and drinking enough water - on the average 2 to 3 liters daily) and for protection from the sun (regular sunscreen application). All these precautions for post-treatment skin care help the skin to return back to normal quickly with a rapid loss of ink pigments, hence diminishing the number of treatment sessions to a minimum.
Hope this helps.