Here are some tips:
1) Start with a short 1 sentence intro.
2) Get right to the point quickly in a clear and easy to understand way. Eliminate all long winded and/or confusing language.
3) Most people will be very wary of clicking links in a cold-call email. Partially because it would take time, and partially because of scam wariness. To get around that negative bias, include a professional looking screenshot of your SaaS and anything else that would convince them that you're legit and that they'd want to use it (1-2 screenshots, 1-3 main features, 1-3 positive reviews, logos of any online news/blog coverage). Have all of this be in-line, not as attachments.
To facilitate their demo call booking, use YouCanBookMe (https://youcanbook.me/). They'll see a simple calendar with times they can book for a demo, without any need to email or call you back to set up a time.
4) If allowed in this project, look into other routes other than emails. For instance:
A) Post it to relevant subreddits (https://www.reddit.com/r/doctors/, etc.).
B) If possible, mail a small gift (e.g. a small chocolate) to your potential leads, and have a note on the chocolate with an intro and a link (use an URL shortener) and/or QR code. Even if they don't go to the link on the note, you could do a follow up email in which you mention that you previously sent them the gift, which will increase your success.
If you'd like to discuss other techniques more tailored to your specific product let me know,
You could offer a reminder, with a calendar entry to make it easy for them.
I'd offer a bonus to keep them engaged, such as a cheat sheet or a compelling case study. For example, tell a story of a patient who went from before to after, and spell out the patient's experience from "My knees were so bad, I couldn't get out of bed" to "I won the Olympic 100 metre sprint". If it's a short video, even better.
Doctors, from my experience, are not impressed by more statistics, or at least not engaged by them. But how this SaaS experience meant that Mrs Johnson never missed her appointment (because it sent her a reminder), or how Mr Smith didn't have to wait around for that old clunky patient CRM system that was keeping the waiting room crowded out, can be more attractive to the doctor.
In other words, you're not selling the solution for the doctor or the clinic; you're demonstrating the improved experience for the patient. Tell the patient's story, and the doctor is more likely to accept that calendar invite for the demo.