I assume that you mean pre-pay for the expenses in 2017 for a procedure to be performed in 2018.
Yes you can pay for a medical expense in 2017 for a procedure in 2018 and report the amount paid with out of pocket funds as an itemized medical deduction on the 2017 Form 1040 Schedule A. However, only your total medical expenses that are greater than 10% of your Adjusted Gross Income (AGI) can be deducted. Your total itemized deductions reported on Form 1040 Schedule A must be greater than the standard deduction for your filing status to have any tax benefit.
Standard deductions for 2017
I found this wording in IRS Publication 502: "Payments for future medical care. Generally, you can't include in medical expenses current payments for medical care (including medical insurance) to be provided substantially beyond the end of the year. This rule doesn't apply in situations where the future care is purchased in connection with obtaining lifetime care of the type described earlier."
Is substantially beyond the end of the year defined? Or are you usually okay to include pre paid medical expenses?
I cannot find substantially defined. I would think a January procedure would be OK, but not December. Anything inbetween is iffy.
The wording the most recent pub 502 (2019) is different. It states:
"What Expenses Can You Include This Year?
You can include only the medical and dental expenses you paid this year, but generally not payments for medical or dental care you will receive in a future year."
What you can do is pay for the total expected cost of dental expenses like braces or dentures in December even if the work will take more than one tax year. But you cannot prepay for unscheduled estimated costs in the future. The doctor needs to actually accept the full payment ... you cannot just put money "on account" to make a deduction.