@Jamie I came home with exercises and PT brought some. Are these okay?
Heel slides incl using a leg lifter to help
Sit on chair, put operative foot back as far as possible. PT said my they or my husband could help it go back; I said no (this can hurt if I push)
Put roll under ankle while sitting to encourage leg to straighten
While at sink, slight knee bends
While at sink, march
Sit on chair, bend leg up and down (this one hurts)
Straight leg raises
We have two steps: put operative leg up and lean forward
That’s about all they have me doing plus walking inside and out.
I feel some portions of the list you provided might lead to problems with pain and swelling, especially in the first couple of weeks after surgery. After all, your knee must heal first before you attempt anything like strengthening or muscle-building! The biggest part of the equation is how much of each of these you were advised to do as well as the way you do them. I had some similar exercises from my excellent therapist following both my knee replacements that I did 2-3 days a week when she came. Then I did a couple of them on my own several times a day for very short periods. The rest of my "exercise" was getting up and down from a chair or the bed and walking from room to room. After a couple of weeks, I added short periods on my recumbent bicycle with no resistance. At first I just rocked the pedals back and forth, as I couldn't do a full rotation even with the seat adjusted way back.
Here is my opinion on the list you were given:
Heel slides - I did short bursts of these in bed, lying on the couch, sitting in a chair, or on the toilet. But no one ever pushed on my leg and I never used any device to push myself. I just went to the point where the discomfort started and then extended. I did this multiple times a day for a couple of minutes, especially if my knee felt a bit tight. It was a good stretch that made me feel better.
Pull leg back while sitting in a chair - I did this throughout the day on a chair or the toilet, with 3-5 movements of my leg each time. It's also a stretch and you don't need to do a whole course of 10 or more for it to be effective. I only went as far as the point where some mild discomfort was starting, held it for maybe a count of 10 and then extended the leg again. I never used any devices to get more bend.
Roll under your ankle while sitting - You can do this if you are trying to improve extension. But again, don't go past any mild discomfort and wait a couple of weeks to start it. I found this to be really uncomfortable and instead chose (after the first 2 weeks) to lie on my tummy on the bed with my knee joint just past the edge of the bed with my lower leg extended in the air, foot pointed down. At first I could only do this leg hang for maybe 15 seconds before it started to become uncomfortable. I gradually and slowly worked up to about 10 minutes and felt this exercise plus my walking helped improve my extension.
Slight knee bends - this is what is termed a "mini or narrow squat" and it mimics the action you must have when sitting or rising from a chair. Holding on to the counter helps with stability and control. There is an image of this exercise in the article Jo linked for you (I copied it below). If you do this one, it's important to push your rear end out and keep your weight forward over your feet. I did no more than 10 and not every day. I'm not sure how beneficial this was as I was moving about each day and getting up and down.
Marching at the sink - I would do this only when the therapist came and only in such a way so there was no pain at all. Holding on to the counter for stability was helpful for balance. Frankly, I'm not sure this exercise was all that much benefit.
Straighten leg while sitting in a chair - I did this one only when the therapist came and only after the second or third week into recovery. If you choose to do this exercise, don't make movements that hurt or do so many repetitions that you feel pain. As with the marching, I didn't feel this exercise did much for me that walking couldn't accomplish.
Straight leg raises - I didn't do this exercise at all once I left the hospital and I see no value for you in doing it. Some therapists will tell you it is to strengthen your quad muscles, but in these early weeks of recovery strengthening is not something to be worried about. That comes later 3-6 months after your surgery when your tender tissues are healed.
Leaning into your operated knee on the steps - my therapist didn't give me this exercise, but I did it on my own. I found it a good way to do a controlled bend and stretch with my new knee and, for me, it was one of my go-to movements when my knee was feeling a bit tight. I used this and short periods (2-3 minutes) on my bike primarily once the therapy visits stopped.
I was icing almost all the time both day and night which I believe helped keep the swelling down. I also did some mild massage on my leg a couple of times a day, rubbing in circular motions from the knee up to the thigh. This is called lymphatic massage and it can help move fluid (swelling) away from your knee.
Remember that your recovery is unique to you. It's important that you listen to the signals your knee is giving you about when to exercise it and when to back off a bit. The idea is to start slow with any movement or activity, wait a day or two and see what happens. If you experience pain or swelling, you're not ready for it quite yet. Stop and try it again later. Expect to have good days and bad days. Recovery is not a linear process. Most of the time any pain or swelling from over exercise or too much activity won't occur right away. In fact, your knee could feel absolutely wonderful as you're doing the activity only to swell and hurt 24-48 hours afterwards. That's your signal you overdid it and rest, ice and elevation are in order for the next day or so until you can start again at a lighter pace.
Many people do just fine with no more exercise than their activities of daily living. Others prefer some moderate, structured exercise (what we term "gentle exercises") and still others feel the need for a more aggressive approach to post-op exercise. The key to success is not really what you do (because everyone is different), it's the impact that what you're doing has on your body and how you react to that message. A few people here on BoneSmart have been able to practice what we would term very aggressive therapy and recovered just fine. Some do no activity and recover just fine. Most people are somewhere in between and just need to be mindful of any pain and swelling when it occurs and take the appropriate action (hint: it's not to push harder!

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Best of luck to you and don't hesitate to ask any questions you may have as you go along. We're here to help you.