I haven't heard back from you, but I do want to leave some thoughts about Tarn's situation. If you can answer the questions above, it will aid me in helping you narrow down the potential causes for her thinness and failure to gain weight. Still I do hope my thoughts help guide you on how we should approach this for Tarn.
Thank you for the additional information.
When we see cats either losing weight or failing to gain weight despite having good appetite and being on a good quality diet, this can suggest a range of issues.
First, with her good appetite, this makes an ‘input’ issue less likely here. Therefore, we’d need to focus on differentials that would cause her to lose or burn up her nutrition such that she fails to devote her food intake to putting on weight and body condition. In regards to common causes in a cat her age, we’d have to consider nutrition loss via parasitism (ie GI worms, protozoa, etc), GI/fecal or urinary protein loss (ie diarrhea, vomiting, urinary protein loss secondary to kidney damage), and metabolic or systemic diseases (ie hyperthyroidism, kidney disease, liver disease, and diabetes). As well, while it isn't nice to think about, we must keep in mind that cancer in cats her age can manifest as weight loss with little other signs (just as it doesn't impinge on the body, only to steal nutrients from her).
Therefore, with all this to consider, I would suggest that the first step here would be to worm her. Ideally, you want to use a good quality broad spectrum wormer. There are a range on the market, but you want to use a good quality wormer that covers both round worms and tapeworms (either OTC from your vet or pet store) In this situation, it would be ideal for you to treat him with Panacur, Drontal (LINK) or Milbemax (LINK) as it will cover all the worms in question. Do make sure to have an idea of her weight before purchase wormer to make sure you get the correct dose for her size.
If you rule out worms and she doesn’t have any of those other aforementioned signs, but Tarn still isn’t gaining weight, then you would want to consider a check up with her vet to rule out the other concerns for her (if she is due for a vaccination soon, you could move it up a wee bit early and have her checked out at that time). The vet will be able to have a feel of Tarn and just make sure there are no sinister lumps and bumps to blame for the weight loss. And if you were able to bring in a urine sample at that point, the vet could check it for signs of diabetes (ie. sugar in the urine) as well as check its specific gravity (how concentrated it is) that can tell us if there are problems with his kidneys troubles are lurking. Urine samples can often be collected by placing the cat in a carpet-less room with an empty (or with non-absorbable litter) litter box overnight.
If after the vet's examination, hyperthyroid or any systemic issues are suspected, then you may want your vet to check a blood sample. This can tell you if she has any issues with her thyroid, or if she has an elevated blood sugar, liver and kidney parameters checked at the same time, giving you a good chance of ruling out the above differentials and determining which was the cause of her abnormal weight loss.
As well, at the same time, you can also take steps to increase the nutrition that Tarn is taking in (even if she doesn’t want to eat more for you). To do this, you can supplement her with Hill's A/D (LINK) from your local vet. This is a critical care diet that is comes as a soft, palatable pate. It is calorically dense, so a little goes a long way nutrition-wise and this could just help get some more calories into her even if we can’t get a huge volume of food in. Alternatively, you can use the animal version of Ensure (balanced for animals dietary requirements) called Clinicare Canine/Feline Liquid Diet (LINK)). It is actually by the same people who make Ensure, but is formulated to meet out pet's dietary needs. Your vet should be able to order it for you but it is available without a prescription (some pet stores and even Amazon stock it as well). It would just be another way to get more nutrition into Tarn to try to increase her weight.
Overall, there are a few differentials to consider here for her. Therefore, it is worth ruling out worms and monitoring her for any of those signs I have noted above. If you worm her and she is giving you no hints of what could be causing her loss, then an exam and a blood (or urine) sample to help you pinpoint which is to blame. And the sooner we determine the cause for her thinness, the sooner we can help deal with this and get some weight on Tarn.
I hope this information is helpful.
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