Spending a long time in weightlessness is unhealthy. One of the

most important negative effects experienced by astronauts is a loss of
muscle and bone mass. Since an ordinary scale won’t work for an astronaut
in orbit, what is a possible way of monitoring this change in mass?
(Measuring the astronaut’s waist or biceps with a measuring tape is not
good enough, because it doesn’t tell anything about bone mass, or about
the replacement of muscle with fat.)

A centrifuge with a strain/stress gauge could be used, or the frequency of vibration on a spring could be measured.

The article at the link shown below describes the method actually used by NASA:

http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm

One possible way of monitoring the change in muscle and bone mass for an astronaut in orbit is by using a dual-energy X-ray absorptiometry (DXA) scan. Also known as a bone density scan, this medical imaging technique measures the density of bone and can determine changes in bone mass over time.

To perform a DXA scan, a specialized machine sends two low-dose X-ray beams through the body, typically targeting the hip and spine, but can also measure other body areas. The machine then calculates the amount of X-ray that is absorbed by the bones, providing information about their density and strength. This data can be used to assess bone mineral content and detect any loss of bone mass.

While a DXA scan primarily provides information about bone mass, it can also indirectly help analyze changes in muscle mass. Since muscle mass and bone mass are closely related, changes in bone density can reflect changes in muscle mass as well. However, it's important to note that a DXA scan is not specifically designed to measure changes in muscle mass, so other methods might be employed to supplement the data.

In conclusion, a possible way of monitoring changes in muscle and bone mass for astronauts in orbit is through the use of a DXA scan, which primarily measures bone density but can also provide information about muscle mass indirectly.