Does Bone Mineral Density affect Height?

Previously, it was though that bone density did not affect height and could only lower height by bone deformities.  However, this study suggests otherwise:

Usefulness of estimated height loss for detection of osteoporosis in women.

"Most of us are the tallest at around 30-35 years old because of the peak bone mass at that time"<-This suggests that higher bone density increases height.  If the authors of the study didn't believe that then they would have suggested that peak height is at age 25 or so.

"A lower bone mineral density had a greater influence on height loss in the femur than in the lumbar vertebrae"<-this is surprising as you'd expect it to have more of an impact in the vertebrae as weak vertebrae would result in poorer posture and thus lower height.  This leads credence to the theory that bone density has more impact on height than just bone strength influencing posture.  Bone Density may have a direct affect on the length of the bones.

The scientist who made these assertations is Yeoum SG.

Longitudinal change in height of men and women: implications for interpretation of the body mass index: the Baltimore Longitudinal Study of Aging.

"Among both men and women, cross-sectional height decreased with age"<-Including between 20 and 35.  However, the change in height between 20 and 40 is very small so it could be related to measurement or study error.  Other data in the study suggest an increasing slope in height between the ages of 17-30(Figure 2).

Increased physical activity is associated with enhanced development of peak bone mass in men: A five year longitudinal study.

"Peak bone mass is believed to be achieved before the end of the third decade in life, depending on 

bone site"<-So before age 39.

"Previous intervention studies in children, adolescents and young adults have reported that physical activity interventions result in increased bone mineral content (BMC), areal bone mineral density (BMD) and cortical bone size."<-So if exercise increases BMC and BMC increases height then exercise will increase height.

"For each hour of increased physical activity, aBMD of the lumbar spine and BMC of 

the total body increased with 0.005 g/cm-squared and 5.4 g, respectively, while cortical cross sectional 

area and total cross sectional area of the tibia increased with 0.36 mm-squared and 0.49 mm-squared,

respectively, between the baseline and follow-up visits"

In the study, the individuals who exercised 4 or more hours per week but hardly exercised at all went from an average of 182.4 height to 183 height.  With the mean age being about 18.9 at the start so natural growth cannot be excluded.  Those individuals who exercised before the study and stopped still increased average height from 181.3 to 181.8.  The individuals who exercised before the study and continued throughout the study had the exact same height growth of 181.3 to 181.8.

So perhaps the people who stopped the exercise maintained the benefits of 0.1cm in height.  The sedentary individuals who stayed sedentary went from 181.7 to 182.2.

Thus, exercise may add at least 0.1cm as individuals who added exercise grew 0.6cm over individuals in all other groups who only grew 0.5 cm.  Additional exercise may add additional height.  A confounding variable however is that the sedentary individuals who added exercise were taking 100mg more calcium then everyone else.  But Calcium relates to Bone Mineral Content so it still shows a trend of Bone Mineral Content being able to increase height.

The BMC increased by 5.4g for each hour of exercise between baseline and follow up visits.  The grew that grew the most exercised for 6.2 hours.  However, the group that started exercising for over four hours a week and ended exercising over four hours exercised for 7.9 hours and gained less height.

Here's another study that shows height loss in adults, unfortunately I could not find the full study for this:

Longitudinal shrinkage in lower legs: "negative growth" in healthy late-adolescent males.

"Forty-one healthy male subjects, aged 15.7 to 19.8 years participated in a study on lower leg length (LLL) growth, body height and weight increments. All subjects were measured and weighed at weekly intervals over a period of one year. Body height was determined by an anthropometer, body weight by conventional scales, and LLL was measured by a hand-held knemometer. The state of maturity of the proximal tibial epiphyses was determined by magnetic resonance imaging (MRI). Skeletal maturity was independently assessed by two radiologists. The growth plates were categorized as being open (category I), centrally but not completely fused (category II), or completely fused (category III).
Our findings demonstrate that in these adolescents, final tibial growth is characterized by longitudinal shrinkage. As shown in the MRI, when the proximal tibial growth plates have fused (i.e., at an age when lower leg growth is commonly believed to have completed), the lower leg of healthy adolescent males begins to shrink with a negative growth rate of -2.4 (SD 2.1) mm/year.
We assume that the final period of growth includes small reductions in bone length, possibly due to stabilization and rearrangements in the formerly growing cartilaginous tissues[so essentially bone modeling reduces height?]."

The height reduction with age is not likely related to something that varies like bone modeling but rather something like bone mineral content which decreases linearly with age.

There is not likely a linear relationship between BMC and height but rather a threshold value of BMC to maximize height.  Supramaximal values of BMC will not increase height past a further point.