Why it is necessary to couple muscle building with bone growth in many grow taller methods

For several methods to build bone and the methods applicable for growing taller it's almost impossible to build up bone without building some muscle up as well. It's possible, to provide the forces needed to build bone without weight via "tapping"(hitting the bone with weights or a hammer) or limb lengthening surgery but then you aren't using all the possible forces on bone you can to cause microfractures(compression, strain, spiral, and impact). And in any case many of the bones are "blocked" by muscle in order to tap the bone you also have to tap the muscle as well(tapping is a bit of an underhyperbole as you want to tap as hard as you can without causing nerve damage).

Now, via Lateral Synovial Joint Loading you are putting load on the ends of the bones lateral to the joint area to provide a stretching force along the entire bone.  But, you need muscle in order to control the weight that you're using to provide the downward forces or you need muscle to help protect your tendons and ligaments from injury if it's an external force providing a stretch with downward pressure on the ends of the bones.

In addition, it is also possible to grow taller via an increase in periosteal width in the short and irregular bones.  You need to use weight to create the shearing forces on the short and irregular bones to increase the periosteal width and you need muscle to stabilize your body so you don't, for example, herniate a disc due to a lack of support.

Also, another method for growing taller is via knee microfracture(and microfracture in other areas) in order to release stem cells that exist within bone marrow that stimulate cartilage growth when provided with blood.  The more muscle you have the more force you can generate to create knee microfractures.

In regards to nerve damage, yes their are nerves that are inside the bone but it doesn't necessarily mean you are damaging them. Imagine a wall with electrical wires inside of it, if you bang on the wall you only hurt the wall and not the electrical cables inside of it. The skeletal tissue of the bone will absorb the impact. It's important that you do any tapping yourself, the punch that hurts the most is the one you don't see coming as they say and if you tap your own bones you learn how hard you can tap safely.

Let's address two possible ways to provide forces on bone: Strain fractures via hanging and compression fractures by holding a weight on your back (i.e. in a squat position). If you try to take a weight that you can't handle the golgi tendon will send a signal to your muscle telling it to relax(this is the basis behind massage) and you will not be able to do the "exercise" for very long and you won't cause very many microfractures. You need to do an exercise with a weight that your body will allow you to handle(sometimes this can be quite heavy) so you can continue to progress in weight and cause more microfractures which are necessary to grow via the articular cartilage method and may be necessary to grow taller via distraction forces on the long bones.

We want to try to maximize the forces we place on the bone when we perform exercises designed to increase their size. So, for example when he hang we should also twirl around which generates spiral and shearing forces on the irregular bones of the spine. And, when we perform a walkout in the squat rack to generate compression forces on the irregular bones we should also stomp to provide additional impact and shearing forces on the knee and the bones of the spine.

If your muscles aren't strong enough for the golgi tendon to allow them to go, you'll only be able to perform the exercises for 2 to 3 seconds rather than the perhaps 20 if your muscles(and CNS) are strong enough to allow the exercises to be fully performed. In addition, your muscles(and CNS) won't adapt and you won't be able to move on to higher weights.

Muscular conditioning is also important. You need to train frequently enough so your muscles adapt and are harder to damage thus more of the forces you want can be targeted to the bone and less to the muscle. We want inclusion of bone not exclusion of muscle. There is no such thing as an "isolation" exercise.

We are just trying to specialize our training to gain height rather than excluding forces that damage the muscle entirely.

It's not an LSJL lengthening study but it still provides insights into LSJL and it might help provide more insight into how to perform LSJL.  Although the loads are axial loads rather than lateral loads.  Also, remember that providing pressure on the muscle increases hydrostatic pressure in the bone.

Mechanical loading, damping, and load-driven bone formation in mouse tibiae.
"Loading can activate anabolic genes.  We investigated the damping capacity of bone, joint tissue, muscle, and skin using a mouse hindlimb model of enhanced loading in conjunction with finite element modeling to model bone curvature. Our hypothesis was that loads were primarily absorbed by the joints and muscle tissue, but that bone also contributed to damping through its compression and natural bending. To test this hypothesis, fresh mouse distal lower limb segments were cyclically loaded in axial compression in sequential bouts, with each subsequent bout having less surrounding tissue. A finite element model was generated to model effects of bone curvature in silico. Two damping-related parameters (phase shift angle and energy loss) were determined from the output of the loading experiments. Interestingly, the experimental results revealed that the knee joint contributed to the largest portion of the damping capacity of the limb, and bone itself accounted for approximately 38% of the total phase shift angle. Computational results showed that normal bone curvature enhanced the damping capacity of the bone by approximately 40%, and the damping effect grew at an accelerated pace as curvature was increased. Although structural curvature reduces critical loads for buckling in beam theory, evolution apparently favors maintaining curvature in the tibia. Histomorphometric analysis of the tibia revealed that in response to axial loading, bone formation was significantly enhanced in the regions that were predicted to receive a curvature-induced bending moment[maybe there's less damping effect for lateral rather than axial loads which could be why lateral loads induce different gene expression]."

"Damping is the potential of the whole musculoskeletal system to effectively dissipate energy associated with loading."

"Loads of 5 N at 0.5, 2, and 20 Hz were applied to this FE model for 10 s"

"The ratio between the phase shift angle of stage V (bone alone) and stage I (intact hindlimb) demonstrated the influence of the tibia alone. This ratio was 43% at 0.5 Hz, 38% at 2 Hz, and 28% at 20 Hz. Removal of the ankle, skin, and muscle exhibited the smallest effects on phase shift angle, contributing to approximately 14% of the total phase shift at each frequency."<-So most of the load absorption is by the bone.

"While similar trends in energy dissipation are seen in response to 2 and 20 Hz waveforms, the magnitude of the energy loss in each sample configuration decreased monotonously as the frequency was increased."

"Skin was found to contribute to approximately 12% of the total dissipated energy at all frequencies, and the remaining energy was lost with removal of the muscle and foot."

"it has been proposed that the curved shape of long bones, while reducing overall axial strength, increases predictability and better distributes stresses within the bone during loading"<-maybe axial loading  increases bone curvature thereby reducing height?

The role of muscle cells in regulating cartilage matrix production.

"We tested the hypothesis that muscle cells directly regulate cartilage matrix production by analyzing chondrocytes cocultured with muscle cells in 2D or 3D conditions. We found that chondrocytes cultured with C2C12 muscle cells exhibited enhanced alcian blue staining and elevated expression of collagen II and collagen IX proteins. Although nonmuscle cells did not promote cartilage matrix production, converting them into muscle cells enhanced their pro-chondrogenic activity. Furthermore, muscle cell-conditioned medium led to increased cartilage matrix production, suggesting that muscle cells secrete pro-chondrogenic factors. Taken together, our study suggests that muscle cells may play an important role in regulating cartilage gene expression."

"Mouse mutants that lack muscle-specific proteins such as dystrophin/utrophin or myogenin also exhibited skeletal abnormalities such as a curved spine or a reduced size of the skeleton"

"C2C12 muscle cell have an elongated, fibroblast-like morphology, while RCS chondrocytes are rounded in shape. When co-cultured, DiI-positive cells still have the fibroblast-like morphology, while all unlabeled cells maintain a round morphology. This indicates that muscle cells and chondrocytes do not change their morphology upon co-culturing"

"upon co-culturing, muscle cells herd the chondrocytes into clusters and the chondrocytes assume a rounder phenotype. Furthermore, chondrocytes (RCS) co-cultured with mouse C2C12 muscle cells expressed higher levels of collagen II and collagen IX proteins"

"muscle secretes a variety of growth factors or cytokines that can be carried away by blood or interstitial fluid. Among them is the known pro-chondrogenic factor IGF-I"

Bone, muscle, and physical activity: structural equation modeling of relationships and genetic influence with age.

"Quantitative trait locus (QTL) analysis was used to identify regions of chromosomes that simultaneously influenced skeletal mechanics, muscle mass, and/or activity-related behaviors in young and aged B6xD2 second-generation (F(2)) mice of both sexes. SEM was used to further study relationships among select QTLs, bone mechanics, muscle mass, and measures of activity. The SEM approach provided the means to numerically decouple the musculoskeletal effects of mechanical loading from the effects of other physiological processes involved in locomotion and physical activity. Muscle mass was a better predictor of bone mechanics in young females, whereas mechanical loading was a better predictor of bone mechanics in older females. An activity-induced loading factor positively predicted the mechanical behavior of hindlimb bones in older males; contrarily, load-free locomotion (i.e., the remaining effects after removing the effects of loading) negatively predicted bone performance. QTLs on chromosomes 4, 7, and 9 seem to exert some of their influence on bone through actions consistent with Wolff's Law."

Here's a diagram of how muscle may interact with bone:

Although body length is used as an independent predictor.

MyoD1 and IGF1R are two genes mentioned as being associated with muscle and bone.