The first approach relies on self-organization paradigm in which the local dynamics of cells leads to large scale structures as self-organization patterns. In TGD framework 3-D self-organization is replaced with 4-D self-organizaton (the failure of strict determinism of classical dynamics is essential motivating zero energy ontology (ZEO)). One can speak about 4-D healing: the space-time surfaces serving as classical correlated is as a whole replaced with the original one during healing process: after the healing process the organism was never sick in geometrical sense!
Second approach could be seen as computational. The basic idea is that the process is guided by a template of the target state and morphogenesis and healing are computational processes. What Levin calls morphogenetic fields would define this template. It is known that organisms possess kind of coordinate grids providing positional information allowing cells to "decide" about the profile of genetic expression. In TGD framework magnetic body forming coordinate grid formed from flux tubes is a natural candidate for this structure. They would also realize topological quantum computation (TQC) with basic computational operations realized at the nodes of flux tubes to which it is natural to associate some biological sub-structures.
The assumption about final goal defining a template can be argued to be too strong: much weaker principle defining a local direction of dynamics and leading automatically to the final state as something analogous to free energy minimum in thermodynamics might be enough. Unfortunately, second law is the only principle that standard physics can offer. Negentropy Maximization Principle (NMP) provides the desired principle in TGD framework. Also the approach of WCW spinor field to the maximum of vacuum functional (or equivalently that of Kähler function) gives a goal for the dynamics after the perturbation of the organism causing "trauma". If Kähler function is classical space-time correlate for entanglement negentropy, these two views are equivalent.
TGD thus suggests an approach, which could be seen as a hybrid of approaches based on self-organizaton and computationalism. The magnetic body becomes the key notion and codes also for learned behaviors as TQC programs coded by the braiding of flux tubes. The replication of the magnetic body means also the replication of the programs behind behavioral patterns (often somewhat misleadingly regarded as synonymous with long term memories). This hypothesis survives the killer tests provided by the strange findings about planaria cut into two and developing new head or tail: the findings suggest that behavioral programs are preserved although planaria develops a new brain (see this).
For details see the chapter Quantum Mind, Magnetic Body, and Biological Body or the article "Morphogenesis, morphostasis, and learning in TGD framework".