Limb development: getting down to the ground state

Gastrulation establishes the three primary tissues of an embryo: the ectoderm, mesoderm, and endoderm. This developmental process relies on a series of intricate cellular movements, which in humans transforms a flat, “bilaminar disc” composed of two cell sheets into a three-tiered structure. In the resulting embryo, the endoderm serves as the bottom layer, and stacked directly above it is the intermediate mesoderm, and then the uppermost ectoderm. Respectively, these tissue strata will form...

The femur is the body's longest and strongest bone spanning the thigh region. Its head articulates with the acetabulum of the hip bone to form the hip joint. A minor indentation on the medial side of the femoral head, called the fovea capitis, serves as the site of attachment for the ligament of the head of the femur. This weak ligament spans the femur and acetabulum and supports the hip joint. The narrowed region below the head is the neck of the femur. The inclination angle between the neck...

The tibia is the main weight-bearing bone of the lower leg. It is larger than the fibula with which it is paired. The tibia is also the second longest bone in the body and is located right below the skin. The proximal end of the tibia forms the medial and the lateral condyle, which articulates with the condyles of the femur to form the knee joint. Between the articulating surfaces is the irregular elevated area known as the intercondylar eminence that serves as the inferior attachment point for...

The upper and lower limb initially develops as a small bulge called a limb bud, which appears on the lateral side of the early embryo. The upper limb bud appears near the end of the fourth week of development, with the lower limb bud appearing shortly after.
Initially, the limb buds consist of a core of mesenchyme covered by a layer of ectoderm. The ectoderm at the end of the limb bud thickens to form a narrow crest called the apical ectodermal ridge. This ridge stimulates the underlying...

Joints form during embryonic development in conjunction with the formation and growth of the associated bones. The embryonic tissue that gives rise to all bones, cartilage, and connective tissues of the body is called mesenchyme.
The mesenchymal stem cells differentiate into chondrocytes that form the hyaline cartilage, and later the cartilaginous model of the bone. This model further transforms into a bone. This process is known as endochondral ossification.
During development, the limbs...

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...