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A dentinal tubule is a microscopic channel in dentine, within the mineralized material formed by odontoblasts. The tubule network records the paths of odontoblast processes as dentine is deposited. A tubule is a structural channel; whether a prepared specimen contains fluid, a cellular process or an empty space depends on the tissue and its preparation.^[ref]

Elephant ivory provides a useful structural example. In a2017 study, observations of different cut planes and computed tomography using synchrotron radiation connected visible tubule profiles with their three-dimensional trajectories. A tube cut across, along or obliquely does not present the same two-dimensional profile. Consequently, a collection of oval profiles in a section need not consist of isolated oval cavities.^[ref]

A deliberately simplified transport example makes the channel size matter. For steady laminar flow through a straight circular tube, the Hagen-Poiseuille equation gives $Q=\pi r^4\Delta p/(8\mu L)$, where $r$ is tube radius, $L$ length and $\mu$ fluid dynamic viscosity. Doubling $r$ would multiply $Q$ by16 at fixed pressure difference and length. Real dentinal tubules branch, vary in width and may be obstructed, so this ideal calculation illustrates sensitivity to geometry rather than predicting a whole tooth's permeability.

A highly mineralized epithelial product formed by ameloblasts, distinct from dentine. fossil tissue distributions and enamel-matrix gene expression support an ancestry in dermal coverings deeper than its familiar deployment on teeth.^[ref]

Ivory is the dentine material of tusks and certain other large teeth. It is a mineralized biological tissue, rather than the enamel coating of a tooth or an undifferentiated piece of bone. In elephant ivory, mineralized collagen fibres form a spatially organized composite: identifying its chemical ingredients does not specify their arrangement.^[ref]

A 2018 structural study combined X-ray scattering, observations with polarized light and a scanning electron microscope. The measurements found changing fibre orientations from the outside toward the inside of the tusk. Mid-dentine fibres lay mainly along its length in layers with oscillating orientations. The authors related this arrangement and collagen birefringence to the visible Schreger pattern, rather than treating light and dark regions as necessarily different chemical substances.^[ref]

An illuminating comparison is to cut two sections of one oriented composite, one across its long direction and one along it. Their patterns can differ even if their average composition is the same. This geometrical example explains why a section's appearance must be interpreted together with its orientation; it is not a species-identification test.

The distinction between composition and organization also motivates solid-state nuclear magnetic resonance. Historical CPMAS demonstrations included an ivory billiard ball, showing how a rigid biological material could yield chemically informative spectra.^[ref]

Mineralized tissue is biological tissue in which mineral forms a substantial structural component of an organic matrix. Bone, dentine and enamel are familiar examples, but they differ markedly in composition and architecture. In bone, mineral based on hydroxyapatite is associated with a collagen-rich extracellular matrix; biological cells form and maintain that matrix. Mineralization describes a material feature, not the absence of living activity.^[ref]

A mineralized tissue is therefore also a biological composite material. Mineral amount, organic matrix, water, porosity and orientation can each affect the response. The Young's modulus of an entire specimen cannot be inferred from mineral content alone: constituent geometry changes load sharing, just as it does in the isostress rule of mixtures and the longitudinal rule of mixtures. These ideal mixture models clarify the role of geometry without being exact models of a real bone.

Even the phrase “mineral fraction” needs a specified measurement. Consider a hypothetical dry two-component specimen with $6\mathrm{mg}$ of mineral of density $3.0mg/m{\mathrm{m}}^3$ and $4\mathrm{mg}$ of organic material of density $1.3mg/m{\mathrm{m}}^3$. Its mineral mass fraction is $0.60$, but its mineral volume fraction isThese chosen numbers describe a bookkeeping example, not a measured tissue composition. Adding water or pores changes which total volume belongs in the denominator. A mechanical mixture calculation needs the appropriate volume fractions, not a mass percentage silently substituted for them.

An instructive primary structural study examined elephant ivory, a form of dentine, with complementary X-ray scattering, polarized-light microscopy and scanning electron microscopy. The investigators found that mineralized collagen orientations differed between the outer and inner parts of the tusk, including an outer wrapping orientation and a predominantly axial, plywood-like arrangement farther inside.^[ref] The result motivates combining methods: a bright pattern in polarized light, an electron-microscope image and a scattering pattern provide different evidence about the same organized mineralized tissue. Observing orientation is not by itself a direct measurement of its full mechanical constitutive equation.

A specialized cell producing dentine. Its tissue contribution differs from that of an ameloblast.

Sarcopterygii is the clade comprising the most recent common ancestor of living coelacanths, lungfish and tetrapods, together with all its descendants. In this crown-based usage, humans are sarcopterygians: acquisition of limbs and loss of a fish-like outline do not remove descendants from a clade. Extinct taxa assigned along the stem require an explicitly broader total-group usage. A diagnosis lists characters useful for recognizing a group; a synapomorphy is a shared derived character whose position has been inferred on a phylogenetic tree. Those are related but not interchangeable statements.

Two particularly instructive traditional diagnostic features are the fleshy, internally supported paired appendages and true enamel associated with the dentition. The first survives conspicuously in our arms and legs. The second survives in our tooth crowns, although modern evidence requires qualification of its traditional status as an exclusively sarcopterygian innovation.

The paired-appendage transformation. A lobed fin contains musculature and a substantial endoskeleton extending into the appendage. In the relevant ancestral pattern, a single proximal skeletal element connects to the girdle: the humerus in the pectoral appendage, and the femur in the pelvic appendage. Subsequent elements elaborate the jointed internal axis. The important comparison is historical organization and articulations, not merely that both a fin and an arm contain bone. fins in other lineages also possess internal supporting elements, so the presence of any fin skeleton is too broad a diagnosis.

Within the lineage leading to tetrapods, the pectoral series can be recognized as humerus, radius bone and ulna, followed by increasingly elaborate distal elements. Tiktaalik retains fin rays but has a distal jointed skeleton capable of limb-like positioning against a substrate. Its combination of characters shows that parts of a wrist-like support system preceded a fully digit-bearing hand. Comparing several articulated specimens and the geometry of joint surfaces constrains the reconstruction better than matching isolated bones by outline.^[ref]

Further changes included anatomical digits, loss of external fin rays in the limb, changes to the girdles and altered force transmission through the trunk. They did not all arise simultaneously. Early digit-bearing tetrapods were not uniformly five-fingered terrestrial walkers; aquatic settings and polydactyly make it misleading to present the modern human hand as the immediate purpose or original endpoint of the transition. Acanthostega, with eight anatomical digits in its forelimb, supplies a concrete counterexample to an ancestrally universal five-digit condition.^[ref]

Our own upper limb retains the proximal single-bone and paired-bone organization, but the shoulder, elbow, wrist and fingers are extensively specialized. Rotation of the radius bone relative to the ulna contributes to turning the forearm; an opposable thumb and independently controlled fingers support grasping. In the lower limb, the femur, tibia and fibula show the corresponding serial organization, while the pelvis, hip, knee and foot transmit loads in habitual bipedalism. These are derived modifications within tetrapods, rather than defining traits of all Sarcopterygii. Comparing our arm with a fish pectoral fin concerns biological homology between organisms; comparing arm and leg also involves serial homology within the body.

The dental transformation and its qualification. human tooth crowns have an outer layer of enamel over dentine. enamel is highly mineralized and is produced by epithelial ameloblasts, whereas dentine is a different tissue formed by odontoblasts. Identifying a fossil surface as enamel therefore requires tissue architecture and developmental or molecular comparison, not simply a shiny hard covering. In our teeth the coating has specialized organization into enamel rods and contributes to wear resistance during biting and chewing. tooth classes and crown shapes diversify the ancestral feeding apparatus; they are not themselves basal sarcopterygian synapomorphies. After eruption, loss of the enamel-producing cellular layer severely limits biological replacement of worn crown enamel.

The traditional contrast between sarcopterygian true tooth enamel and other hard coverings needs an explicit historical correction. Qingming Qu and colleagues combined fossil histology with evidence for enamel-matrix genes in the skin of gar. In Psarolepis, external odontodes carried enamel while the teeth lacked an enamel coating. Their evidence supported an origin in dermal coverings followed by expansion into the mouth, and an ancestry deeper than Sarcopterygii alone.^[ref] Thus enamel and its oral deployment must be coded separately; tooth enamel remains a useful traditional diagnostic comparison, but the tissue itself is not a uniquely sarcopterygian synapomorphy. Shared tissue can undergo heterotopy, loss and later modification.

The two histories illustrate different forms of transformation visible in our bodies: an internally supported paired fin became a jointed, digit-bearing, specialized limb, and an inherited mineralized epithelial covering acquired a complex role in our dentition. A rigorous diagnosis states the anatomical level being compared and distinguishes inherited organization from later functional specialization. Neither the modern function nor the external human appearance determines membership of Sarcopterygii.

The Schreger pattern is the recurring light-and-dark motif visible in sections of elephant ivory, the dentine of the tusk. Sections across the tusk can show a checkerboard-like motif, whereas lengthwise sections show alternating bands. This is an example of how the appearance of a three-dimensional biological tissue depends on the plane of observation.^[ref]

In2017, a study based on one elephant tusk compared several section orientations with microscopic observations and computed tomography using synchrotron radiation. The researchers related darker regions to dentinal tubules running obliquely to the cut surface and brighter regions to tubules running more nearly parallel to it. They proposed a three-dimensional tubule arrangement to connect those observations.^[ref]

The optical mechanism also involves the surrounding material: a2018 study combined X-ray scattering, polarized-light observations and scanning electron microscopy to investigate mineralized collagen orientations. Its authors proposed that the layered collagen architecture and birefringence contribute to the pattern. Thus a visible band is evidence about structure and light interaction, rather than a direct map of a single chemical constituent.^[ref]