1. Stepwise substantiation:

The cardiovascular system becomes a progressively substantiated design of the vector field of divergent distribution in the nutrition system.
   The peculiarity that front part of intestine in bivalves goes right through the heart (Ez) could be taken as a particular manifestation of this close relation.
   As mentioned earlier a branched front part of intestine may replace a blood system in certain of the simplest invertebrates.
   In simple species the circulation of the nutrient fluid is also performed by amoeboid cells and /or by contractions of muscles, before development of a blood system.

Among types of tissues (file Levels) fluids became the 5th "tissue" at the final step. Blood cells derive from mesenchyme cells and reticular tissue, next last tissue type. Later blood is produced from bone, also a supporting tissue of reticular type.
   (The fact that blood cells come to lose their nucleus might be a result of their character of last step in a chain of tissues, anticenter in the dimension model: their function as only transporting vehicles?)

2. Geometry in the development:

The development of the blood system is a typical example of a process through geometrically increasing dimension degrees (d-degrees) as in steps 0 →> 1 →> 2 →> 3 →> 4:

~ 0: scattered blood islands from free mesenchyme cells, migrating inwards,
~ 1: blood islands aggregating to strings,
~ 2-3: strings developed into tubes, where outer cells form inner wall of the vessel           (endothelium), and inner cells become blood corpuscles.
Channels curve in convolutions through opposite directed currents:
~ 3: swellings grow together into a central organ, a heart,
~ 4: a pump with currents outwards - inwards as a two-way directed vector field of d-degree 4 in terms of the dimension model.

Fig Bl-1-39-1

The transformation of the blood canals to a heart has perhaps (?) similarities with what plasma physicists call "two streams instability" (Frances F. Chen: Introduction to Plasmaphysics, 1977): according to the author a state difficult to analyze. The function has a gap at vx = 0. (So has life when the heart stops!)

We can observe the geometry:
- Upper, dorsal side, representing primary 00-pole: direction of the blood stream backwards (~ inwards).
- Lower, ventral side, representing primary 0-pole: direction of blood stream forwards, (~ outwards).
   Swellings of the S-shaped curve form through a kind of overthrust upper and lower heart (atria - ventricles):
      

Fig Bl-2-40-1

3. Evolution of heart chambers:

In a simplified description the evolution goes from a 2- to 3 - to a 4-chamber heart, as gradual steps of polarizations.
   A 2-chamber heart is found in mollusks and among chordates in bonefishes (Fc p. 660).

The evolution among chordates goes from a tube-shaped heart in lancelets and proceeds to a 3-chamber heart in amphibians, a "3.5"-chamber heart in most reptiles (2 atria and a not quite divided ventricle) and to the 4-chamber heart in birds and mammalians with complete division between the arterial blood in the left half, venous blood in the right half.

(Biologists may argue that a 4-chamber heart was triggered by life on land requiring lungs and with that a double circulation, but one could imagine the reverse: that dimensionally given polarization steps led to both lungs and the subsequent double circulation, which allowed the general upward direction from sea to life on land and in air. Why didn't animals stay in the water?! )


4. Heart in humans:

Divisions of the 4-chamber heart agree with the polarizations in coordinate axes of the embryo: Front - Back (from Animal - Vegetative poles) and Left - Right.
   Two divisions give 4 parts, the atria and ventricles, and diagonally as in 45° in complex combination the big systemic circuit and the small pulmonary circuit.

Fig Bl-3-41-2

There are notable details that seem derived from those primary poles.
   The coordinate axes Front - Back as derived from A-V-poles represents a secondary axis 00 <=====> 0 (file Embryology. This implies in terms of the dimension model that we get
- outward direction from the ventricles that have the lower, rear position, corresponding to original vegetative 0-pole, with blood forced forwards towards the 00-pole,
- inward direction from atria that have the upper, front position, corresponding to original animal 00-pole, with blood forced downwards, backwards towards the center pole.
   This in spite of the fact that it entangles the connection to blood canals.

We have also that it is the ventricles (from 0-pole) that during evolution get divided later. (Polarizing force from anticenter in our model.)

The very triangular form of the heart as a whole corresponds to a 0-00-polarity with apex as center closer the back pole, the breadth at the front. Apex is also turned more to the ventral side.
   The heart as a 3-dimensional organ, polarized mass (muscles) — space (with blood), shows also the radial structure (pole 3b in the dimension model) in its papillary muscles that depart from near bottom of ventricles (the apex).

Another detail is that the right ventricle is partly bent around the left one (Mf p.105), which seems guided by the venous direction inwards, hence reflecting the function of 00-pole as anticenter and inward direction in relation to the 0-pole as center and outward direction.
   A similar feature is that atria from inward direction have thinner walls (highly expandable) and can be more flattened (Aph) - as d-degree 2 in relation to ventricles of d-degree 3 with the aspects here.

Still another, similar feature is that the channels for flows outwards from both ventricles are centered at the median of the heart, while the inflows are peripherally located: also a feature of center - anticenter relation.

In addition, the fact that inflows (have to) pass an antechamber before entering ventricles, while the outflows go directly to canals, can be interpreted as an illustration of origin of directions in a dimension chain:
- Inflows via atria as 3-dimensional rooms, i.e. from anticenter and lower d-degree towards d-degree 4.
- Outflows from higher d-degree 5 and 0-pole to d-degree 4 and straight to canals that can be regarded as substantiated structures of d-degree 4b.

Valves:
The aortic and pulmonary valves for outflows are both 3-lobated, the half-moon shaped cusps.
   The valves for inflows however differ in a way that seems to reflect the opposition between the big systemic circuit and the small, pulmonary one. It's
   3-divided in tricuspid valve for venous blood from the big body circuit,
   2-divided in bicuspid valve for the small circuit with blood from lungs.
It happens to correspond also in number with our interpretation of the coordinate axes (file Embryology) as representing d-degree 3, Font - Back, and d-degree 2, R - L respectively.
   It's surely interpreted in other, more physical terms by biologists. Yet, there is the similar 3-2-relation between lungs: right lung with 3 lobes, left lung with 2 lobes. (A division of number 5!) Hardly referable to the same physical causes. Neither could the fact that 2/3 of the heart is located on the left side of the middle be an explanation. Why this asymmetry? It indicates sooner that asymmetries appearing along the coordinate axis L - R have a deeper root, inherited from original complementary poles of higher d-degrees in terms of the dimension model. There is the asymmetry too in ways of arteries to head and body (as there is between the cerebral hemispheres).

5. Canals - the vascular system:

The big, systemic circuit is mainly branched 180° along the F-B-axis (front - back). The small pulmonary small circuit to the paired lungs branches naturally along the R-L-axis (right - left).
   With the earlier view on these axes as representing d-degrees 3 - 2 it could be noted that it's connected with the d-degree step in phases: between exchange of chemical molecules in the big circuit and of gases (CO2 - O2) in the small circuit.

Number relation 2 - 1:
Arteries and the deep veins are together enclosed in a capsule of connective tissue as an expression for the two-way Direction of d-degree 4.
   Often 2 veins go parallelly with the one artery, a number relation 2 to 1 between inward direction from 00-pole and outward direction from 0-pole. These data concerns humans.
      Fig Bl-4-42-2

Similar 2-1 relations appear in the canals of lancelets, the simplest chordate with a developed blood vessel system:
   Ventral canals, both front and back parts, are single, unpaired canals.
   Dorsal veins are paired. So is front part of dorsal artery canal, not its back part (resembles a fork).
   Dorsal side represent primary anticenter, the animal 00-pole, the front part the secondary anticenter (00') in the embryological development. Hence, the doubling of canals (veins) or branching of canals (arteries) seems guided by the 00-pole, in opposition to ventral 0-pole representing singularity. The opposition 2 - 1 affects both axes: Distal - Ventral and - in distal artery - the Front - Back axis. (A simplified figure below after Kz p. 19.)
   In the dimension model the 00-pole, from which follows inward direction, is defined as primary polarizing force. It's difficult to imagine any biological reason or other necessity for the duplication in inward direction (distal, front, blood direction in veins), than the simple numerical one: the polarization of 1 to 2.

      Fig Bl-5-43-1

A radial - circular polarity:
In the human body there is a net of superficial skin veins without corresponding arteries, (Mf p. 117) as a kind of "circular structure" of d-degree 3 towards the surface, while the arterioles instead are branched more "radially" outwards: a polarization of type 3a-/-3b in the dimension model.

Dimensional steps in size of arteries:
With biologists' designations we get a whole chain of dimensional decrease in size, (simultaneously as the ramification of vessels increases the dimensional structure as a whole 1→ 2 → 3):

      

Fig Bl-6-43-2

Simplified, 4 types of tissue layers can be distinguished in the arterial system:
5-4: Heart: striated, special musculature of branched cells.
4-3: Aorta - thicker arteries: 3 layers with intermediate layers of mostly elastic threads.
3-2: Thinner arteries and arterioles: 3 layers, intermediate layers of smooth muscles.
2-1: Capillaries: 2 to 1 layers, outer layer only a net of reticular web.
1-0/00: Synapses: Transportation through walls of capillaries to/from the tissue fluid.
   The "pole exchange" outward/inwards) through the walls of the capillaries from the arterial to the venous system implies a kind of reverse relations in hydrostatic and osmotic pressure between arterial and venous capillaries (Zf), which could be regarded as expression for a "pole exchange" in terms of the dimension model in last d-degree 0/00 of motions.
    (The surplus of outflow pressure is taken care of by the evolutionary later developed lymphatic system.)

From vibration to rotation:
It is noteworthy that the blood flow at an early stage of evolution (e.g. in annelids) is bi-directional: one moment inwards, next moment outwards in the same vessel à la vibration. It develops during evolution to the circular system with separated out-/inflow vessels, what may be apprehended as a rotation, a 2-dimensional motion.
      Fig Bl-7-41-1

The development corresponds to the presumed d-degrees of motions in d-degree 4 and 3 in our model. We get outward - inward flows, poles 4b - 4a (from 0- and 00-poles respectively) of d-degree 3 in different canals.
   The appearance of special lymphatic vessels, later in evolution, implies a secondary polarity of the character 00-0, here between veins and lymphatic vessels: the opposition blood from cells as centers in veins versus blood from extracellular fluid (anticenter) in the lymphatic vessels.

Vibration →> Rotation →> Translation in 3 dimensions?
A 3-dimensional motion as "translation in 3 directions" - could perhaps be identified with the further branching of vessels in the whole body - and/or more specifically the capillary networks in all tissues as the 3-dimensional motion presumed in d-degree 2.

The lymph:
With the evolution of a lymphatic system, we have once again the relation 2 to 1, here in number of systems: 2 systems for inward direction, 1 for the outward direction. The lymphatic system connects to the venous system.
   In our model the 00- pole represent the primary polarizing force, upholding potentials when in balance with the integrating 0-pole or when stronger breaking them.
   This property could be seen expressed in the role of lymph in the immune system with activities of macrophages etceteras.

Geometry of lymphatic nodes seems to reflect proposals in the dimension chain:
The nodes have one convex side, one concave, which is one of the geometrical polarities of d-degree 2 proposed in our model: 2a convex →> 2b concave.
   In agreement with this geometry vessels inwards the nodes go to the convex side while the outgoing vessels depart from the concave side.
   Further, there is the polarity of many incoming vessels, few outgoing ones as secondary manifestations of the 00- and 0-poles, a-poles versus b-poles.

Pathways of lymphatic vessels show the same bilateral asymmetry as arteries, in fact a rather curious asymmetry: right side vessels come mostly from right side front, head and arm, while left side vessels comes from the whole body, trunk, intestines and head and arm on left side. There is a certain similarity with ventricles of heart: right ventricle pumping blood to lungs, i.e. only a front part, while left ventricle pumps it to the whole body. Yet, this cannot explain the asymmetry of pathways out in the body.
   (If left hemisphere of the brain governs muscles in vessels of right side, shall we then assume that it doesn't care about the whole and only manages to serve half of the front?)

6. The liver:

The liver develops during evolution from a tube-shaped gland to a separated 3-dimensional organ. It could be said to represent the very transition between the nutrition and blood systems. It continues the breaking-down process of nutrients in the alimentary canal (proteins, lipids) but performs also synthesis, for instance of a carbohydrate as glucose. (Hence, backwards relative the process of glycolysis.)
   As the liver has a double-directed performance of breaking-down and synthesis, it has double exits: excretion of dross products via the bile in one direction and distribution of nutrients in the other direction, through vena cava.
   It is regarded a part of the venous system but blood from both arteries and veins enter the liver and merge in sinusoids: roughly 1/3 and 2/3 respectively (Aph, p. 890); note the returning 2-1-relation if so. According to other sources the quotient is circa 1/4 and 3/4 (Mf, Wikipedia).

Geometry of the liver shows up to be remarkably regular and strict internally:
   It is the most massive gland and its cell masses and blood rooms, the sinusoids, can illustrate the polarization mass - space of d-degree 3 in our model.
   Each lobule has a hexagonal (5 - 7 edges) shape and the blood canals and fluid directions illustrate to an exceptional degree the fundamentals of step 4 →> 3 in the dimension model: inward direction from anticenter, that's from the corners in the hexagons, outward direction from the center, the central vena cava inferior. There is simultaneously the polarity between a manifold inwards from anticenter versus unity from the center.
   The lobules illustrate further the geometrical poles of d-degree step 3-2 (3b - 3a) in the radial arrangement of cells versus the circular blood rooms.

Fig Bl-8-45-1

Lobules are plates, only 1 cell thick, i.e. 2-dimensional. Thus, they give a picture of how radial/circular poles 3b-3a could characterize d-degree 2 in a way not presumed before in the dimension model. In their 3-dimensional storing they show at the same time the polarities of higher d-degrees 4 and 3, center-anticenter, outward-inward directions.

(On the macro-scale the liver is divided in 4 lobes of different sizes, right - left - quadratic and caudate lobes, as if mass was differentiated along a separate dimensional chain 4-3-2-1. With size associated with d-degrees we could imagine two levels: a) d-degree 5 polarized 4-1= quadratic + caudate lobes, b) 5 polarized 3-2 = right and left lobes.
   It's said (Aph p. 891) that each lobe contains about 10⁵ lobules, in number of 10-powers as from a dimension chain.)

Cells in the liver can have several nuclei, what is called plasmodia, the fission type where nuclei divide without division of cell plasma; this in opposition to the multi-nucleate muscle cells of the heart that are the result of fusion between individual cells, syncytium (Kz p.150).
   This polarity fusion - fission on the cell level agrees in directions with the relative polarity F -B (00-0) of mesodermal muscles from front somites versus liver as a gland from vegetative pole. The same polarity is expressed in positions of heart versus liver, on opposite sides of diaphragm.
   It's notable that liver cells also in human beings have the capacity to regenerate, showing a highdimensional potential.

7. Liver and lungs:

Gills and lungs belong naturally to the blood system. Liver and lungs illustrate in several respects the differences between higher and lower d-degrees and the complementary polarities derived from 0- and 00-poles in origin, directions, positions and shapes:

- Lungs develop from front part of the alimentary canal, partly from ectoderm,
  the liver as a gland from central part of endoderm.

- Lungs are positioned in front part of the body, liver in back part, below diaphragm.

- Lungs are pairs, liver an unpaired organ.

- Ways of the blood: in lungs one-way directed venous →> arterial, v →> a,
  in the liver v + a → a plus the double direction to bile and vena cava inferior.

- Phases of substances: in lungs exchange of gases, in the liver fluids and organic molecules.

Phases:
      Fig Bl-9-46

Geometrical arrangement of blood vessels can illustrate the complementary polarities of d-degree steps 2-1 versus 3-2 in the dimension chain: In lungs as an organ of the surface blood vessels get structured as half-spherical nets outside of and around the alveoli*, with gas exchange between outside and inside as poles 2a - 2b. In the liver the vessels are organized vertically and radially along perpendicular coordinate axes with blood in the inner "rooms", both features of poles 3a - 3b.

*Compare the kidneys where the blood vessels themselves get shaped as balls within a bowl-shaped capsule, a kind of inversion of the structure in the lung alveoli.

Number 5 again:
In the lungs the number 5 appears again as so often in biology- and the asymmetry left-right. Together the lungs have 5 lobes, divided 3 (right lung) - 2 (left lung). (Right bronchial tube goes also more straight downwards as a direct continuation of the windpipe.)
   Each lung is then divided in 10 segments with an own bronchus to each, divided on the 3 right lobes 5 - 3 - 2 and on the 2 left lobes 5 - 5. (fusing to 8).

To 06. Muscles