„Secret fluids” - biological fluids overview, modelling, problems Anna Kucaba-Piętal Rzeszów University of Technology, Poland Biological fluids due to its vital function in living organism have highly complicated structure which changes up to the health and living conditions. They are composed mainly of water and specific nano- and microstructures formed by organic substances or morphotic elements . In the last few decades the fluid-dynamic and rheological study of biological fluids has received more and more attention for its influence on several phenomena linked to human health. It is well known that several diseases imply changes both in the properties of human biofluids and their components, It seems, that crucial point is the general use of rheology in the medical field, which should be seen as an interesting support, for instance, in diagnosis. School of Engineering, University of Liverpool Liverpool L69 3GH, UK , May 13th 2013

Contents Overview of biological fluids, contents, modelling, problem formulation Fundamental biofluid rheology Blood rheological parameters of blood factors which effect on blood viscosity diaseses Synovial fluid rheological parameters of s.f factors which effect on s. f. viscosity Plasma and lymph as Newtonian fluid Conclusion

Aim of Lectures Questions: What influences the change of rheological properties of biological fluids and what are the consequences? Why is it important to predict rheological parameters of biofluid? Answers: Due to the formulation bioflow equations To maintain nonbiological fluids that has rheological properties comparble to real biofluid To use it in diagnostics of clinical disorders Starting from a mean value of about 3,51 cP (with share rate = 100 sec.-1), the viscosity grows (for share rates up to 0,1 sec.-1) until 57,09 cP [5]. Therefore the knowledge of the viscosity, including its variations, is extremely important in the study of the blood rheology. 3

Fluid Environment

Body fluids Total amount of fluid in the human body is approximately 70% of body weight Body fluid has been divided into two compartments – Intracellular fluid (ICF) Inside the cells 55% of total body water Extracellular fluid Outside the cells 45% of total body water Body fluid, bodily fluids, or biofluids are liquids originating from inside the bodies of living people. They include fluids that are excreted or secreted from the body as well as body water that normally is not. The dominating content of body fluids is body water. Approximately 60-65% of body water is contained within the cells (in intracellular fluid) with the other 35-40% of body water contained outside the cells (in extracellular fluid). This fluid component outside of the cells includes the fluid between the cells (interstitial fluid), lymph and blood. There are approximately 6 to 10 liters of lymph in the body, compared to 3.5 to 5 liters of blood

Body fluid compartments Extracellular fluid includes: Interstitial fluid Present between the cells Approximately 80% of ECF Plasma Present in blood Approximately 20% of ECF Also includes Lymph synovial fluid aqueous humor cerebrospinal fluid vitreous body endolymph perilymph pleural, pericardial and peritoneal fluids

Body fluid compartments The dominating content of body fluids is body water. Approximately 60-65% of body water is contained within the cells (in intracellular fluid) with the other 35-40% of body water contained outside the cells (in extracellular fluid). This fluid component outside of the cells includes the fluid between the cells (interstitial fluid), lymph and blood. There are approximately 6 to 10 liters of lymph in the body, compared to 3.5 to 5 liters of blood In some animals, including mammals, the extracellular fluid can be divided into two major subcompartments, interstitial fluid and blood plasma. The extracellular fluid also includes the transcellular fluid; making up only about 2.5 percent of the ECF. In humans, the normal glucose concentration of extracellular fluid that is regulated by homeostasis is approximately 5 mM. The pH of extracellular fluid is tightly regulated by buffers around 7.4. The volume of ECF is typically 15L (of which 12L is interstitial fluid and 3L is plasma). Interstitial Fluid makes up 16% of your body weight and blood plasma 4% of your body weight.

Body fluid compartments

Barriers separate ICF, interstitial fluid and plasma Plasma membrane Separates ICF from surrounding interstitial fluid Blood vessel wall Separate interstitial fluid from plasma

Composition of body fluids Organic substances Glucose Amino acids Fatty acids Hormones Enzymes Inorganic substances Sodium Potassium Calcium Magnesium Chloride Phophate Sulphate

Difference Na+ /K+ pumps play major role in keeping K+ high Most abundant cation - Na+, muscle contraction Impulse transmission fluid and electrolyte balance Most abundant anion - Cl- Regulates osmotic pressure Forms HCl in gastric acid Most abundant cation - K+ Resting membrane potential Action potentials Maintains intracellular volume Regulation of pH Anion are proteins and phosphates (HPO42-) Na+ /K+ pumps play major role in keeping K+ high inside cells and Na+ high outside cell

Control of body fluid volume (Homeostasis) In health the volume and composition of various body fluid compartments are maintained within physiological limits even in face of wide variations in intake of water and solutes .

Body fluids Amniotic fluid Aqueous humour and vitreous humour Bile Blood Breast milk Cerebrospinal fluid Cerumen (earwax) Chyle Chyme Endolymph and perilymph Feces - see diarrhea Female ejaculate Gastric acid Gastric juice Lymph Mucus (including nasal drainage and phlegm) Pericardial fluid Peritoneal fluid Pleural fluid Pus Rheum Saliva Sebum (skin oil) Semen Sputum Sweat Synovial fluid Tears Vaginal secretion Vomit Urine

Specialized fluids of the body Lymph Milk Cerebrospinal fluid Amniotic fluid Aqueous humor Sweat Tears

Transport problems Microscopic level Macroscopic level Transport Mechanisms Membrane Transport Intracellular membrane transport ICF-ECF Exchange ISF-Plasma Exchange Capillary Pressures Macroscopic level Blood Flow CFD simulation  synovial fluid This section reviews the basic forces of diffusion, membrane transport of solutes, and the osmosis of water across membranes. Since the section probably repeats information from your undergraduate studies, you may safely skip it if you feel completely comfortable with its definitions and demonstrations. Fluid movement is caused primarily by the application of pressure. In a macroscopic sense, the application of hydrostatic pressure causes bulk flow, e.g. blood flowing through your artieries. Pressure also moves fluid at a microscopic level. Through pores within cell membranes, and between the cells, pressure causes water and its dissolved particles to move. The amount of movement is equal to the pressure gradient, the area, and the leakiness of the barriers. The random movement of particles in the presence of a concentration gradient is called diffusion, which also acts as a microscopic pressure that causes movement within solutions and across membranes. The mechanism by which water and other solutes move across cell membranes is reviewed here in the section on membrane transport. Diffusion of water is called osmosis, which is another critical microscopic pressure controlling fluid movement. These forces control the exchange of water and solutes between the intracellular and extracellular fluids as well as between the interstitial and the plasma compartments of the ECF. Follow these sections to examine these forces in more detail.

Navier-Stokes equations Wstawie pozniej In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities shear stresses or forces to strains or deformations. (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or forces to strains or deformations.

Rheological parameters, a constitutive equation The viscosity and elasticity determine the pressure required to produce bioflows. Viscosity is an assessment of the rate of energy dissipation Elasticity is an assessment of the elastic storage of energy How is relations between shear stress and deformation? In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities shear stresses or forces to strains or deformations. (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or forces to strains or deformations.

Body fluid percentages

Rheology as an interdisciplinary science Physics Chemistry Rheology (of Liquids) Mechanics of Continuum Technology/ Engineering Rheology is the science of plastic deformation and the flow of materials under stress. Rheology is the study of the flow of matter, under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force.[1] Rheology is the science of plastic deformation and the flow of materials under stress. The term "rheology" was proposed under the influence of the suggestions inspired by the famous statement of Heraclitus: “Panta Rhei”, or "everything flows". Ideal solids deform as elastics. Energy consumed to produce deformation is completely recovered after removal of stress. When an elastic material is deformed due to an external force, it experiences internal forces that oppose the deformation and restore it to its original state if the external force is no longer applied. The ideal fluid deforms in an irreversible way - flows. In the complex continuous energy used for deformation is dissipation and can not be recovered after removal of stress. Viscosity is a measure of flow resistance due to the internal friction. Viscoelasticity defines the fluid tends to respond to stress. It is a feature of elastic solids and viscous fluids. Viscous and viscoelastic properties of fluids are expressed by a coefficients, which can be determined experimentally.   Quantitative and qualitative changes of biological fluid microstructure affect the reaction. Different conditions cause specific changes in nano-and microstructures of a biological fluid, resulting in change in value of the rheological coefficients 19 19

Viscosity Viscosity = F(S,T,p,s,t, V) S- physico-chemical properties of substances, T-temperature, p- pressure, s-velocity of shear, t-time, V-voltage The shear viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds. If the speed of the top plate is small enough, the fluid particles will move parallel to it, and their speed will vary linearly from zero at the bottom to at the top. Each layer of fluid will move faster than the one just below it, and friction between them will give rise to a force resisting their relative motion. In particular, the fluid will apply on the top plate a force in the direction opposite to its motion, and an equal but opposite to the bottom plate. An external force is therefore required in order to keep the top plate moving at constant speed. The magnitude of this force is found to be proportional to the speed and the area of each plate, and inversely proportional to their separation . That is, One of the major tasks of rheology is to empirically establish the relationships between deformations and stresses, respectively their derivatives by adequate measurements, although a number of theoretical developments (such as assuring frame invariants) are also required before using the empirical data. These experimental techniques are known as rheometry and are concerned with the determination with well-defined rheological material functions. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics.

Models . t = f(g) NEWTONIAN FLUID F y u(y) NON-NEWTONIAN FLUID 21 Newton's law of viscosity is a constitutive equation (like Hooke's law, Fick's law, Ohm's law): it is not a fundamental law of nature but an approximation that holds in some materials and fails in others. A fluid that behaves according to Newton's law, with a viscosity μ that is independent of the stress, is said to be Newtonian. Gases, water and many common liquids can be considered Newtonian in ordinary conditions and contexts. There are many non-Newtonian fluids that significanly deviate from that law in some way or other. For example: Shear thickening liquids, whose viscosity increases with the rate of shear stress. Shear thinning liquids, whose viscosity decreases with the rate of shear stress. Thixotropic liquids, that become less viscous over time when shaken, agitated, or otherwise stressed. Rheopectic liquids, that become more viscous over time when shaken, agitated, or otherwise stressed. Bingham plastics that behave as a solid at low stresses but flows as a viscous fluid at high stresses. Shear thinning liquids are very commonly, but misleadingly, described as thixotropic. NON-NEWTONIAN FLUID . t = f(g) 21

Blood Blood is a concentrated suspension of Red Blood Cells; outside the range of dilute suspension Particles change their shape in response to the fluid forces The nature of RBC membrane and its deformation stress/strain is much less established RBC tends to form agregates known as rouleaux

Blood - components Constituents of Blood % Plasma proteins 3.2 – 4.4 Red blood cells 40 – 54 White blood cells 0.03 - 0.05 Water 42 –58 Electrolytes < 0.001 Organic nutrients Organic wastes Platelets ~ 0.1

Blood – formed elements TYPES OF LEUKOCYTES PLATELETS RBCs

Physical properties of blood RANGE Density (g/cm3) 1.050-1.064 Viscosity (cP) 2.18-3.59 pH 7.35-7.45 PROPERTY Factors affecting the blood rheology: a) hematocrit b) deformation and agregation of red blood cells c) biochemical properties of plasma d) temperature e) the geometry and flow parameters

Composition of blood plasma: Plasma is the straw-colored liquid in which the blood cells are suspended. Composition of blood plasma: Component Percent Water ~92 Proteins 6–8 Salts 0.8 Lipids 0.6 Glucose (blood sugar) 0.1

Plasma Water : 90% Solids: 10% organic constituents: proteins, lipids, carbohydrates , hormones, enzymes, Ketone bodies , and other organic compounds. Inorganic compounds: Na, K Ca,Cl,and CO2.

Comparison of Newtonian plasma and blood viscosity

Lymph Clear and colorless fluid 96% water and 4% solids Solids – Proteins 2-6% of solids albumin, globulin, fibrinogen, prothrombin, clotting factors, antibodies, enzymes Lipids 5-15% Chylomicrons Lipoproteins Carbohydrates Glucose mainly NPN Urea and creatinine Electrolytes Sodium, calcium, potassium, chloride, bicarbonates

Functions of lymph Return protein from tissue spaces into blood Redistribution of fluid Removal of bacteria, toxins and other foreign bodies from tissues Maintain structural and functional integrity of tissue Route for intestinal fat absorption Transport lymphocytes

Lymphatic fluid What is it? It is a fluid that resembles plasma but with a much lower concentration of suspended proteins Functions? Transports hormones, nutrients, and waste products from peripheral tissues to the general circulation Returns fluid and solute from peripheral tissues to the blood Maintains blood volume and eliminates local variations in the composition of the interstitial fluid

Newtonian behavior Newtonian fluid: constant viscosity at all shear rates at a constant pressure and temperature. Relationship between shear stress and shear rate is linear.

Synovial fluid The synovial fluid is a dialysate of blood plasma. It consists to 94% of water. Moreover, it contains a very specific and very important polymer known as a hyaluronic acid (HA - hyaluronate). It also contains some macromolecular components like glycoproteins, phospholipids and low molecular compounds e.g. liquid crystalline cholesterol ester and ions. Hyaluronan is a water soluble polysacharide and can create, under suitable concentration, liotropic liquid crystalline phase within the range of physiological temperatures. 33

Synovial fluid Contents value Dry matter 0,133,5 Density(20oC) 1,00811,015 pH 7,27,4 viscosity (20oC) water, g/kg 960988 hyaluronic acid (HA ) 2-3% The content of dry matter g/kg 1240 Albumins, globulins g/l Phospholipids,glycoprotein's 10,721,3 10,2 0,5 Mucyns, g/l 0,681,35 Glucoses, g/l jak w surowicy krwi Urynial Acid, mg/l 73,4 The synovial fluid is a dialysate of blood plasma. It consists to 94% of water. Moreover, it contains a very specific and very important polymer known as a hyaluronic acid (HA - hyaluronate). It also contains some macromolecular components like glycoproteins, phospholipids and low molecular compounds e.g. liquid crystalline cholesterol ester and ions. Hyaluronan is a water soluble polysacharide and can create, under suitable concentration, liotropic liquid crystalline phase within the range of physiological temperatures. 34

Functions Minimise the friction between during bones movement or weight bearing Provides nutrition for cartilage. 0.15-3.5ml

Synovial fluid Main Factors affecting the rheological properties: a) Hyaluronic Acid concentation c) Molecular weigh of Hyaluronic Acid d) Temperature Sodium Hyaluronate, Hyaluronan Made up of repeating glucuronic acid and N-acetylglucosamine subunits High molecular weight: 0.2 to 10 million Dalton Major component of synovial fluid Exhibits viscoelastic properties . Hyaluronan is a water soluble polysacharide and can create, under suitable concentration, liotropic liquid crystalline phase within the range of physiological temperatures 36

Perspectives Pathophysiological significance of biofluid rheology Develop an understanding of how the micro- and nano-structure of blood influences its rheology Explore to use of rheological parameters in diagnostics and menagement of clinical disorders and inoptimisation of blood processing Explore new methods of measurement suited for clinical application Maintain new type apparatus for such measurements

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