Chapter 5: Energy
In the living body, the conversion of the energy operates the life activity, maintains
the body temperature, and controls the movement of the material. In this chapter, welearn the basic technology of the energy with examples: the movement of substances
through the biological membranes, and the work rate of the heart.

5.1 State of substance
5.1.1 Temperature
The temperature [K] is used to represent the energy state (see Chapter 2).

The stateof the object changes with the increase of the temperature.

The volume of the solidincreases.

A solid melts to a liquid at the “melting point”.

The volume of the liquidincreases.

The liquid changes to the gas at the “boiling point”.

The volume of thegas increases.
The gas, in which the molecules have zero volume and no interaction among them,is called an “ideal gas”.

The equation 5.1 represents the relation among thetemperature (T), the volume (V), and the pressure (P) in the n moles of ideal gas.

P＝(n／V) R T(5.1)

In the Eq. 5.1, R is the “gas constant” of 8.3 J K－1 mol－1.
The pressure of the gas is caused by the molecular motion.

The absolute zerotemperature (0 K) is defined, when the pressure is zero without the molecular motion.
The point, where the water vapor, the water and the ice coexist, is called the “triple
point” of water: 273.16 K, 611.73 Pa (Fig. 5.1).

The standard scale of the temperature

is defined by the triple point of water.

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Fig. 5.1: Triple point of water.

The melting point (the freezing point) and the boiling point are used for thereference of the temperature scale, as a stable temperature.

At the standard

atmospheric pressure 101325 Pa, the freezing point of tin and gold are 505.078 K and
1337.33 K, respectively [22].
The volume varies, when the phase of substance changes among the solid, the liquid,
and the gas.

The pressure affects the change of the volume.

When the reaction system has equilibrium, the balance moves to the direction to
reduce the change.

It is called “Le Chatelier’s principle”.

The volume of the substance increases with the change of the phase from liquid togas.

Therefore, the boiling point is lowered under the low pressure, and is raised under

the high pressure.
The volume increases, when the phase of substance changes from solid to liquid.
Therefore, the melting point rises under the high pressure.

In the case of water, on the© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanother hand, the volume decreases, when the phase of substance changes from solid (theice) to liquid (see 5.1.4).

Therefore, under the high pressure, the melting point of theice is lowered.
In the diluted solution, the boiling point is raised and the freezing point is lowered inproportion to the increase of the molar concentration of the non-volatile solutes.

Theboiling point elevation and the freezing point depression are applied to measure theconcentration of the solution.

The osmotic pressure can be calculated by theconcentration of the solution (see 5.3.2).

5.1.2 Hydrogen ion concentration index
Three-dimensional structure of biological macromolecules in the aqueous solution
varies with the hydrogen ion concentration of the surrounding.

The hydrogen ion

concentration is represented by pH (power of hydrogen).
In the diluted solution,
pH＝－log10[H＋](5.2)[H+] is the hydrogen ion concentration [mol dm－3] (dm = 0.1 m, dm3 = 0.001 m－3).
The value of pH = 7 in the neutral solution.
The control of pH is important, because the three-dimensional structure of
biological macromolecules affects the chemical reaction in the body.

Because theconcentration of carbon dioxide is higher in vivo than that in the atmosphere, pH of thephysiological solution is biased to alkaline in vivo.
at 7.40.

The pH of the blood is controlled

The chemical equilibrium controls carbon dioxide and hydrogen ion throughcarbonate.
H＋＋HCO３－⇔H２CO３⇔H２O＋CO２（5.3）© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

5.1.3 Heat
The heat is transferred according to the difference of the temperature: from thehigher to the lower.

The unit of the heat is J (Joule).

The transfer of the heat iscategorized to three kinds of paths: the conduction through the contact, the convection
through the flow of fluid, and the radiation via the electromagnetic wave.
The heat is not transferred at the thermal equilibrium.

The amount of the heatrequired for 1 K rise of the temperature of the object is called the heat capacity.

The

－1

unit is J K .
The amount of heat required for 1 K raise of the temperature of a substance of 1 kg
is called the specific heat capacity.

The unit is J kg－1 K－1.

The amount of heatrequired for 1 K raise of the temperature of a substance of 1 kg under the constantpressure is called the specific heat at constant pressure.

The amount of heat requiredfor 1 K raise of the temperature of a substance of 1 kg under the constant volume iscalled the specific heat at constant volume.
The enthalpy (H) is used to represent the energy state change associated withexothermic and endothermic reactions.

The unit is J.

H＝U＋PV(5.4)

In equation (5.4), U is the internal energy, P is pressure, and V is the volume.

Theheat to the outside (exothermic) or the work to the outside lowers the enthalpy.
Conversely, the heat received from the outside (endothermic) or the work received fromthe outside raises the enthalpy.
In a system, entropy dS [J K－1] increases, when the system has received amount ofheat δQ [J] from the heat source at temperature T [K].

The entropy dS is the quotientof the quantity of heat δQ divided by temperature T [K] of the system (Eq. 5.5).
dS ＝δQ／T(5.5)© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

The entropy represents disorder in a system.
entropy increases.

In an irreversible process, theThermal vibration of atoms and molecules tends to be random.

In the biological activity, each function is realized by being controlled based on theregularity.

Against the law of entropy increase, homeostasis is maintained.

The thermal insulation material serves to impede the movement of heat.

The

thermal conductivity of the gas is low, since the gas has the low density of molecules.
The gas is used for insulation: fibers to impede the convection of the gas, and small
foams of the gas trapped in the solid (Fig. 5.2).

Fig. 5.2: Insulation material.

The internal energy increases and the temperature rises at the adiabatic
compression by the external pressure, because the system receives the external work.
Conversely, the internal energy decreases and the temperature falls at the adiabatic
expansion by the internal pressure, because the system produces the work to the outside(Fig. 5.3).

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Fig. 5.3: Adiabatic compression and expansion.

The physical quantity, which varies with temperature, is used to measure thetemperature: the pressure of the gas (e.g., the vapor pressure), the density of the liquid(e.g., mercury), the deformation of the solid (e.g., bimetal), the electrical resistance (e.g.,
platinum resistors, thermistors), the thermal electromotive force (e.g., thermocouple),the infrared radiation, the viscosity coefficient, and the propagation speed of the elastic
wave.
When the temperature of the sensor element itself should be same as that of theobject, it is necessary to pay attention to the heat transfer phenomena.

The amount ofheat transfer per unit parameters (area, time, and temperature difference) is called theheat transfer coefficient Hc.

The unit is J m－2 s－1 K－1 or W m－2 K－1.

The heattransfer Q [J] is proportional to the area A [m2], the time t [s], and the temperature
difference ΔT [K].
Q＝Hc A tΔT(5.6)

It takes time to measure temperature, when the heat capacity of the sensor element is© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanlarge.

It also takes time, when the heat transfer rate to the sensor element is small.

The temperature of the object might change by the heat transfer during themeasurement.
The thermal energy [J s－1 m－2], which passes through unit area in unit time, divided
by the temperature gradient [K m－1] is called the thermal conductivity.
s－1 m－1 K－1 or W m－1 K－1.

The unit is J

The thermal conductivity is high in the solid of metal.

It is lower in the liquid than in the solid.

It is lower in the gas than in the liquid.

Human body temperature is maintained at around 310 K.

With the change of thetemperature, the three-dimensional structure of biological macromolecules changes,
which change the function.
plays an important role.

In maintaining biological activity, the temperature control

For example, through changes in chemical bonding, such as

phosphoric acid binding, the heat (exothermic, endothermic) occurs.

The body

temperature is maintained by several effects: the insulating effect by the skin and by thefat layer, and the heat transfer effect of the blood flow.
The water absorbs the heat during the phase transition from the water to the vapor.
The heat of vaporization of water is 40.8 kJ mol－1. The heat of vaporization of wateris larger than that of other substances, because of the hydrogen bonds between
molecules of the water.

The vaporization in sweating makes radiation of the heatthrough the skin in the body.
The phase transition from ice to water absorbs heat.

The heat of fusion of the ice

is 6.01 kJ mol－1. Conversely, the phase transition from water to ice generates heat.
Both the heat of vaporization and the heat of fusion are referred to latent heat.
In some warm-blooded animals, the body temperature is lowered during hibernation[12].

In the hypothermia therapy, the metabolism is suppressed by lowering the bodytemperature.

In the heart-lung machine, the blood temperature is lowered during

cardiac surgery by the heat exchanger (Fig. 5.4).

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Fig. 5.4: Heat exchanger.

A fluctuating magnetic field produces an alternating electric current.

The electric

current generates heat through the resistance. The electric current also generates heatthrough the living tissue.

Cells are destroyed at high temperature.

In some cases, on

the other hand, the high body temperature is applied to medical treatment(hyperthermia).

In hyperthermia, cancer cells are selectively killed by slightly

elevated temperature.

In the treatment, heat generated by the local current is applied.

The effect of the magnetic field on the living body has been investigated [32-34].
The effect of the temperature rise due to local currents induced by the magnetic fieldshould be distinguished from the effect of the magnetic field itself.

The effect oftemperature rise by a heater can be compared with that by the magnetic field (Fig. 5.5).
The effect of the magnetic field, on the other hand, can be eliminated, when cells arecultured in the space shielded by a metal sheet of magnetic material (Fig. 5.6).

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Fig. 5.5: Thermography.

Fig. 5.6: Cell culture in magnetic field.

Thermography is used to measure the surface temperature distribution [32].

The

thermography detects the amount of infrared rays radiated from a substance inproportion to the fourth power of absolute temperature.
Electrical pulses also give a variety of effects on the organism (see 7.2.1) [35].

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5.1.4 Phase transformation
Substances changes own phase with the lowering of temperature: from a gas to aliquid, or from a liquid to a solid.
these phase change.

In most of substances, the density increases withThe density of the water, on the other hand, decreases (thevolume increases) with the phase change from a liquid to a solid.

At freezing bycooling the bottle containing the water, the container may burst.

The burst occurs

because of the increase of the volume of the water against the decrease of the capacityof the bottle.
A biological cell contains a large amount of water.
membrane of the cell might be broken (Fig. 5.7).

At the rapid freezing, theThe water should penetrate throughthe membrane fast enough to inhibit the rupture of the membrane.

For thecryopreservation of red blood cells, the rupture of the membrane accompanied byfreezing of water should be controlled.

Several methods have been proposed:

regulation of cooling speed, or replacement of the water with other solvents.

Fig. 5.7: Membrane destruction during freeze.

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, JapanA state, in which atoms are arranged regularly, is called “crystal”.

A state, inwhich sequences are not developed, on the other hand, is called “amorphous”.

When

you heat the synthetic resin or the natural rubber, fluidity is rapidly increased above acertain temperature. The temperature is called the “glass transition temperature”.
The amorphous state below the glass transition temperature is called the glass state.

Atthe higher temperature above the glass transition point, the solid becomes a liquid or
rubbery state.
At the aggregation of molecules of polymer, both conformation of each moleculeand arrangement of the molecules vary with temperature.

A state, which has regularity

as crystal and fluidity as liquid, is called “liquid crystal”.

The liquid crystal shows an

optical anisotropy.

Biopolymers also form the regular structure, such as a lipid bilayer(Fig. 5.8) in biological membranes.

Fig. 5.8: Lipid bi-layer.

5.2 Energy conversion
5.2.1 Form of energy
A machine works.

The machine not only transmits the motion to the motion, butalso converts gravitational field, heat, electricity to the motion. The conversion can becalculated by a common physical quantity of “energy”: “kinetic energy”, “potential© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanenergy”, “thermal energy”, and “electrical energy”.

The energy is described by acommon quantity with a unit of J (joule) as the quantity conserved during theconversion (law of conservation of energy).
The friction between the skins increases the temperature of the surface of the skin.
In this case, the kinetic energy is converted into heat energy through the friction.
the falling motion in a gravitational field, the velocity increases during falling.
case, the potential energy is converted into the kinetic energy.

In

In thisThe electric motor

converts the electrical energy to the kinetic energy.
In the gravitational field, an object falls from a higher position to a lower position.
The potential energy is higher at the higher position.

In the shunt for hydrocephalus,

the change of the attitude of an individual varies the head of fluid between the two
positions, which are connected with the shunt.

The flow rate through the shunt

depends on the head of fluid (see 4.1.1) [20].
The flow rate can be measured by temperature change.
the pulmonary artery through the right atrium.

A catheter is inserted into

The temperature of the blood flow,which is warmed by hot wire upstream in the right atrium, is measured downstream ofthe pulmonary artery.

The blood flow is calculated by the equation, in which thereceived energy at the blood is equal to the added energy at the heat wire (see Question
5.2).

A certain volume of cooled physiological saline can be injected to the rightatrium instead of using the hot wire (Fig. 5.9).

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Fig. 5.9: Flow measurement with catheter.

5.2.2 Conversion efficiency
In the energy conversion, the ratio converted into the targeted energy is called
efficiency.

For example, the muscle is heated, when you move the muscle.

In themuscle, 100% of chemical energy cannot be converted into the kinetic energy.

The

rest of energy becomes heat energy, which raise the temperature of the surroundings.
Through friction, “work” is converted to heat.
the other hand, to convert heat into work.

A “heat engine” is necessary, on

A “Carnot cycle” a heat engine, which

utilizes the energy flow from the high-temperature heat source to the low temperature
heat source.

In the Carnot cycle, four processes repeat: the adiabatic compression

process (see Fig. 5.3), the isothermal heat absorption expansion process, the adiabatic
expansion process, and the isothermal heat dissipation compression process.

It is notpossible to make the efficiency of conversion from heat to work 100%.
At the implanted machine, such as artificial organs, the low efficiency generates
excess heat.

For example, the low efficiency of the implanted artificial heart generates

heat to be dissipated.

If the heat cannot be dissipated through the blood of circulationand the air of respiration, the temperature of the surrounding tissue is elevated.
At transmitting the energy from outside into the body, the low efficiency generates© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

the excess heat.

When the implanted battery is charged through the skin from theoutside, the low efficiency raises the temperature of surrounding tissue.
The left ventricle ejects the cardiac output against the pressure difference between
the left atrium and the aorta. The power of the pumping is equivalent to 1 W at the left
ventricle of an adult at rest.

Consider a blood pump driven by an electric motor.

When the conversion efficiency from the electrical energy into mechanical energy is25%, the required electrical energy is 4 W, which corresponds to the product of thevoltage of 4 V and the current of 1 A.

5.3 Substance transportation
5.3.1 Permeability through membrane
In the living body, transportation is realized by the pressure gradient, theconcentration gradient, the temperature gradient, the electric gradient, and the flow.
As a result, the state tends to uniform state.
According to the law of entropy increase (see 5.1.3), the state of nature tends tobecome disorder.

Consider how to counter the "direction to the chaotic state".

example, separation by a wall can control the movement of the material.

For

Severalpartitions control the movement of the material in vivo: the vessel wall, the tissue
membrane, and the cell membrane.
In the lung, oxygen is taken up in the blood and carbon dioxide is discharged fromthe blood.

The gases are exchanged between the air and blood through the membraneof the alveolus.

The permeate flow rate of the gas (Q) through the membrane is

proportional to the partial pressure difference (ΔP) of the gas and to the area of themembrane (S).

The flow rate is inversely proportional to the thickness of themembrane d (Fig. 5.10).

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Fig. 5.10: Transport through membrane.
Q ∝S ΔP／d(5.7)

The volume percentages of nitrogen and oxygen in the air are 80% and 20%,
respectively.

Water vapor is saturated in the trachea.

water vapor in the air is 6.2 kPa at 310 K.
carbon dioxide is 5%.

The partial pressure of the

In the trachea, the volume percentage of the

The wall thickness of alveolus is about 1 μm, whichcorresponds to the blood vessel wall thickness of the capillary.

From the average

diameter and the number of alveoli, the sum of the lung membrane area of adults is
estimated to be 100 m2.
The membrane area at the membrane oxygenator of the heart-lung machine usedduring the cardiac surgery, on the other hand, is about 1 m2.
oxygenator consists of hollow fibers.

The membrane

The wall thicknesses of hollow fibers are 200

μm in case of silicone and 25 μm in case of polypropylene, respectively.

Compared tothe adult lung, the oxygenator has smaller membrane area, and thicker membrane.
The gas partial pressure in the vicinity of the membrane depends on the fluid flow inthe vicinity of the membrane. The agitation of the fluid prevents the accumulation of© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japangas content in the boundary layer near the membrane (see 4.2.3).

Both the pulsatileblood flow and the vibration of the membrane produce a stirring effect (Fig. 5.11).
Turbulence also exerts the stirring effect as a non-steady flow.

Fig. 5.11: Acceleration of permeability.

For example, agitation of the fluid by the pulsatile flow or membrane vibration
improves the gas exchange efficiency of the oxygenator.

At the silicone tubes bundled

in the gas exchanger, the gas exchange efficiency is improved by several methods: thepulsatile blood flow, the pulsatile gas flow, and the vibration of the membrane by adding
cyclic pressure to the membrane.

When the blood flow path contains one-way valve,

the blood can be pumped by the cyclic pressure.

The method realizes the device,

which integrates the pump and the gas exchanger (Fig. 5.12) [36].
The lung of a living body, on the other hand, has the huge total membrane area.
The lung can exchange enough gases even in a non-pulsatile flow [37].

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Fig. 5.12: Vibrating membrane oxygenator.

5.3.2 Osmotic pressure
At the capillary wall, substances are transported by the pressure difference and by
the osmotic pressure difference.

When the solution is divided by the semi-permeable

membrane, through which a particular solute cannot pass, the solvent moves to balance
the concentration of the solute at both sides of the membrane.

The driving force isexpressed by the osmotic pressure P.

P＝(n／V) R T(5.8)

In the equation (5.8), (see equation (5.1)) n / V is the molar concentration of thesolution [mol m-3], R is the gas constant, and T is the temperature [K].
The solution, which has the higher osmotic pressure, is called “hypertonic
solution”.

The solution, which has the equal osmotic pressure, is called “isotonic

solution”.

The solution, which has the lower osmotic pressure, is called “hypotonic

solution”.

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The unit of the osmotic pressure is Pa, which is the same unit as the pressure.

The

serum, which is the supernatant of blood, includes the constant concentration of ions
(Na+, Ca2+, K+, Cl－, etc.). The solution, which contains the equal concentration ofions, is called the isotonic solution.

The NaCl aqua solution of 0.9% massconcentration has the osmotic pressure of 7.7 × 105 Pa at 310 K, which is isotonic to theserum.

The isotonic solution for serum is called the saline solution.

At the movement of substances in vivo, the attractive force between molecules
works effectively.

The osmotic pressure of the polymer is estimated smaller.

Because the number of molecules of polymers is smaller than that of ions in vivo, theosmotic pressure of polymers is estimated smaller, which may play a major role in the
movement of a solvent.
function to the water.

Polymers such as carbohydrate in plasma have the attract

This is called a colloid osmotic pressure (oncotic pressure).

In a transfusion during the circulatory assist, it is important to regulate not only theosmotic pressure by smaller molecules, but also the colloid osmotic pressure by larger
molecules [38].
At the red blood cells, the transportation of the solvent occurs across the membrane.
In hypertonic solution, the water comes out to the outside, which makes the crenatedcell.

Conversely, in hypotonic solution, the water comes into the inside, which makes

the swollen cell (Fig. 5.13).

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Fig. 5.13: Erythrocyte deformation with osmotic pressure.

The hemolysis owing to the rupture of the membrane of erythrocyte by swelling isapplied to the erythrocyte osmotic fragility test.

Osmotic pressure is measured,

when the red blood cells causing hemolysis: “start of hemolysis”, and “hemolysis at
every erythrocyte” (Fig. 5.14).
individuality and timing.

Measurement value detects variations due to

The method is applied to compare hemolysis in artificial

hearts, and to distinguish the cause of the hemolysis [39].

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Fig. 5.14: Erythrocyte osmotic fragility test.

The kidney discharges the unnecessary components in the blood.

Thehemodialyzer moves the substances into the dialysate from the blood through thedialysis membrane.

Both emissions of carbon dioxide at the lungs and the discharge ofhydrogen ions at the kidney maintain pH in the blood (see Eq. 5.3).
The difference of the concentration of each ion between both sides of biologicalmembranes generates the membrane potential (Fig. 5.15).

The selective channel ofpotassium at the biological membrane is equivalent to an electromotive force, which is abattery directed to the extracellular.

When the selective channel of sodium at thebiological membrane opens, the transmembrane potential changes by the opposite
electromotive force.
neurons [24].

Signals are transmitted by variations of membrane potential at

Electrical pulses, on the other hand, promote mass transfer in theelectrolyte gel [19].

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Fig. 5.15: Membrane potential.

Questions (Exercises)
Q 5.1: How much is the heat of vaporization of water of 10 cm3.

Q 5.2: Calculates the rise of the temperature of the water downstream, when the flowing
water at the flow rate of 10 ml per second is heated through electrical resistance of 1 kΩat the electric current of 0.1 A in the following condition: the specific heat of water is
4.2 × 103 J kg-1 K-1, the density of water is 1 × 103 kg m-3, and all of the electricalenergy is converted to a temperature rise of the water.

Q 5.3: Find the work rate of the pump to send the blood in place of the right ventricle
by an electric motor, when the parameters are as follows: the cardiac output is 1.0 × 10-4
m3 s-1, the pressure difference between the pulmonary artery and the right atrial is 2 ×
103 Pa, and the energy conversion efficiency from electrical energy to work to send theblood is 25%.

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, JapanQ 5.4: Find the temperature rise rate of the surrounding water 1 × 10-4 m3, when the restof the energy is converted into heat in the case of the question 5.3. Specific heat of thewater is 4.2 × 103 J kg-1 K-1, and the density of water is 1 × 103 kg m-3.

Q 5.5: A solvent is passing through a semipermeable membrane. How many times moreof solvent pass through the membrane when the parameter changes as follows: themembrane area becomes four times more, the film thickness becomes 2-fold more, theosmotic pressure difference becomes doubled?

Q 5.6: Calculate osmolarity of plasma, as an aqueous solution containing cations andanions: each molar concentration of 1.5 × 102 mol m-3.

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan