Chapter 2: Unit and Measurement

Quantitative description of organism is necessary to comprehend organism foranalysis in engineering.

A unit is necessary to describe the physical quantity.

Ingenuity is necessary to measure biological phenomena quantitatively [3-5].

In thischapter, you learn the basics of the unit and the measurement.

2.1 Unit and Significant Figures
2.1.1 Unit
The parameter and the method to measure the parameter are necessary to describe
biological phenomena quantitatively.
Primitive units are related to human body: a hand, a finger, and a foot.

One second

is approximately equal to the cardiac cycle. 100 in Fahrenheit is close to the bodytemperature.

The relationship between the Celsius (C) and Fahrenheit (F) isrepresented by the equation 2.1.

F＝(9/5)C＋32(2.1)

The variables should have the same units, when you calculate the sum or thedifference between variables.

Do not subtract kg from m.

It is inconsistent with theconcept of the unit system, if you use a value obtained by subtracting the weight fromthe height to represent a physique.

On the other hand, the unit of the new variables

defined by the multiplication or division of variables can be determined by themultiplication or the division of the units.

For example, the unit of speed is defined bym/s.
SI unit system (Le Systeme international d’unites) is used for a universal systemof units. The seven base units are defined: s for the time, m for the length, kg for the
mass, A for the electric current, K for the temperature, mol for the amount of a
substance, cd for the luminous intensity (Table 2.1). Each unit has been defined, whilepursuing accuracy and reproducibility.

The force of magnetic fields is studied as a

new reference to the mass, although the prototype of kg (a cylinder consisting of© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanplatinum and iridium) have been used.
Table 2.1: SI base unit.

A unit assembled by the multiplication and division of the basic unit is called“assembled unit” [3]. Some of the assembled units have the unique name derived
from the person's name: Newton [N] = [m kg s－2], Pascal [Pa] = [m－1 kg s－2], Joule [J]= [m2 kg s－2], Watts [W] = [m2 kg s－3], and others.
basic units is called “dimension”.

An aggregate of the exponents ofFor example, the dimension of the density is a

product of “mass” and “the minus third power of length”.

The dimensionless quantity

has no unit.
“Frequency” is the number of times per second.

Although SI unit is s－1, thespecific unit of Hz (Hertz) is also available.
“Radioactivity” is expressed in dose per unit time. Although the unit is s－1, thespecific unit of Bq (becquerel) is also available.
The absorbed amount of the radiation is represented as “energy absorbed per massof the body”.

Although the unit is J kg－1, the specific unit of Gy (gray) is alsoavailable. The unique unit of Sv (Sievert) is used for the effects of the absorbed amountof the radiation on a living body.
multiplied by “quality factor”.

Although the unit of Sv is also J kg－1, the value is

The factor depends on the type of radiation to evaluate

the effect of radiation to the living body.
To express a large value or a small value, the prefixes are used to represent thepower times of ten: Y, Z, E, P, T, G, M, k, h, da, d, c, m, μ, n, p, f, a, z, y (Table 2.2).
In time, on the other hand, one minute for 60 seconds, or one hour for 60 minutes areused, rather than ks (kilo seconds), or Ms (Mega seconds).
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Table 2.2: Powers of ten and unit prefixes.

Around the living body, the conventional units other than SI unit are often used.
For example, mmHg is often used for the blood pressure.

The unit of the pressure is

Pa in SI unit. 1 mmHg is equal to 133 Pa.
For the quantity of heat in human, cal (calorie) or kcal (kilocalorie) is used.
Originally, 1 cal was defined as the amount of heat required to raise 1 degree of thetemperature for 1 g of water at the standard atmospheric pressure.

Since the amount ofheat depends on the temperature of the water, it is necessary to define the temperature of
the starting point.

In order to unify the variation due to the temperature, 1 cal isdefined to be equal to 4.184 J.
For the concentration of the aqueous solution, g dl－1 is sometimes displayed as %,because the density is close to 1 g cm－3 = 100 g dl－1.

Do not confuse the percentage

The unit of density in SI unit is kg m－3.

The unit is indispensable forwith SI unit.

the physical quantity.

2.1.2 Significant Figures
A measured value includes errors depending on the accuracy.
the error, the probable value is called “significant figures”.

In consideration of

The leading number of© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanzero at decimal fraction is not included in the significant digits. The number of zero at
smallest digit is included in the significant digits, which contains the error.
For example, 0.0304 has three significant digits: 3, 0, and 4, except for the zero on
the leading side.

The number of 3600 has four significant digits: 3, 6, 0 and 0.

Because the error propagates in the calculation, it is necessary to pay attention to thesignificant digits.

In the calculation of addition and subtraction, the error propagates atthe position according to the decimal point. In the calculation of multiplication anddivision, the error propagates according to the significant digits (see Q 2.3).
The cancellation of significant digits may occur in the subtraction.

For example,

in the calculation of 3.14－3.13 = 0.01, 0.01 has only one significant digit, although
3.14 has three significant digits.
50 years are 1.5 × 109 s = 60 seconds × 60 minutes × 24 hours × 365 days × 50
years.

Six hours are 2.2 × 104 seconds = 60 seconds × 60 minutes × 6 hours.

Thus, 6hours are 1.4 × 10-5 times of 50 years, and the fifth significant digits of 50 years.
brain death is judged again after six hours.
with life time of human.

The

Six hours might not too long, comparedIf you measure the height of 1.70 m, the number has threesignificant digits.

2.2 Measurement
2.2.1 Resolution
The minimum value to distinguish two closest points is called “resolution”.

Sinceeach value changes at every moment in the living body, the value should be measured at
the right time.

The fast phenomena of variation should be measured within asufficiently short interval (time resolution; cf. spatial resolution).

On the other hand,the phenomenon to be evaluated by the average in the time should be measured over thesufficiently long period.
The potential fluctuation of the body surface due to the pulse propagation of the cell
membrane potential at the heart (see 5.3.2) is called an “Electrocardiogram”.

Theelectrocardiogram is measured as a potential difference between two points in the body.
The different timing of the depolarization and repolarization between Va and Vb ismeasured as a waveform of Va－Vb (Fig. 2.1).

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, JapanIf the action potential varies at the same time at every point, the potential between
two points is zero.

However, the timing of the depolarization and re-polarization are

different at each point, so that the potential difference between two points is not zero.
The counter direction of propagation of the electrical pulse of the action potential causes
the reversal electrocardiogram (from plus to minus, or vice versa).

Fig. 2.1: Principle of electrocardiograph.

The propagation situation of potential pulses in the heart is estimated by fluctuation
cycle, timing, and change direction of the electrocardiogram.
classified by spectral analysis [6].

The waveforms can be

It helps the diagnosis of heart disease as a screening

test.
There are events that cannot be determined in the instantaneous measurement. In thedetermination of brain death, the electroencephalogram is measured again after 6hours.

The Holter monitor records the electrocardiogram over 24 hours.

It is useful

to detect arrhythmia, or the function of the pacemaker.
In the non-uniform and non-equilibrium subject, it is necessary to decide the range© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

of measurement: local or wide (spatial resolution).

In the immunostaining, thedistribution of the targeted protein in tissues and cells is measured by applying theantigen-antibody reaction (Fig. 2.2).

Fig. 2.2: Immuno-staining.

Dimension is 0.25 mm from left to right.

2.2.2 Measurement System
Not only the measured object, but also the situation of the entire system including
the measuring device should be controlled in the measurement.

For example, it isnecessary to consider the frequency characteristic of the electric circuit of the measuring
device, when the measuring system including an electric circuit in the measuring device
side.
The four-terminal method (four-terminal method) is applied in the measurement of
the electrical resistance, when the resistance of the electrode of the measurement device
is not small enough compared with that of the specimen.

In the method, the terminals

are divided into two kinds of terminals: the “current terminals” and “voltage terminal”.
The higher current flows through the current terminal.

The lower current flows, on theother hand, through the voltage terminal. The effect of the drop in voltage at thevoltage terminal is minimized by reducing the current.
The number of electrodes inserted to the specimen is reduced to one in thevibrating electrode technique (Fig. 2.3 (a)).

In the method, the resistance between

the fixed electrode and the vibrating electrode varies between R and R + ΔR.

This ΔR

reflects the information of the resistance at vicinity of vibrating electrode.
The local electric resistance at vicinity of the electrode is measured by picking up© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

the signal corresponding to the frequency [7].

For example, by replacing the positionof the fixed electrode and the vibrating electrode between the egg yolk and the egg
white, the different signal can be detected.

The difference of the signal depends on the

difference between the electric resistance of the egg yolk and the electric resistance ofthe egg white (see 4.1.2).

The thin electrode tip can be inserted into the small

biological cell (Fig. 2.3(b)).
The human himself can be studied in comparison with the measurement system: thesensory organ as a sensor, the nervous system as a signal transmission device, and thebrain as a signal processing and a memory (Fig. 2.4).

Fig. 2.3(a): Vibrating electrode (principle).

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Cell

ElectrodeFig. 2.3(b): Vibrating electrode. Dimension is 0.25 mm from left to right.

Fig. 2.4: Biological system.

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

The cell membrane consists of lipid bilayer. Both the adipose tissue and the cell
membrane have a large electrical resistance to direct current (Fig. 2.5). They are
similar to the capacitor in the electric circuit.
At the capacitor, the fluctuation of the voltage generates the movement of the charge,
but the timing of the peak of the voltage shifts from that of the current.

When thecharge transfer speed (the current) becomes zero after the peak value, the accumulationof the electric charge saturates. At that time, the voltage reaches to the peak value.
Through the cell membrane, the high frequency signal is more selectively transmitted
than the low frequency signal.

Fig. 2.5: Electric current through lipid bilayer.

The combined signal periodically displays the figure of ellipse in the xy-plane, when
the sinusoidal signals are simultaneously displayed at x-axis and at y-axis: the sine waveof the alternating current i is displayed at x-axis, and the sine wave of the alternating© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanvoltage v is displayed at the y-axis, respectively.

The locus of points drawn by two

simple harmonic vibrations, which is orthogonal each other, is called Lissajous figure.
In Fig. 2.6, t is time, T is the period, and the arrow indicates the rotational direction of
the tracings.
The ratio of the capacitance component reflects the distribution of cell membranes
and fat tissue.

The ratio of the capacitance component of the tissue impedance

detected by the Lissajous figure can categorize the type of tissue: according to thedensity of cells, arrangement of cells, and the fat components (Fig. 2.7) [8].

Fig. 2.6: Lissajous figure.

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Fig. 2.7: Tissue grouping.
2.2.4 Non-invasive
In the physiological liquid, pH (see 5.1.2) is an important environmental conditions
for the physiological activity.
the solution.

It is usually measured by a pH electrode immersed in

The transmittance of light, on the other hand, would help for local

measurement without immersing the electrode (Fig. 2.8).

When the pH indicator isdissolved in the culture solution, the transmittance of light of a specific wavelength of
the indicator is available [9].

Fig. 2.8: pH measurement with light.
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Laser light has an uniform wavelength, and has the straight advancing property (Fig.
2.9).

It has advantage for non-contact measurement and local measurement.

light from the light source is led to the target, through a filter or a prism.

The

It can be

applied to the measurement of the pulsatile deformation of the arterial vessel wall [10],and of shrinkage of the cultured myotube [11].
The process of the measurement might change the state of the object to be measured.
To prevent the artifact of the contact, the non-contact measurement is effective.
artifact on the living body is called invasive.

The

The non-invasive measurement is theideal.

Fig. 2.9: Measurement with laser.

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Light source &Detector

Fig. 2.10: Measurement of skin temperature with infra-red ray.

The probe of the conventional thermometer contacts with the measurement point.
The infrared thermometer, on the other hand, can measure the temperature at the skin ofa hibernating animal without contact (Fig. 2.10) [12].
The pressure difference at both ends of the inserted flow resistance is often used tomeasure the flow rate (see 4.2.1).

The movement of the float is used for themeasurement of the flow rate. These devices inserted into the flow path, however,disturb the original stream.
The “Doppler effect” at the reflected wave from the floating particles is available tomeasure the flow speed of the fluid.
original stream.
fluid.

The method does not mechanically disturbe the“The wave propagation speed” also depends on the flow speed of the

Doppler effect at the reflected wave from an erythrocyte in the blood flow isalso available to measure the flow rate of blood.
The electromagnetic flowmeter can be applied to measure the flow of thephysiological liquid, because the physiological liquid includes electrolytes.

When theconstant magnetic field is perpendicularly applied to the electric current, a voltage is© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japangenerated in a direction perpendicular to both. The voltage value is proportional to thecurrent.

The increase in the flow rate of the physiological fluid has the same effect as

the increase of the current, the flow rate is measured by the voltage (Fig. 2.11).

Fig. 2.11: Principle of electromagnetic flowmeter.
2.2.5 Non-linear and equilibrium
When the output is proportional to the input, a linear relationship is available.
Non-proportional relation, on the other hand, is called non-linear.
the first signal does not often appear below the threshold.

In the living body,

The variable region of themeasurement should be carefully selected in the non-linear system.
In the measurement dependent on the environment, the accuracy of measurement
can be improved by comparison with a standard signal placed in the same environment.
The balance with the standard signal is called “zero method”.
For example, by equilibrium with a standard weight in the balance, the mass can bemeasured independent of gravity change (Fig. 2.12): on the moon, or on the earth.
When the current i does not flow through the galvanometer G at the “Wheatstonebridge” (Fig. 2.13), the potential at point b is equal to that at point c.

In this case, Eq.

2.2 is established among the resistors R1, R2, R3, and Rx.
R2／R1＝R3／Rx(2.2)© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

When the three resistances R1, R2, R3 are known, the unknown resistance Rx is
calculated.

Fig. 2.12: Gravitational equilibrium.
2.2.6 Noise and Statistics
The received signal often includes the various signals.
to noise.

The extra signal is referred

The ratio between the targeted signal and the extra signal is called SN ratio(signal to noise ratio).
Using an appropriate probe, the targeted signal can be emphasized by the principleof resonance.

For example, the secondary coil inserted in the cylindrical cage of the

primary coil (Fig. 2.14(a)) is effective to improve the quality of the magnetic
resonance image of the cartilage of the knee joint (Fig. 2.14(b)) [13]. The fitting of
the secondary coil to the knee improves capturing the signals from the knee by the highSN ratio.
A living body has individual difference.
every time, including the growth.

The state of the living body changes

The variation of the measured value should beconsidered in the bio-measurement.

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Fig. 2.13: Wheatstone bridge.

Fig. 2.14: MRI (magnetic resonance image).

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, JapanIn order to correct the errors due to scattering, μ is used as the mean value of thevalues xk measured N times (from k=1 to k=N).

1

𝜇 = 𝑁 ∑𝑁
𝑘=1(𝑋𝑘 )(2.3)

The standard deviation σ is used for the index of fluctuation.

∑𝑁 (𝑋 −𝜇)2

𝜎 = � 𝑘=1 𝑁𝑘(2.4)

The statistical test of the difference between the mean values is one of thestatistical techniques to determine the effect of the specified condition applied on theliving body.

The significance is statistically tested on the difference between the meanvalues of two groups: the condition applied group, and the control group.
The number of data to determine the statistical trend is called number of samples.
The normal distribution is often applied to statistical calculations.

The distribution

pattern of data should be examined before statistical calculations.

The sufficientnumbers of samples are necessary for the statistical analysis.
Two groups (A and B) are described in the following example.

Each group has thesame number of samples N, and the same standard deviation σ at the normal
distributions.

The mean value of each group is μA or μB.

average values (μA－μB) is equal to σ.

The difference between the

In this case, it is estimated that there is adifference between the mean values between the group A and group B with thesignificance level of 5% at the number of samples of 9, and of 1% at the number ofsamples of 16 (Fig. 2.15).

The smaller significance level shows the smaller error in

the estimation for the whole data.

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Fig. 2.15: Test of difference in the mean value.

Questions

Q 2.1: Display each value with the product of base unit of SI. Arterial pressure of 100
mmHg, cardiac output of 6.0 liters per minute, pulse rate of 70 times per minute, one
day metabolism of 1000 kcal, heart power of 1.0 W.

Q 2.2: Explain that 1 + 1 + 1 is not always equal to 3 in measurements.

Q 2.3: Confirm the significant digits of the calculation result of 3.14 × 2.236. Consider
each value as a result of rounding in the lower position.

Q 2.4: List the example of “zero method” with explanation.

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