Organs and Artificial Organs

Introduction to Units of Measure

For me to understand the circulatory system well enough to entertain the idea of replacing parts of it, I need a way of describing the specifications of the circulatory system and its components so that I know what parameters my replacement parts will need to satisfy. In other words, I have to develop a set of measures that I can use to describe the various processes that take place in moving blood around the body. The following information on base and derived units is adapted from information provided by the National Institute of Standards and Technology. ⁶

Base Units of Measurement

The first fundamental measurement quantities that I will use are length, time and mass. These quantities are sufficient to describe many physical systems. Since artificial parts may require a power source, I will also discuss the quantities related to describing electrical phenomena.

I introduced several units that I can use to measure length and time in the two prior examples. For my purposes, I will use meters (m) to measure lengths, and seconds (s) to measure time. These units and the mass unit of kilograms (kg) that I will choose below are also members of the International System of Units (SI). If the lengths and times that I encounter are measured in other units, I will usually convert them to meters and seconds. The idea is to translate all calculations about quantities into the same language so that comparing one set of numbers with another can be consistent and clear.

The final fundamental quantity, mass, is one that most people think they have a pretty good understanding of, but mass is actually a tricky concept. Mass is not weight. The pound (lb) is a measure of weight or force, but not a measure of mass. Kilograms (kg) are measures of mass, but not of weight or force. The more mass an object has, the harder it is to move, and if it is already moving, an object with more mass is harder to stop. Mass is also the quality possessed by matter that allows other matter to attract it by gravity. For my purposes, I will simply say that mass is the quality of matter that I can measure in kilograms.

Derived Units

From these three basic quantities of length, time, and mass, I can derive other quantities that I need to describe the function of the circulatory system or any other system for that matter. Derived units often have names of their own to simplify writing expressions. Derived unit names have also become a way for scientists to honor those who have made great contributions to knowledge.

Area is measured in units of length•length. In my chosen SI units, area is measured in meters•meters or meters ² (m ²). Volume is measured in length•length•length or meters ³ (m ³) in SI. Density is mass/volume or kg/m ³.

An object in motion will travel a certain distance in a certain time. The most fundamental quantity dealing with this motion is called speed. Speed in a particular direction is called velocity. Speed can only be positive or zero. Velocity can be negative or positive or zero based on the conventions of direction within a coordinate system. Speed and velocity both carry the units of length per time (length/time) or, using my chosen measures, meters per second (meters/second or m/s). Other common measures of speed are miles per hour (miles/hour), or feet per second (feet/sec), but if I encounter these, I will usually convert them to SI units.

In some cases, the speed of an object will change. For example, when I step on the accelerator when a light turns green, the car goes from a speed of 0 miles per hour to a speed of 60 miles per hour in maybe 10 seconds. The rate that speed or velocity changes with respect to time is called the acceleration. Acceleration has units of length/time ², or in SI units, meters per second squared (meters/second ², m/s ²). Acceleration in the same direction as velocity will speed an object up, while acceleration in the opposite direction of the velocity will slow an object down.

Force is the quantity that can change an object's velocity. My intuitive notion of a force is a push and this is not very far from the scientific notion of force. One of the most famous formulas in science was first stated by Sir Isaac Newton:

F = m•a

This formula states that force is equal to mass times acceleration. From this formula, I can see that force in SI units will be measured in kilograms•meters per second squared (kg•m/s ²). This specific combination of units, kg•m/s ², is named the Newton (N) in honor of Sir Isaac. The Newton is a derived unit. (Pounds are also a measure of force.) The formula simply says that if you are a given mass and I push you, you will stop standing still and move away from me. If I push you harder with a greater force, then you will move away from me even faster because your acceleration will be larger, which means that your velocity away from me will also be larger.

Pressure is the application of a force over a given area and has the units of force/area. Pressure can be written in standard units as N/m ² (also called the Pascal (Pa) after the scientist Blaise Pascal) or in basic units as (kg•m/s ²) /m ² = kg/(m•s ²) in simplified form. To get an idea of what pressure is, consider my friend Amanda walking across a lawn in flipflops. Since the bottom of her heel is fairly wide and has a large area, she does not sink into the soil. If Amanda walks across the same lawn in 6 inch stiletto high heels, however, she will find herself immediately stuck with five of those inches of heel in the ground. The difference is that the point of her high heel has a much smaller area than the area of the heel of the flipflops. In both cases, the force applied is just Amanda's weight, but in the case of the pointed high heel, the area is maybe 100 times smaller. This means that force is divided by a much smaller number which creates a pressure that is 100 times greater than the flipflop heel. This greater pressure easily pierces the soil and poor Amanda sinks into the ground.

In the medical context, pressure is most frequently measured in units of millimeters of mercury (mmHg; also called a Torr after Evangelista Torricelli), which seems like a very strange unit and it is. It is important to keep in mind that the unit is the whole thing "mmHg." As a unit, mmHg has nothing to do with a length and will not reduce out mm in a calculation. The unit mmHg can only reduce out mmHg. This particular unit is the result of the historical circumstances of the invention of the barometer, the weight of air, and the fact that mercury is the heaviest known liquid at room temperature. The conversion factor I need to convert the Torr unit to my chosen ones (SI) is about 133.32 Pa/Torr. This means that my blood pressure of 130 over 85 mmHg would be 17,332 Pa over 11,332 Pa, which might explain why doctors keep using the traditional units. In fact, one important purpose of having different units to measure things is to help express physical phenomena in numbers that are easy to remember (i.e. 130 over 85 is easier to remember than 17,300 over 11,300).

Energy is a measure of the ability of a system to do work. Energy can come in a variety of forms, but is always measured in units of mass•length ²/time ² or in SI units kg•m ²/s ². This set of units is also known as a joule (J), after the scientist James Joule. Kinetic energy is the energy associated with motion. For an object of mass, m, with velocity, v, the kinetic energy of the object is

KE = mv ²/2

Applying a force to an object through a distance is called work. Work is a form of energy. As an equation this is written: work=force•distance. The force that Earth's gravity exerts on an object of mass, m, is m•g, where g=9.8 m/s ². The amount of work that I do to raise an object of mass m, a height, h, is m•g•h. The work that I do to raise my 4 kg cat 1.5 m up is equal to 4 kg•1.5 m•9.8 m/s ²= 58.8 kg•m ²/s ² = 58.8 joules. Since my cat is now above the ground, she has potential energy. Potential energy can be thought of as stored energy. The amount of potential energy that she has is exactly equal to the amount of work I did to pick her up. If I let go of her, her potential energy transforms into kinetic energy as she accelerates, picks up velocity and drops to the ground.

Power is the rate at which work is done or the rate at which energy is used. I require more power to lift a weight quickly than to lift the weight slowly even though the total work done in both cases is the same. In SI units, power is measured in joules per second (J/s) = watts (W) (after James Watt) or in basic units kg•m ²/s ³. In the case of artificial organs that require active components—those that move or consume energy for other functions—the rate at which energy is consumed has direct implications for how that energy can be supplied to the device.

Base and Derived Units for Electrical Systems

Because there is a high probability that active devices will require electrical power, I also introduce the additional basic unit of electrical current flow, the ampere (A) (after Andre-Marie Ampere). The unit of electric charge is the Coulomb (C) (after Charles-Augustin de Coulomb). A current flow of 1 coulomb/second = 1 ampere. The flow of charges though an electrical circuit is what makes electronic devices work.

The volt (V) (after Alessandro Volta) is the unit of electrical potential. One joule of energy will move 1 coulomb of charge through an electrical potential difference of 1 volt. The volt has units of joules/coulomb (J/C). In an electrical circuit, charge flows through a conductor because of the difference in voltage potential between one end of the conductor and the other. Conductors possess a quality known as resistance, and the resistance of a conductor is measured in ohms (Ω) (After Georg Simon Ohm). A current of 1A will flow through a conductor with a resistance of 1Ω if a potential of 1V is placed across the conductor. Ohm's Law states this as a general equation: V=IR. V is the voltage in volts, I is the current in amps, and R is the resistance in ohms. From Ohm's law I can deduce that the unit for ohms is J•s/C ².

An important observation is that the product of 1 volt and 1 ampere is equal to 1 watt: 1 V•1 A=1 (J/C)•1 (C/s)=1 J/s=1 W. This will be an important relationship for the analysis of power usage in electrical devices replacing parts of the circulatory system. For the most part, I will not further convert electrical calculations into kilograms, meters, and seconds unless it is absolutely necessary to draw a conclusion.