BG3105 Biomedical Instrumentation - Introduction To Bioinstrumentation 2024 PDF

BG3105 Biomedical Instrumentation Faculty : Dr Pui Tze Sian School : School of Chemistry, Chemical Engineering and Biotechnology (CCEB) Email : [email protected] Office : N1.3-B2-12 (ph: 6790 4485) Introduction to Bioinstrumentation  Introduction to B...

BG3105 Biomedical Instrumentation Faculty : Dr Pui Tze Sian School : School of Chemistry, Chemical Engineering and Biotechnology (CCEB) Email : [email protected] Office : N1.3-B2-12 (ph: 6790 4485) Introduction to Bioinstrumentation  Introduction to Bioinstrumentation General Information Reference Books: Webster, J. G. (2020). Medical Instrumentation: Application and Design. 5th Ed. John Wiley: New York. Carr, J. J. & Brown, J. M. (2001). Introduction to Biomedical Equipment Technology. 5th Ed. Prentice Hall. 2  Introduction to Bioinstrumentation Lecture Schedule Every Monday 9.30-11.30 AM, LT11. All lectures will be physical unless otherwise communicated. Week Contents Remarks 1 (12/08) Topic 1: Introduction to Bioinstrumentation - Part 1 2 (19/08) Topic 1: Introduction to Bioinstrumentation - Part 2 3 (26/08) Topic 2: Pressure, Flow, Temperature 4 (02/09) Prof Chen’s class 5 (9/09) Topic 3: Electrical Safety 6 (16/09) Topic 4: Lung Anatomy and Spirometers 7 (23/09) Topic 5: Pacemaker, Defibrillator, and Oxymetry Recess week 8 (07/10) Topic 5: Pacemaker, Defibrillator, and Oxymetry 9 (14/10) Prof. Chen’s class 10 (21/10) Prof. Chen’s class 11 (28/10) Prof. Chen’s class 12 (04/11) Prof. Chen’s class 13 (11/11) Prof. Chen’s class 3  Introduction to Bioinstrumentation Tutorial Schedule Every Monday 12.30-1.30 PM (CBE-SR2), 3.30-4.30 PM (CBE-SR3), 4.30-5.30 PM (CBE-SR3) All tutorial sessions will be face to face as usual. Please attend your respective tutorial sessions. Week Contents Remarks 1 (12/08) Online Pro/Engineer tutorial for self Self learning week for Pro E learning Computer labs: N1.3-B2-25 and N1.2- Computer labs N1.3-B2-25 and N1.2- B4-02 B4-02 2 (19/08) Pro/Engineer help session. If anyone Dr Pui will be in the computer lab needs help on Pro E, please drop by the N1.2-B4-02. lab N1.2-B4-02. 3 (26/08) Pro/Engineer session Self learning week for Pro E 4 (02/09) Tutorial Dr Pui 5 (9/09) Adaptive learning using ChatGPT No physical class, communicate through Telegram chat group 6 (16/09) Tutorial Dr Pui 7 (23/09) Tutorial Dr Pui Recess week 8 (07/10) Tutorial Dr Pui 9 (14/10) Tutorial Prof Chen 10 (21/10) Tutorial Prof Chen 11 (28/10) Tutorial Prof Chen 12 (04/10) Tutorial Prof Chen 13 (11/11) Tutorial Prof Chen 4  Introduction to Bioinstrumentation Homework Creo Elements/Pro (formerly known as Pro\ENGINEER) homework due by end of mid-term break, 18th October, Friday, 6 PM. Learn yourself using web resources. Excellent work will make it to Hall of Fame. Please make sure you are able to access the computer labs using your student card. If not please contact Wong Wen Keen Lestor [email protected] to get access to the computer labs (when emailing cc to me as well) with your student card. You can access the computer labs any time, provided it is not reserved for any other module. 5 5  Introduction to Bioinstrumentation Pro/E Software Computer labs N1.3-B2-25 and N1.2-B4-02 are equipped with Pro/E software. The newer version of the software is known as Creo Parametric (or PTC Creo). There are additional help file (ProEngineer_help.pdf) and few more Youtube links for your own viewing (ProEngineerYouTubeTutorial.pdf) 6  Introduction to Bioinstrumentation PTC Creo Elements (Pro/Engineer) designs – Hall of Fame 7  Introduction to Bioinstrumentation Creo Elements Class of 2014-21 8  Introduction to Bioinstrumentation Creo Elements Class of 2014-21 9  Introduction to Bioinstrumentation Creo Elements Class of 2022-23 10  Introduction to Bioinstrumentation Creo Elements Class of 2024 11  Introduction to Bioinstrumentation https://www.onshape.com/en/ Onshape 12 12  Introduction to Bioinstrumentation Topic Objective At the end of this topic, you should be able to: To understand different components of a medical instrumentation system To understand basic electrical components and circuitry To understand measurement error/ sensitivity and how they are interpreted in actual measurements To understand signals and noise and how to quantify them To understand some basic biostatistics method used in bioinstrumentation field 13  Introduction to Bioinstrumentation Medical Instrumentation System 14  Introduction to Bioinstrumentation Example of Bioinstrumentation 15 15  Introduction to Bioinstrumentation Click here to watch ‘Biomedical Instrumentation’ 16  Introduction to Bioinstrumentation General Information Medical instrumentation is about operational principles, analysis and design, and applications of instruments, devices and equipment's in hospitals and health care units. Engineers in medical instrumentation may work in medical equipment manufacturers, R&D research institutes, and hospitals and health care units. Medical instrumentation is a multiple discipline area involving science, engineering, and computing. Medical instrumentation is a special area requiring uses and applications of most high quality and high standard technologies. 17  Introduction to Bioinstrumentation General Information Instruments and devices in medical practices are mainly for three purposes: – Diagnostic – Therapeutic – Assistive Diagnostic instruments acquire information to tell the present state of the human conditions. Therapeutic instruments are used to capture or control physiological processes that have been away from the normal condition or function due to disease, trauma, or some other agent. Assistive instruments are used to make up for diminished body or organ function, or to provide a lost function. 18  Introduction to Bioinstrumentation Medical Instrumentation System Medical Instrumentation System Control and feedback Sensor Power source Perceptible Primary Variable output Measurand Signal Output sensing conversion processing display element element Calibration Data Data signal storage transmission Radiation, electric current, or other applied energy 19  Introduction to Bioinstrumentation Medical Instrumentation System Measurand: The physical quantity, property, or condition to be measured. Sensor (Transducer): A device that converts one form of energy to another, usually to electric signal. Signal Conditioning: Processing (amplifying, filtering, impedance matching, sampling, etc) signals for transmission, storage, and display purposes. Output Display: To display the measurement in a form that the human operator can perceive. Signal Output Measurand Sensor Processing Display 20  Introduction to Bioinstrumentation Medical Instrumentation System Biomedical instruments can be classified by: Measurement quantity (pressure, flow, temperature, etc.). Transduction property (resistive, capacitive, ultrasonic, X-ray, etc.). Organ system (cardiovascular, nervous, endocrine, etc.). Clinical specialty (pediatrics, cardiology, radiology, etc.). 21 Introduction to Bioinstrumentation 22 22  Introduction to Bioinstrumentation Basic Electronic Circuit Terms 1. Current: Electrical current is a flow of electric charge. SI unit is ampere (coulomb/sec). 2. Voltage: Voltage is equal to the work done per unit charge against a static electric field to move the charge between two points. SI unit volts 4. Power: Electrical power, like mechanical power, is the rate of doing work, measured in watts. 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 × 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Basic symbols used for independent sources: VS VS IS a) battery b) ideal voltage source c) ideal current source 23  Introduction to Bioinstrumentation Kirchhoff’s Current Law Node Current Law: For any node of the circuit, the sum of the currents flowing into the node is equal to the sum of the currents i1 i2 flowing out of the node. In other words, the algebraic (net) sum of current flow is zero, if you assign inward and outward currents with different signs. i4 i3 KCL: -i1 - i2 + i3 + i4 = 0 24  Introduction to Bioinstrumentation Kirchhoff’s Voltage Law Voltage and current Closed paths are identified as convention CP1, CP2, and CP3 V1 + V2 - i CP3 Circuit Circuit 1 Element Element A CP1 CP2 Circuit V Circuit Circuit Circuit Element V3 Element V4 Element V5 Element 2 B Voltage Law: The algebraic sum of −𝑣𝑣3 +𝑣𝑣1 +𝑣𝑣4 = 0 all the voltages across individual −𝑣𝑣4 +𝑣𝑣2 +𝑣𝑣5 = 0 components around any loop of a −𝑣𝑣3 +𝑣𝑣1 +𝑣𝑣2 + 𝑣𝑣5 = 0 circuit is zero 25  Introduction to Bioinstrumentation Resistor, Capacitor, and Inductor Ohm’s Law I i(t) 𝒅𝒅𝒅𝒅 𝑰𝑰 = 𝑪𝑪 𝑽𝑽 = 𝑰𝑰𝑰𝑰 𝒅𝒅𝒅𝒅 R v(t) V C 𝒅𝒅𝒅𝒅(𝒕𝒕) 𝒗𝒗(𝒕𝒕) = 𝒊𝒊(𝒕𝒕)𝑹𝑹 𝒊𝒊(𝒕𝒕) = 𝑪𝑪 𝒅𝒅𝒅𝒅 Click here to download the simulation of Ohm’s Law. 𝒅𝒅𝒅𝒅 Short Circuit Open Circuit 𝑽𝑽 = 𝑳𝑳 V 𝒅𝒅𝒅𝒅 i i i = 0A 𝒅𝒅𝒅𝒅(𝒕𝒕) L 𝒗𝒗(𝒕𝒕) = 𝑳𝑳 𝒅𝒅𝒅𝒅 𝑅𝑅 = 0Ω V = 0V R =∞ V 26  Introduction to Bioinstrumentation Equivalent Circuit I R1 I VS R2 VS R Series circuit: 𝑅𝑅 = 𝑅𝑅1 + 𝑅𝑅2 + 𝑅𝑅3 R3 I I Parallel circuit: 1 1 1 1 VS R1 R2 R3 VS R = + + 𝑅𝑅 𝑅𝑅1 𝑅𝑅2 𝑅𝑅3 27  Introduction to Bioinstrumentation Equivalent Circuit Example: 2kΩ 1kΩ ? 1kΩ 2kΩ ? 28  Introduction to Bioinstrumentation Voltage and Current Divider Derive them on your own! If you have difficulty, remind me during tutorial, I will derive it! I R1 I I1 I2 + Vs R2 V2 Vs R1 R2 - Voltage divider: Current divider: 𝑹𝑹𝟐𝟐 𝟏𝟏/𝑹𝑹𝟐𝟐 𝑽𝑽𝟐𝟐 = 𝑰𝑰𝑹𝑹𝟐𝟐 = 𝑽𝑽𝒔𝒔 𝑰𝑰𝟐𝟐 = 𝑰𝑰 𝑹𝑹𝟏𝟏 + 𝑹𝑹𝟐𝟐 𝟏𝟏/𝑹𝑹𝟏𝟏 + 𝟏𝟏/𝑹𝑹𝟐𝟐 29  Introduction to Bioinstrumentation OP-AMP (Operational Amplifier) Eight-Terminal Op-Amp The terminal NC is not connected, and the two terminal offset nulls are used to correct imperfections (typically not connected). V+ and V- are terminal power to provide energy to the circuit. Offset Null 1 8 NC Circuit element symbol for the op-amp 2 7 Inverting Input V+ Eight-Terminal Op-Amp V+ Noninverting Input 3 6 Output Inverting Input V- 4 5 Offset Null Output Noninverting Input V- 30  Introduction to Bioinstrumentation OP-AMP (Operational Amplifier) Basic rules for ideal op-amp circuit When the Op-Amp output is in its linear range, the two input terminals are at the same voltage (Virtual Ground) No Current flows into either input terminal of the Op-Amp Op-Amp Circuit Examples R2 R1 V2 R1 Vout Vout V1 Vin R2 Vout=Vin Vout=(V1 –V2)R2/R1 31  Introduction to Bioinstrumentation OP-AMP (Operational Amplifier) Inverting amplifier i Rf in Ri Vo = (-Rf /Ri) Vi Vi Vo Non-inverting amplifier i i Ri Rf Vo = (1+Rf /Ri) Vi Vi Vo 32  Introduction to Bioinstrumentation Active Analog Filters |H(j ω)| Passband |H(j ω)| Stopband ω M ω1 𝑀𝑀 |H(j ω)| Stopband Passband Stopband 2 Passband Stopband ω ω2 |H(j ω)| A realistic magnitude-frequency Stop- Passband band Stopband response for a band-pass filter. Note ω1 ω2 ω that the magnitude M does not |H(j ω)| necessarily need to be one. The passband is defined as the frequency Stopband Passband Passband interval when the magnitude is greater 𝑀𝑀 ω1 ω2 ω than. 2 Ideal magnitude-frequency response for four filters, from top to bottom: low-pass, high-pass, band-pass, and notch. 33  Introduction to Bioinstrumentation Activity 34 34 Introduction to Bioinstrumentation Measurement Specifications 35  Introduction to Bioinstrumentation Measurement Specifications Fundamental units: Basic physical quantities from which all other physical quantities are defined. Derived units: All other quantities. International System of Units (SI) Examples of derived quantities Physical quantity SI unit Symbol Force newton (N) = kg x m/s2 Length Meter m Power watt (W) = N x m/s Mass Kilogram kg Voltage volt (V) = W/A Time Second s Electric current Ampere A Temperature Kelvin K 36  Introduction to Bioinstrumentation Measurement Specifications Range: The region between the limits wherein a variable is measured. Span: The difference between the lower and upper range limits. Example: A thermometer range 35oC ~ 42oC span 42 – 35 = 7oC 37  Introduction to Bioinstrumentation Measurement Specifications Sensitivity: The change in output of an instrument as a result of a change in input. 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 Example: Lets say an instrument is used to measure the body temperature. For each degree change in temperature, there is a 10 mV increase in the measurement. Thus sensitivity will be 10 mV/0C. 38  Introduction to Bioinstrumentation Measurement Specifications Resolution: The smallest change that can be detected in the instrument reading. Example: A digital voltmeter which can measure to three decimal places has a resolution of 0.001 V or 1 mV. 39  Introduction to Bioinstrumentation Measurement Specifications Errors: 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 − 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 − 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑑𝑑𝑑𝑑 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = = = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑥𝑥 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 × 100% Example: Lets say you are measuring the body temperature of patient with a thermometer. The actual body temperature is 370C. You have measured 340C. What is the error in your measurement? 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 37 − 34 = 3 0𝐶𝐶 3 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = = 0.08 37 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 × 100% = 8% 40 Introduction to Bioinstrumentation Measurement Error 41  Introduction to Bioinstrumentation Measurement Error Accuracy: The maximum possible error. Example: An ammeter has a 0~1 𝐴𝐴 range and a stated accuracy of 3% of full scale. Then the maximum possible error in the reading is 3% × 1 𝐴𝐴 = 0.03 𝐴𝐴 = 30 𝑚𝑚𝑚𝑚. Therefore, for any measurement say 0.5 𝐴𝐴, it will be written as 0.5 ± 0.03 𝐴𝐴. 42  Introduction to Bioinstrumentation Measurement Error Sum, difference, and product of quantities: When estimating the effect of errors due to more than one source, it should be assumed that the errors combine in the worst possible way. Sum: Let 𝑎𝑎𝑚𝑚 and 𝑏𝑏𝑚𝑚 be measured values of 𝑎𝑎 and 𝑏𝑏, and ∆𝑎𝑎 > 0 and ∆𝑏𝑏 > 0 be corresponding measurement errors, respectively. 𝑐𝑐 = 𝑎𝑎 + 𝑏𝑏 = 𝑎𝑎𝑚𝑚 ± ∆𝑎𝑎 + 𝑏𝑏𝑚𝑚 ± ∆𝑏𝑏 = 𝑎𝑎𝑚𝑚 + 𝑏𝑏𝑚𝑚 ± ∆𝑎𝑎 + ∆𝑏𝑏 Thus, absolute error in c is the sum of absolute error in 𝑎𝑎 + absolute error in 𝑏𝑏. 43  Introduction to Bioinstrumentation Measurement Error Difference: 𝑐𝑐 = 𝑎𝑎 − 𝑏𝑏 = 𝑎𝑎𝑚𝑚 − 𝑏𝑏𝑚𝑚 ± ∆𝑎𝑎 + ∆𝑏𝑏 Product: 𝑐𝑐 = 𝑎𝑎𝑎𝑎 = 𝑎𝑎𝑚𝑚 ± ∆𝑎𝑎 𝑏𝑏𝑚𝑚 ± ∆𝑏𝑏 ≈ 𝑎𝑎𝑚𝑚 𝑏𝑏𝑚𝑚 ± ∆𝑎𝑎𝑏𝑏𝑚𝑚 ± ∆𝑏𝑏𝑎𝑎𝑚𝑚 ∆𝑎𝑎∆𝑏𝑏 ≈ 0 = 𝑎𝑎𝑚𝑚 𝑏𝑏𝑚𝑚 ± ∆𝑎𝑎 𝑏𝑏𝑚𝑚 + ∆𝑏𝑏 𝑎𝑎𝑚𝑚 ∆𝑐𝑐 ∆𝑎𝑎 𝑏𝑏𝑚𝑚 + ∆𝑏𝑏 𝑎𝑎𝑚𝑚 ∆𝑎𝑎 ∆𝑏𝑏 The % accuracy in 𝑐𝑐 = 𝑎𝑎𝑎𝑎 is = = = + 𝑐𝑐 𝑎𝑎𝑚𝑚 𝑏𝑏𝑚𝑚 𝑎𝑎𝑚𝑚 𝑏𝑏𝑚𝑚 It is % accuracy in 𝑎𝑎 + % accuracy in 𝑏𝑏. Another approach: 𝑐𝑐 = 𝑎𝑎𝑎𝑎 𝑑𝑑𝑐𝑐 = 𝑏𝑏. 𝑑𝑑𝑑𝑑 + 𝑎𝑎. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑏𝑏. 𝑑𝑑𝑎𝑎 + 𝑎𝑎. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑎𝑎 𝑑𝑑𝑏𝑏 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 = = + = + 𝑐𝑐 𝑎𝑎𝑎𝑎 𝑎𝑎 𝑏𝑏 𝑐𝑐 𝑎𝑎 𝑏𝑏 44  Introduction to Bioinstrumentation Measurement Error Division: 1 1 𝑑𝑑𝑑𝑑 1 𝑐𝑐 = 𝑎𝑎/𝑏𝑏 𝑑𝑑𝑐𝑐 =. 𝑑𝑑𝑑𝑑 + 𝑎𝑎. 𝑑𝑑 = − 2. 𝑎𝑎. 𝑑𝑑𝑑𝑑 𝑏𝑏 𝑏𝑏 𝑏𝑏 𝑏𝑏 𝑑𝑑𝑑𝑑 𝑎𝑎. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 − 2 = 𝑏𝑏 𝑏𝑏 = 𝑑𝑑𝑎𝑎 − 𝑑𝑑𝑏𝑏 𝑐𝑐 𝑎𝑎/𝑏𝑏 𝑎𝑎 𝑏𝑏 If limiting errors are represented as ±𝑑𝑑𝑑𝑑 and ±𝑑𝑑𝑏𝑏, then 𝑑𝑑𝑑𝑑 𝑑𝑑𝑎𝑎 𝑑𝑑𝑏𝑏 𝑑𝑑𝑑𝑑 𝑑𝑑𝑏𝑏 =± ∓ (max error occurs when and 𝑐𝑐 𝑎𝑎 𝑏𝑏 𝑎𝑎 𝑏𝑏 have opposite sign) 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 =± + = + 𝑐𝑐 𝑎𝑎 𝑏𝑏 𝑐𝑐 𝑎𝑎 𝑏𝑏 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 = + 𝑐𝑐 𝑎𝑎 𝑏𝑏 Thus, percentage accuracy in c is the sum of percentage accuracy in 𝑎𝑎 + percentage accuracy in 𝑏𝑏. 45  Introduction to Bioinstrumentation Measurement Error Example: Lets say you have measured a resistance value 𝑅𝑅, and the 1 measurement has a 2% error. What is the percent accuracy in ? 𝑅𝑅 Answer: 2%. Can you explain why? 1 𝑐𝑐 = 1/𝑅𝑅 𝑑𝑑𝑐𝑐 = − 𝑑𝑑𝑑𝑑 𝑅𝑅2 𝑑𝑑𝑑𝑑 𝑑𝑑𝑅𝑅 𝑑𝑑𝑑𝑑 𝑑𝑑𝑅𝑅 =− = 𝑐𝑐 𝑅𝑅 𝑐𝑐 𝑅𝑅 Example: A DC voltage across a resistor is measured with an accuracy of 3%. If the resistor is valued with a 5% accuracy, what is the percent accuracy in determining the power dissipated by the resistor from values of the resistor and measured voltage? Answer: 11% 46  Introduction to Bioinstrumentation Questions 1. The range of a thermometer is -10°C to 110°C. What is the span of the thermometer? 2. An instrument shows a reading of 75 units when the true value is 80 units. What is the percentage error? 3. A digital scale reads 99 grams when the actual weight is 100 grams. What is the absolute error? 47 47  Introduction to Bioinstrumentation Measurement Sensitivity 48  Introduction to Bioinstrumentation Measurement Sensitivity Sensitivity: The change in output of an instrument as a result of a change in input, i.e., 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 Example: In a Wheatstone bridge for measuring resistance, 𝑅𝑅𝑇𝑇 is the resistor to be measured. The bridge circuit is balanced by adjusting 𝑅𝑅1 and 𝑅𝑅2 such that the voltmeter indicates zero reading. Then the value of 𝑅𝑅𝑇𝑇 can be represented in terms of the bridge resistors. What is the measurement sensitivity and how to select 𝑅𝑅1 and 𝑅𝑅2 such that the measurement is most sensitive? R1 R3 E V R2 RT 49  Introduction to Bioinstrumentation Measurement Sensitivity 𝑅𝑅2 𝑅𝑅𝑇𝑇 𝑅𝑅1 𝑅𝑅3 When the bridge is balanced, = , i.e., = = 𝑐𝑐 𝑅𝑅1 +𝑅𝑅2 𝑅𝑅3 +𝑅𝑅𝑇𝑇 𝑅𝑅2 𝑅𝑅𝑇𝑇 If there is a very small change ∆𝑅𝑅𝑇𝑇 in the measured resistor so it becomes 𝑅𝑅𝑇𝑇 + ∆𝑅𝑅𝑇𝑇 , the change in the output voltage is 𝑐𝑐∆𝑅𝑅𝑇𝑇 ∆𝑉𝑉 ≈ − 𝐸𝐸 1 + 𝑐𝑐 2 𝑅𝑅𝑇𝑇 ∆𝑉𝑉 𝑐𝑐 The measurement sensitivity is ≈− 𝐸𝐸 ∆𝑅𝑅𝑇𝑇 1+𝑐𝑐 2 𝑅𝑅𝑇𝑇 𝑅𝑅1 Hence the measurement is most sensitive when 𝑐𝑐 = =1 𝑅𝑅2 50 Introduction to Bioinstrumentation Signals and Noise 51  Introduction to Bioinstrumentation Signals and Noise Signal is the component of a variable which contains information about the measurand quantity. Noise is the component unrelated to the measurand quantity in the measurement. Example: Electromyogram (EMG) measures the potential generated by muscles, giving information about the muscle activity. Thus the EMG can be regarded as a signal. But EMG is an unwanted component from the potential measurement for another observer who is interested in obtaining nerve acting potentials. In this case, the EMG component is considered as noise. In practical measurements, there are no general rule on how signals and noise can be distinguished from the measurement quantity. 52  Introduction to Bioinstrumentation Signals and Noise Amplitude and power are often used in signal measurements. If 𝑥𝑥 𝑡𝑡 is a signal, it has the following Fourier transformation pair: ∞ 𝑋𝑋 𝜔𝜔 = 𝑥𝑥 𝑡𝑡 𝑒𝑒 −𝑗𝑗𝜔𝜔𝑡𝑡 𝑑𝑑𝑑𝑑 −∞ 1 ∞ 𝑥𝑥 𝑡𝑡 = 𝑋𝑋 𝜔𝜔 𝑒𝑒 𝑗𝑗𝜔𝜔𝑡𝑡 𝑑𝑑𝜔𝜔 2𝜋𝜋 −∞ 1 ∞ 2 𝑑𝑑𝜔𝜔. The power of 𝑥𝑥 𝑡𝑡 is given by 𝑥𝑥 2 𝑡𝑡 = ∫ 𝑋𝑋 𝜔𝜔 2𝜋𝜋 −∞ The function 𝑋𝑋 𝜔𝜔 2 can be understood as a component of power corresponding to the angular frequency 𝜔𝜔, so it is called power density. 53  Introduction to Bioinstrumentation Signals and Noise The root-mean square amplitude is a convenient measurement of a signal which is; 𝑥𝑥 2 𝑡𝑡 The signal-to-noise ratio is generally defined as the ratio of the power of the signal to that of the noise, often denoted as SNR. SNR is often expressed in decibel (dB), i.e., 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑆𝑆𝑆𝑆𝑆𝑆 = 20𝑙𝑙𝑙𝑙𝑙𝑙10 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 54  Introduction to Bioinstrumentation Signals and Noise Example: In the measurement of a signal with magnitude 𝑉𝑉𝑠𝑠 in the presence of noise with magnitude 𝑉𝑉𝑛𝑛 , the signal to noise ratio (SNR) is defined as: 𝑉𝑉𝑠𝑠 𝑆𝑆𝑆𝑆𝑆𝑆 = 20𝑙𝑙𝑙𝑙𝑙𝑙10 𝑉𝑉𝑛𝑛 If the noise is random, it is possible to enhance SNR by signal averaging. The averaged SNR for 𝑁𝑁 repetitive signal measurements is: 𝑉𝑉𝑠𝑠 𝑆𝑆𝑆𝑆𝑆𝑆𝑁𝑁 = 20𝑙𝑙𝑙𝑙𝑙𝑙10 𝑉𝑉𝑛𝑛 / 𝑁𝑁 An EEG system processes a 10 mV signal in the presence of a 100 mV random noise. Find the measurement SNR and the averaged SNR with 100 repetitive measurements, respectively. 55  Introduction to Bioinstrumentation Signals and Noise Answer: For the EEG system processes a 10 mV signal in the presence of a 100 mV random noise. The measurement SNR is: 10 𝑆𝑆𝑆𝑆𝑆𝑆 = 20𝑙𝑙𝑙𝑙𝑙𝑙10 = −20𝑑𝑑𝑑𝑑 100 The averaged SNR with 100 repetitive measurements, 10 𝑆𝑆𝑆𝑆𝑆𝑆𝑁𝑁 = 20𝑙𝑙𝑙𝑙𝑙𝑙10 = 0𝑑𝑑𝑑𝑑 100/ 100 56 Introduction to Bioinstrumentation Biostatistics 57  Introduction to Bioinstrumentation Biostatistics Statistical methods are widely applied to medical data and experiments. These include: Summarizing, exploring, analyzing, and presenting data Estimation and hypothesis testing Diagnostic evaluation Clinical decision making 58  Introduction to Bioinstrumentation Biostatistics Let 𝑿𝑿𝒊𝒊 : 𝒊𝒊 = 𝟏𝟏, 𝟐𝟐, … , 𝒏𝒏 be a set of measurement data. The mean is the sum of observed data divided by the number of observations. = ∑ 𝑿𝑿𝒊𝒊 𝑿𝑿 𝒏𝒏 The standard deviation is a measure of the spread of data about the mean. ∑ 𝑿𝑿𝒊𝒊 − 𝑿𝑿 𝟐𝟐 𝑺𝑺 = 𝒏𝒏 − 𝟏𝟏 At least 95% of the values lie between –2s and +2s about the mean. 59  Introduction to Bioinstrumentation Biostatistics Assessment parameter of a diagnostic procedure Sensitivity Specificity Prior probability (= prevalence) 𝑻𝑻𝑻𝑻 𝑻𝑻𝑻𝑻 𝑻𝑻𝑻𝑻 + 𝑭𝑭𝑭𝑭 𝒂𝒂 + 𝒄𝒄 = 𝑻𝑻𝑻𝑻 + 𝑭𝑭𝑭𝑭 𝑻𝑻𝑻𝑻 + 𝑭𝑭𝑭𝑭 𝑻𝑻𝑻𝑻 + 𝑻𝑻𝑻𝑻 + 𝑭𝑭𝑭𝑭 + 𝑭𝑭𝑭𝑭 𝒂𝒂 + 𝒃𝒃 + 𝒄𝒄 + 𝒅𝒅 Gold Standard Disease No Disease Total a 40 b 30 70 Positive True-Positive False-Positive a+b c 20 d 10 30 Negative Test False-Negative True-Negative c+d 60 40 Total 100 a+c b+d TP: true positive 𝑎𝑎 𝑑𝑑 Sensitivity Specificity TN: true negative 𝑎𝑎+𝑐𝑐 𝑏𝑏+𝑑𝑑 FP: false positive FN: false negative 60  Introduction to Bioinstrumentation Biostatistics Receiver Operating ROC CURVE Characteristic (ROC) curve 1 Sensitivity and True Positive (Sensitivity) specificity depends on Good Test cut-off value Y-axis : Sensitivity, X- Worthless axis : 1-Specificity Test Area under the curve (AUC) ranges from 0.5 (useless test) to 1.0 0 0 1 False Positive (1-specificity) (perfect test) 61  Introduction to Bioinstrumentation Biostatistics The correlation coefficient 𝒓𝒓 is a measure of the relationship between numerical values 𝑿𝑿 and 𝒀𝒀 for paired observations 𝒀𝒀𝒊𝒊 − 𝒀𝒀 ∑ 𝑿𝑿𝒊𝒊 − 𝑿𝑿 𝒓𝒓 = ∑ 𝑿𝑿𝒊𝒊 − 𝑿𝑿 𝟐𝟐 ∑ 𝒀𝒀𝒊𝒊 − 𝒀𝒀 𝟐𝟐 The correlation coefficient ranges from –1 for negative linear relationship to +1 for a positive relationship. 0 indicates that there is no linear relationship between 𝑿𝑿 and 𝒀𝒀. 62  Introduction to Bioinstrumentation Topic Summary Introduction to Medical Instrumentation: instrumentation systems, terminologies Basic Electrical circuitry: Voltage, current, power, ohm’s law, equivalent resistance, OP-AMPS, inverting, non-inverting OP-AMPS circuitry. Measurement Specifications: fundamental units, derived units, range, span, resolution, errors, accuracy. Measurement Errors: absolute error, percent error, errors in the sum, difference and product of measurements Signals and Noise: amplitude, power, power density, root-mean- square amplitude, signal-to-noise ratio. Biostatistics: mean, standard deviation, sensitivity and specificity, ROC curve 63  Introduction to Bioinstrumentation Quiz Information This quiz is not graded. Its purpose is to assess your understanding of ROC measurements. The quiz is available after 19th August. Instructions 1. Log in to your NTULearn 2. Access Biomed Instrumentation course 3. Click on “ROC Measurement quiz” to start the quiz 64 64 Introduction to Bioinstrumentation Introduction to Bioinstrumentation End of Lecture 65