Page 1 © J.Paul Robinson - Purdue University Cytometry Laboratories BMS 631 – LECTURE 8 Flow Cytometry: Theory J.Paul Robinson Professor of Immunopharmacology School of Veterinary Medicine, Purdue University Hansen Hall, B050 Purdue University Office: Fax \; WEB Electronic Measurements & Signal Processing Material taken from 3 rd Ed. Shapiro p

Page 2 © J.Paul Robinson - Purdue University Cytometry Laboratories Electricity and Electronics Electrons and protons posses equal and opposite charge Charge is measured in coulombs (C) is 6 x times the charge on an electron which is 1 x C

Page 3 © J.Paul Robinson - Purdue University Cytometry Laboratories Charge & electric fields The potential energy of a charged particle in an electric field is proportional to its charge - the electrical potential difference between two points in the field of which a potential energy of 1 C charge changes by 1 Joule, is defined as 1 volt (V). 1 Amp represents the transfer of 1 coulomb of charge per second

Page 4 © J.Paul Robinson - Purdue University Cytometry Laboratories Resistance, voltage, power, Ohm’s law All materials offer resistance to the flow of electrons Based on Ohm’s Law, the flow of a current of 1 Amp through a material of resistance of R ohms (  ) produces a drop in electrical potential or a voltage difference of E volts across the resistance such that E=IR

Page 5 © J.Paul Robinson - Purdue University Cytometry Laboratories AC and DC current DC - direct current - the polarity of a current source remains the same when the current is DC AC - Alternative current - this is generated by using a magnetic field (generator) to convert mechanical into electrical energy - the polarity changes with motion AC is characterized by its frequency (f) measured in hertz (Hz) (cycles per second) The AC output of a generator is frequently in the form of a sine wave - thus the voltage V(t) at any given time (t) is related to the maximum voltage V max by V(t) = V max sin (2  ft)

Page 6 © J.Paul Robinson - Purdue University Cytometry Laboratories Inductance, A wire loop or coil exhibits inductance and responds to alternative current in a frequency dependent fashion. AC produces a changing magnetic field - generates a voltage opposite in polarity to the applied voltage

Page 7 © J.Paul Robinson - Purdue University Cytometry Laboratories Reactance In an inductance of 1 Henry (H) a voltage of 1 volt is induced by a current changing at the rate of 1 Amp/second - this property is called reactance Reactance like resistance provides an impediment to the flow of current, but unlike resistance is dependent on the frequency of the current

Page 8 © J.Paul Robinson - Purdue University Cytometry Laboratories Capacitance A capacitor is a device with 2 conductors separated by an insulator If a DC current is applied to a capacitor a transient current flows but stops when the potential difference between the conductors equals the potential of the source If the source is removed the charge remains and can be release as current The capacitance measured in Farads (F) is equal to the amount of charge on either electrode in Coulombs divided by the potential difference between the electrodes in volts - 1 Farad = 1 coulomb/volt DC current will not flow “through” a capacitor - AC current will and the higher the frequency the better the conduction

Page 9 © J.Paul Robinson - Purdue University Cytometry Laboratories Impedance In a circuit that contains both inductance and capacitance, one cancels the other out The combined effect of resistance, inductive reactance and capacitive reactance is referred to as impedance (Z) of the circuit Impedance is not the sum of resistance and reactance z=(R 2 +(X l -X c ) 2 ) ½ (X l = inductive reactance, X c = capacitive reactance)

Page 10 © J.Paul Robinson - Purdue University Cytometry Laboratories The Coulter Principle Cells are relatively poor conductors Blood is a suspension of cells in plasma which is a relatively good conductor Previously it was known that the cellular fraction of blood could be estimated from the conductance of blood As the ratio of cells to plasma increases the conductance of blood decreases

Page 11 © J.Paul Robinson - Purdue University Cytometry Laboratories The Coulter Principle 2 chambers filled with a conductive saline fluid are separated by a small orifice (100  m or less) Thus, most of the resistance or impedance is now in the orifice. By connecting a constant DC current between 2 electrodes (one in each chamber), the impedance remains constant. If a cell passes through the orifice, it displaces an equivalent volume of saline and so increases the impedance.

Page 12 © J.Paul Robinson - Purdue University Cytometry Laboratories Electrical Opacity This is similar to impedance, except that you use an AC current across the electrodes of a coulter cell When the frequency used is in the radio frequency range (RF) the parameter measured is known as electrical opacity This reflects the AC impedance of cells and is dependent on cellular structure and less on size

Page 13 © J.Paul Robinson - Purdue University Cytometry Laboratories Summary so far Electrical properties of cells and fluids Impedance: inductive reactance and capacitive reactance Coulter principle

Page 14 © J.Paul Robinson - Purdue University Cytometry Laboratories Hansen Hall, B050 Purdue University Office: Fax \; WEB Shapiro p Signal Processing

Page 15 © J.Paul Robinson - Purdue University Cytometry Laboratories Beam geometry From Shapiro

Page 16 © J.Paul Robinson - Purdue University Cytometry Laboratories Pulse characteristics Pulses collected in flow cytometers are analog events detected by analog devices These pulses have a duration of no more than a few microseconds If you can’t digitize this pulse in that time you have to deal with a combination of analog and digital pulse processing Until recently it took several microseconds to digitize a pulse so this was not fast enough for high speed collection New systems which have all digital electronics can digitize the pulse directly at rates of several megahertz allowing all digital computation

Page 17 © J.Paul Robinson - Purdue University Cytometry Laboratories Pulse processing: Thresholding & Peak detection Since the analog pulse is very short (microseconds typically) the only way to retain this pulse is to charge a capacitor The capacitor serves as a storage device for a signal For peak detection, the capacitor is charged from a circuit that allows only a build up of signal (a diode achieves this) and the final or peak signal represents the maximum signal obtained

Page 18 © J.Paul Robinson - Purdue University Cytometry Laboratories Integral and width measurements In an integrator the charge on the capacitor represents the signal integral between the reset and the hold signals A pulse width is collected by charging a capacitor from the output of a linear ramp generator which starts at a preset time and ends when a signal reached a predetermined minimum – the voltage stored in the capacitor is proportional to the duration (time length) of the pulse

Page 19 © J.Paul Robinson - Purdue University Cytometry Laboratories Trigger signals The purpose of a trigger signal is to be sure that the measurement made is made on an appropriate signal not noise or an unwanted signal Frequently we use larger rather than smaller signal – example include light scatter or fluorescence The key component is called the comparator circuit which is designed around an analog and a digital input. The circuit is designed to have a constant voltage (set by the operator) and a signal from the sample – by comparing the preset signal with the sample signal, a cell is collected if it meets the criterion (digital signal is 1, or rejected (digital signal is 0). Noise of no cells passing through the observation point means that the comparator circuit output is a logical - so no signal is collected or passed onto the rest of the detection circuit (this means the computer does not have to waste valuable time)

Page 20 © J.Paul Robinson - Purdue University Cytometry Laboratories Dead time Of course it takes time to set and reset the comparator circuit so this added to the time required for a complete measurement cycle The length of time it takes to complete a full cycle of analysis will determine the analysis rate

Page 21 © J.Paul Robinson - Purdue University Cytometry Laboratories Coincidence detection Coincidence occurs if a second cells arrives before the circuit has been reset – this could mean both cells are aborted, however with more sophisticated electronics, all the signals can be collected in “pipeline” which can be interrogated to resolve the conflict without losing either signal

Page 22 © J.Paul Robinson - Purdue University Cytometry Laboratories Analog to Digital Conversion Since the analog signal only lasts for a few microseconds at maximum, it must be converted to a digital pulse for longer term processing This is achieved by an ADC – which has an analog input but a digital output The circuit divides the signal into a preset number of channels based on the number of bits collected 8 bits will have 256 channels 10 bits will have 1024 channels The higher the number of bits the more complex the computation and higher cost

Page 23 © J.Paul Robinson - Purdue University Cytometry Laboratories Successive Approximation ADCs ADCs generate a comparison voltage using a digital to analog (DAC) converter using a process of successive approximation Essentially this process converts each bit and compares it with the original until all the bits are converted. Because of design specifications the lower the number of bits the higher the inaccuracy Thus to increase accuracy it is useful (and more costly) to collect more bits and throw the least significant bits (LSBs) away. Thus an ADC with 12 bits might only have the bottom 8 bits used

Page 24 © J.Paul Robinson - Purdue University Cytometry Laboratories Summary Electrical properties of cells and measurement systems Beam Geometry Pulses and their characteristics Coincidence detection ADC WEB