BMS 631 – LECTURE 8
Flow Cytometry: Theory
J.Paul Robinson
Professor of Immunopharmacology
School of Veterinary Medicine, Purdue University
Electronic Measurements & Signal
Processing
Material taken from 3rd Ed. Shapiro p 145-149
Hansen Hall, B050
Purdue University
Office: 494 0757
Fax 494 0517
email\; robinson@flowcyt.cyto.purdue.edu
WEB http://www.cyto.purdue.edu
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© 1988-2002 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 1018 times
the charge on an electron which is 1 x 10-19 C
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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 Vmax by
V(t) = Vmax sin (2ft)
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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=(R2+(Xl-Xc)2)½ (X = inductive reactance, X = capacitive reactance)
l
c
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© 1988-2002 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
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© 1988-2002 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.
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© 1988-2002 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
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© 1988-2002 J.Paul Robinson - Purdue University Cytometry Laboratories
Summary so far
• Electrical properties of cells and
fluids
• Impedance: inductive reactance and capacitive
reactance
• Coulter principle
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© 1988-2002 J.Paul Robinson - Purdue University Cytometry Laboratories
Signal Processing
Hansen Hall, B050
Purdue University
Office: 494 0757
Fax 494 0517
email\; robinson@flowcyt.cyto.purdue.edu
WEB http://www.cyto.purdue.edu
Shapiro p 149-162
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© 1988-2002 J.Paul Robinson - Purdue University Cytometry Laboratories
Beam geometry
From Shapiro
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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)
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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
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© 1988-2002 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 http://www.cyto.purdue.edu
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© 1988-2002 J.Paul Robinson - Purdue University Cytometry Laboratories