How to Present and Compare Data Obtained by Particle Tracking Analysis and Other Related Methods

© 2019 HORIBA, Ltd. All rights reserved.© 2019 HORIBA, Ltd. All rights reserved. 1
How to present and compare data
obtained by particle tracking analysis
and other related methods
Kuba Tatarkiewicz PhD, R&D Global Director
3-6-2019

© 2019 HORIBA, Ltd. All rights reserved. 2
• Measuring sizes of individual particles
hydrodynamic diameter dh > d0 due to diluent drag
• Counting tracked particles in a given volume
investigated volume depends on size and refractive index
• Testing small volume of a sample
• statistical process of estimating particle size distribution
• volume tested about 100,000x smaller than sample volume
Particle tracking analysis

• Definition of CN: counts per volume [part/mL]
other defs: mass CM [mg/mL] or volume CV [μL/mL]
• Typically CN is given for a range of sizes
e.g. between 100 nm and 1 μm diameters
• Hence use of plots with size bins
• bin widths not necessarily equal
• some software do not support unequal bins (notably Excel)
Concentration measurements

• Error in counting proportional to
this applies to total counts and individual bin counts
• Number of bins depends on expected errors
N=10,000 and 100 bins, average error 10 counts/bin or 10%
• To obtain “nice”, smooth distributions:
• decrease number of bins and use wider bins
• use narrow bins to calculate parameters of a distribution
Statistical considerations
𝑁

Example plots of size distributions
Counts Density of PSD
logarithmic bins
Cumulative
0
200
400
600
800
1,000
1,200
1,400
1,600
0 400 800 1,200 1,600 2,000
Countsperbin[N]
Diameter [nm]
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1,000
Cumulativecounts
Diameter [nm]
D50=217 nm

• Definition of a bin:
• d ∈ [bi, bi+1[ where i=1,…,N
• equivalent definition: bi ≤ d < bi+1 (non-overlapping bins)
• typically b1 = 0 and bN = max size to be measured
• Strange bins definition encountered:
Binning

• Concentration is just a rational number, also per bin
• Histogram uses area to represent a distribution
• With unequal bins natural measurable is:
density of particle size distribution (PSD)
units: number of particles per bin width and
per investigated volume [part/nm/mL]
total concentration ≡ area of a histogram
What is really plotted

• When plotting concentration vs. size,
DO NOT connect points*
• Total concentration is a sum of numbers, not an integral
• When plotting density of PSD, one can connect
middle of bins ☛ linear approximation
• Total concentration CN is then
an area under the curve
Dimensional analysis
*There’s no data between points – by definition of a bin

• Create a list of measured sizes
typically diameters of nanoparticles are given in [nm]
• Bin those sizes in specific binning
typically logarithmic binning
(bi+2 – bi+1 ) / (bi+1 – bi ) = const
• Calculate density of PSD [part/nm/mL]; V0 needed
• Plot as a histogram of density of PSD
• Calculate parameters of a distribution (AV, SD, D50 ...)
Practical procedure

Example of real data in logarithmic binning
Concentration from 50 nm to 700 nm = area of histogram of density of PSD
DensityofPSD

• Most standards of size are mono-disperse
there are no standards for concentration…
• Typically real life samples are poly-disperse
e.g. multiple sizes or continuous distributions
• Natural samples like sea water or blood:
• highly poly-disperse with dominating small particles
• Junge distribution N(d) ∼ d-x where x=3.5÷4
Real data vs. standards

• Fitting unknown distribution of sizes
• Assumed binomial(s) distribution
• Height (or area) of different peaks
is NOT conserved during fitting
(not invariant of any fitting procedure)
• Looks great but lacks numerical accuracy
• Artificial peaks can be created
Fitted data problem (NanoSight FTLA)
cf. van der Pol et al. J Thrombosis and Haemostasis, 12, 1182 (2014)

© 2019 HORIBA, Ltd. All rights reserved.
• Concentration
• Average size
• Standard deviation
• D50
13
Parametric description of distributions
Dk =
1
𝑁𝑡𝑜𝑡𝑎𝑙
𝑖=1
𝑘
𝑛𝑖 definition Dk = 0.5 ☛ k ☛ bk equal D50
𝑆𝐷 =
1
𝑖=1
𝑁
𝑛𝑖 ∗ 𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 − 𝑏𝑖 +
𝐵𝑖
2
2
Bi = (bi+1 - bi) 𝑁𝑡𝑜𝑡𝑎𝑙 =
𝑖=1
𝑁
𝑛𝑖
𝐵𝑖
𝐵𝑖 =
𝑖=1
𝑁
𝑛𝑖
𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =
1
𝑖=1
𝑁
𝑛𝑖 ∗ (𝑏𝑖 +
𝐵𝑖
2
)

D50 & mode depend on binning!
Mode?
_30min+
6/2018
10:12
A
n
3417,
5.74 [nm/pixel]
ter_30min+
l 5, 350 rpm between videos
]
ntration: 0 [particles/mL]
Processing information
Detection threshold type: Polydisperse
Detection threshold: 2
AutoThreshold: Enabled
Feature radius: 35 [pixels]
Tracking starts on: 1 [frame]
Drift correction: 0 [%]
Results
Integrated from 30 nm to 1900 nm
Report ABT-308_after_30min+
Measurement date: 2/16/2018
Measurement time: 10:10:12
Measurement type: NTA
Operator: QT
Instrument information
Serial number: 024
Software version: 1.8.0.3417,
1.0.7 WeekBuild 2617
Calibration constant: 195.74 [nm/pixel]
Sample information
Sample ID: ABT-308_after_30min+
Sample description: Vial 5, 350 rpm between videos
Diluent: Custom 2.7 [cP]
Diluent impurities concentration: 0 [particles/mL]
Dilution: 1 [times]
Recording information
Frame rate: 30 [fps]
Results
Operator: QT
Serial number: 024
Sample information
Dilution: 1 [times]
Results
Operator: QT
Serial number: 024
Sample information
Dilution: 1 [times]
Results
narrow equal bins wide equal bins logarithmic bins variable bins
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 400 800 1,200 1,600 2,000
Cumulativecounts
Diameter [nm]
D50=321.50 nm
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 400 800 1,200 1,600 2,000
Cumulativecounts
Diameter [nm]
wide equal binsnarrow equal bins logarithmic bins
D50=307.33 nm
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 400 800 1,200 1,600 2,000
Cumulativecounts
Diameter [nm]
D50=316.10 nm
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 400 800 1,200 1,600 2,000
Cumulativecounts
Diameter [nm]
D50=317.50 nm
variable bins
most accurate
which one is mode?which one is mode?

• Parametric description using AV and SD
is not accurate or unique!
Anscombe’s quartet – same AV and SD, various shapes
• Even higher moments do not give enough info
• Basic experimental question:
How similar are two measured distributions?
Lies, damned lies, and statistics

Kolmogorov-Smirnov statistics
max
Non-parametric test:
Kolmogorov-Smirnov statistics
dav = 256 nm, SD = 145 nm, CV = 0.57
dav = 163 nm, SD = 68 nm, CV = 0.42
D A,B alpha D A,B,α Reject?
0.2335 0.05 0.0338 yes
Comparing parameters:

Anderson-Darling statistics
Area between two cumulatives is a good measure of distance between two or more distributions with unknown shape.

• Normalize area between cumulatives
extreme case: a) particles at 10 nm, b) particles at 1000 nm
• Distance is a number from the range [0,1]
same distributions have distance 0
extreme case – distance 1
• If areas are calculated between distributions in
same normalization, it can be a good measure
Distance between distributions
d
cumulative

How to Present and Compare Data Obtained by Particle Tracking Analysis and Other Related Methods

Recommended

Recommended

More Related Content

What's hot

What's hot (15)

Similar to How to Present and Compare Data Obtained by Particle Tracking Analysis and Other Related Methods

Similar to How to Present and Compare Data Obtained by Particle Tracking Analysis and Other Related Methods (20)

More from HORIBA Particle

More from HORIBA Particle (14)

Recently uploaded

Recently uploaded (20)

How to Present and Compare Data Obtained by Particle Tracking Analysis and Other Related Methods