Download probability distribution model for predicting cell

PROBABILITY
PROBABILITYDISTRIBUTION
DISTRIBUTIONMODEL
MODELFOR
FORPREDICTING
PREDICTINGCELL
CELLCAPTURE
CAPTUREFROM
FROMDILUTE
DILUTESAMPLES
SAMPLESFOR
FORMICROFLUIDIC
MICROFLUIDICBIOSENSORS
BIOSENSORS
Yifei Zang1,2, Nathan Mosier1,2, Benjamin Tyner4, Xingya Liu1, Amanda Stewart1,2, WanWan-Tzu Chen1,3, Miroslav Sedlak1, Bruce Craig4, and Michael R. Ladisch1,2,3
1Laboratory
ABSTRACT
ABSTRACT
STATISTICAL
STATISTICALMODEL
MODELOF
OFPURIFICATION
PURIFICATIONAND
ANDSAMPLING
SAMPLING&&EXPERIMENTS
EXPERIMENTSSIMULATION
SIMULATION
• Purification : (recovery of each purification step) ~ Normal Distribution, N(µ=50%,σ=5%)
• Sampling: ( number of cells sampled for each sampling step) ~ Binomial Distribution B( n= total # of cells available to
be sampled, p=(sampled volume)/(tatol volume available for sampling))
• Simulate a process with 3 purification steps and 2 sampling steps: N3 B2. Each step is simulated by Monte-Carlo
method.
• Initial concentration ranges from 40 to 800,000 cells/L, corresponding to 10 to 200,000 cells in 250 ml buffer. Each
concentration is repeated 10,000 times.
The probability of capture one cell increases as the sample is
more concentrated.
Stomacher/Blend
Filtration
250 ml
Solids
Disposal
Sample Liquid
250 ml, .04 – .2 cells/ml
Sample
Purification
… (Centrifugation,
Filtration etc.)
Assay Liquid
0.5 ml, 4 – 20 cells/ml
Sample
Biochip
• Experiments/Tests:
¾ Purification recovery distribution
¾ Cell distribution: homogeneous or clustered
¾ False positive
• Sensitivity analysis, det.limit, purification steps etc.
• Optimization of whole process
Linear Regression of Sample Size v.s. Sample Concentration (LOG)
ACKNOWLEDGENENTS
ACKNOWLEDGENENTS
log(Vol)=-(Slo)log(Conc)+(Int) Assume that all assay liquid is sampled
1000
1000000
Sample volume (ml)
50 g, 10 – 50 target living cells
• Concentrating the sample before assay will
increase the probability of detection or decrease
the sample size.
• Enlarging sample size will improve the probability
of detection.
•The statistical model could be extended to any
rapid detection of pathogens in any food sample
using microfluidic devices.
WORK
WORKIN
INPROGRESS
PROGRESS
•The probability of capture one cell in a sample with 10 cells is 0.751,
while the probability for a sample with 50 cells increases to 0.997.
•The probability data as a function of sample concentration fit well with a
logistic correlation.
•Assume that all sample liquid is concentrated and all assay liquid is
sampled.
ASSAY
ASSAYPROCEDURE
PROCEDURE
Food (Meat)
CONCLUSIONS
CONCLUSIONS
RESULTS
RESULTSAND
ANDDISCUSSION
DISCUSSION
Det.Limit = 1
100000
10000
1000
100
10
90% confidence
95% confidence
99% confidence
1
0.01
0.1
1
Det.Limit = 5
Sample volume (ml)
The detection of low numbers of organisms in
large volumes of liquids is a challenge for both the
fermentation and food industries. The detection of
microbial contamination or the presence of
pathogens requires that the sample be rapidly
processed, concentrated, and assayed to detect
living cells. The rapid concentration and detection of
the pathogen Listeria monocytogenes from liquid
extract of meat is one application where sampling
size to achieve adequate detection confidence
levels is crucial. The prediction of the minimal
sample volume required to enable detection of a
specified microorganism must be carefully carried
out, so that the probability of detection meets predetermined criteria. This poster shows that detection
of 10 to 50 living cells extracted from a 50 g meat
sample into 250 mL of buffer can be calculated or
simulated using the Normal and Poisson/Binomial
distributions. The significance of these results in the
context rapid detection of pathogens using
microfluidic devices for purposes of bioprocess
monitoring and control is discussed.
Buffer
of Renewable Resources Engineering, 2Agricultural and Biological Engineering, 3Biomedical Engineering, 4Statistics
Purdue University
10
100
1000
100
10
90% confidence
95% confidence
99% confidence
1
100
1000
Initial concentration (cell #/ml)
Larger Sample Size Is Better Than Duplicating Samples
• Poisson Distribution, P(λ = total # of cells available
to be sampled, k= biochip detection limit)
• (sample volume) ≤ (total volume)/10
• The medium is homogeneous
• Simulate sample step from assay liquid to biochip
• The conclusion is expandable to the sample liquid
because N3 B2<1
10000
Biochip Detection Limit : 1
Confidence Slo
Int
90%
.9791
4.235
95%
.9844
4.372
99%
.9423
4.446
Biochip Detection Limit : 5
Confidence Slo
Int
90%
1.0153 4.895
95%
.9892
4.883
99%
1.0091 5.072
R2
.9988
.9984
.9954
R2
.9996
.9991
.9972
This research was supported through a
cooperative agreement with the ARS of the United
States Department of Agriculture project number
1935-42000-035.
REFERENCES
REFERENCES
• Microbiological Analysis in Water Distribution
Networks: Sampling Strategies, Methods and
Computer Programs, Armand Maul, Ellis Horwood
Limited, England
1991
• Microorganism s in Foods 2, Sampling for
microbiological analysis: Principles and specific
applications, M. Ingram, University of Toronto Press
1974
• Quality Sampling and Reliability, New Uses for the
Poisson Distribution, John Heldt, CRC Press LLC,
Florida,1999
• Microbiology in Pharmaceutical Manufacturing,
Richard Prince, PDA, MD 2001