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Functional DOE to optimise single peak shape AND position

Hi,

A JMP Pro user is interested in using FDOE to optimise a Cell Assay.

Each run produces a signal vs time curve with one peak. The shape AND position of the curve is dependent on the factors. The goal is to find factor conditions to achieve a sharp peak at 17 hours.

Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)

I am thinking this will require DTW to align the peaks and then FDE should be able to model different curve shapes. But then we will need to model the DTW shift against the factors to find out how to optimise.

Has anyone looked at an example like this?

Thanks,

Phil

Re: Functional DOE to optimise single peak shape AND position

Hi Phil,

How about using a "Fit curve" if data follow gaussian distribution? Please see the attached simulated data. My colleague asked me a similar question before.

 

• Analyze > Specialized Modeling > Fit Curve
• Assign the factors to the Y, X, Group, and Z roles.
• Fit Gaussian Peak model
• Select "Curve DOE Analysis" from the red triangle.

 

Re: Functional DOE to optimise single peak shape AND position

Great idea, @yuichi_katsumur . I guess it will depend on how well the real data follow a gaussian distribution. But I suspect that, even if it is not a perfect fit, it could be good enough to answer their scientific objectives.

Thanks,

Phil

Re: Functional DOE to optimise single peak shape AND position

The DTW will align all the curves to a reference and lose the peak's location (feature). It would be better, in this case, not to use DTW. Here is an example to illustrate the approach without and with DTW. I arbitrarily used ID=1 as the golden curve, and I arbitrarily used ID=2 for the DTW. You won't be able to optimize for location in the second analysis.

Names Default to Here( 1 );

dt = New Table( "Peak Shape and Location",
 New Column( "Peak ID", "Character", "Nominal" ),
 New Column( "X", "Numeric", "Continuous" ),
 New Column( "Y", "Numeric", "Continuous" )
);

nPoints = 100;
nFunctions = 5;
id = {};
domain = Transpose( Index( 1, 100 ) );
response = time = [];

For( c = 1, c <= nFunctions, c++,
 Insert Into( id, Eval( Repeat( List( Char( c ) ), nPoints ) ) );
 time |/= domain;
 response |/= Normal Density( domain, 10*c+20, c );
);

:Peak ID << Set Values( id );
:X << Set Values( time );
:Y << Set Values( response );

// launch and fit P-splines without DTW
dt << Functional Data Explorer( Y( :Y ), X( :X ), ID( :Peak ID ),
 Data Processing( Load Targets( "1" ) ),
 P Splines( Functional PCA( 1 ) )
);

// launch and fit P-splines with DTW
dt << Functional Data Explorer( Y( :Y ), X( :X ), ID( :Peak ID ),
 Data Processing( Load Targets( "1" ), Dynamic Time Warping( Reference( "2" ) ) ),
 P Splines( Functional PCA( 1 ) )
);

 

Re: Functional DOE to optimise single peak shape AND position

HI @Mark_Bailey ,

Nice example data!

Yes, that is what I thought.

In this case, optimising for peak location is the main objective, so the Curve DOE approach from @yuichi_katsumu1 seems like the best option.

Thanks,

Phil

Re: Functional DOE to optimise single peak shape AND position

This looks like is a chromatography example.  Another simpler approach is to just record the elution time of the peak and the peak width, which most modern chromatography systems will determine automatically or semi-automatically.  Then use the elution time and peak width as responses.   

Re: Functional DOE to optimise single peak shape AND position

Hi @SamGardner ,

Yes, it does look like chromatography data - that was my first thought too. Actually, it is a cell-based assay, and the data are coming from a plate reader, so I don't know that they will have any peak picking software.

The Curve DOE approach that @yuichi_katsumur suggested seems like the best solution here. It is maybe overkill and I can't imagine anyone buying Pro just to do this. But it would still be a nice example and I think it meets the objectives of the scientist involved.

Thanks!
Phil