METHODS FOR AUTOMATIC PEAK FINDING IN
CALORIMETRIC DATA
BACKGROUND
[0001] The invention relates to methods for analyzing calorimetric data obtained
from calorimetric instrument, and in particular, to methods for automatically
identifying peaks and/or peak positions in calorimetric data.
[0002] Differential scanning calorimetry (DSC) is a thermo-analytical technique
that is used for thermal analysis. DSC is used across a range of applications, both as a
routine quality test and as a research tool. For example, DSC may be used to study
stability of compounds, security screening, drug analysis or drug analysis.
[0003] In calorimetric applications, several peak-finding methods are used to
identify multiple peaks in calorimetric data. Most of these methods use user-supplied
initial guesses for the number of peaks and each peak location. In the manual
procedure, the user visually evaluates the single-peak fit and decides whether an
additional peak might exist. However, in low-signal/high-noise data, multiple peaks
become indistinguishable to the user, forcing the user to assume a single peak.
Further, a manual procedure also introduces user-related variability.
[0004] Therefore, it would be desirable to provide automated methods for
analyzing calorimetric data that requires minimum user input to determine number
and location of peaks in the calorimetric data, including peaks that are not visible to
the user.
BRIEF DESCRIPTION
[0005] In one embodiment, a method for automatically determining a position of
one or more calorimetric peaks in a set of calorimetric data is provided. The method
comprises a) providing a non-linear fit for the calorimetric data, b) calculating a
residual by subtracting the non-linear fit from the calorimetric data, c) calculating an
error based on the residual, d) comparing the error with a predetermined error, and e)
providing another non-linear fit if the error is greater than the predetermined error.
[0006] In another embodiment, a method for automatically determining a position
of one or more calorimetric peaks in a set of calorimetric data is provided. The
method comprises a) providing a first non-linear fit for the calorimetric data, b)
determining a first residual by subtracting the first non-linear fit from the calorimetric
data, c) calculating a first error based on the first residual, d) providing a second non
linear fit for the calorimetric data, e) determining a second residual by subtracting the
second non-linear fit from the calorimetric data, f) calculating a second error based on
the second residual, g) comparing the first and second errors, and f) selecting the non
linear fit corresponding to a lower error.
DRAWINGS
[0007] These and other features, aspects, and advantages of the present invention
will become better understood when the following detailed description is read with
reference to the accompanying drawings in which like characters represent like parts
throughout the drawings, wherein:
[0008] FIG. 1 is a flow chart for an example method for automatic peak fittings for
calorimetric data;
[0009] FIG 2 is a flow chart for another example method for automatic peak
fittings for calorimetric data;
[0010] FIG 3 is a graph of an example of calorimetric data for automatic peak
fitting; and
[0011] FIG. 4 is a graph for determining the RMS with regard to the number of
peaks fitted in the calorimetric data of FIG. 3 .
DETAILED DESCRIPTION
[0012] One or more examples of the methods of the invention relate to analyzing
calorimetric data with minimal or no user input for determining the number and
location of calorimetric peaks, including peaks that are not easily visible to human
eye. In certain examples, the method for automatically determining a position of one
or more calorimetric peaks comprises performing a non-linear fit for the position of
the maximum peak, subtracting the non-linear fit from the calorimetric data to obtain
a residual, calculating an error based on the residual; comparing the error with a
predetermined error; and providing another non-linear fit if the error is greater than
the predetermined error.
[0013] Although one or more examples of the methods are used to analyze
calorimetric data, the methods may accommodate and model other data types having
similar distribution. The peaks in the calorimetric data may be determined using the
method where the peaks are otherwise invisible to a user or operator. In one example,
the peaks may be invisible due to high noise levels in the data. The methods may be
modified to suit the type of data to be analyzed. For example, instead of calculating
root mean square error, other possible evaluation metrics include mean squared error,
mean absolute error, chi-squared error, correlation coefficient, or coherence error.
[0014] In one embodiment, a theoretical expression used to model the curve may
include thermal models, such as but not limited to, an independent two state transition
model, a non-two-state, or a non-independent (i.e. cooperative) model. In one
example, the non-linear fit may be population based. For example, the shape of the
peak may be related to the number of proteins that unfold at a given point of time
during the course of the experiment, the peak may occur at the point where 50 percent
of the proteins have been unfolded, thereby representing an integral change in
enthalpy. Non-limiting examples of non-linear fit may include Gaussian,Cauchy,
weighted mixture of Gaussian and Cauchy profile, asymmetric Gaussian, monotonic
transition from Gaussian to Cauchy profile). Equations 1-3 are examples of a
theoretical expression for modeling the curve. The model is based on the two state
transition model. The equations 1-3 comprise parameters specific to the calorimetric
system.
AH (T) AHm +ACp (T -
m ) -Eq. 2
[0015] where B0, Bi are constants, domains A and B refer to different stages in
which proteins may unfold, T is temperature, TmA is the temperature at which 50
percent of the proteins have unfolded in domain A, Cp is a molar heat capacity, ACp
is a change in molar heat capacity, KA is an equilibrium constant for domain A, 
is a change in a molar heat enthalpy for domain A, CPAis a change in a molar heat
capacity for domain A, and AHmA is a change in a molar heat enthalpy for domain A
at temperature TmA.
[0016] FIG. 1 is a flow chart of an example of a method of the invention. At step
10, the method begins by providing a non-linear fit for the calorimetric data. Nonlimiting
examples of the non-linear fit may include Levenb erg-Mar quardt algorithm,
or a polynomial fit. The calorimetric data may be directly received from a
calorimetric device. The calorimetric data may also be accessed from a memory or a
data file comprising data previously collected from, for example, an experimental
setup.
[0017] Optionally, at step 12, the experimental data may be pre-processed. For
example, the experimental data may be pre-processed to subtract a baseline. It may
not always be required to have a baseline subtraction from the calorimetric data. The
need for pre-processing step may depend on the level of complexity of the system.
Pre-processing may be performed to reduce the noise level in the experimental data.
Alternatively or in addition, the pre-processing may be performed to estimate the
noise level in the experimental data. The calorimetric data may comprise a
combination of calorimetric signal and baseline. Baseline features may be subtracted
from the data to obtain a signal having reduced noise. This signal with reduced noise
may then be used for fitting a non-linear curve. The calorimetric data may be
processed to reduce the noise. In one embodiment, the method for automatically
removing baseline features from the calorimetric data comprises repeatedly fitting one
or more polynomial functions one at a time to the baseline, subtracting the best fit
polynomial function from the calorimetric spectrum so as to provide a current
baseline-corrected spectrum, evaluating the quality of the fit, as measured by a sum of
squared residuals (SSR), and proceeding until SSR changes, from iteration to
iteration, by less than a predetermined percentage of its original value.
[0018] At step 14, a maximum peak in the calorimetric data may be located based
on the fitted non-linear fit. The maximum peak may also be referred to as "maxima"
or "global maxima". In one embodiment, the maxima may be located by calculating
enthalpy change with respect to temperature. Optionally, the position of the maxima
may be stored. In one example, a position of the maxima and the value of the molar
enthalpy at the maxima may be stored or displayed. The position of the maxima may
be determined with respect to time or temperature or both.
[0019] At step 16, a residual may be determined for the non-linear fit. The
residual may be obtained by subtracting the non-linear fit from the experimental data.
The residual may be sum of all the residuals at various locations on the experimental
data. In one embodiment, the residual may be determined by subtracting an area
under the fitted curve from an area under the calorimetric data curve.
[0020] At step 18, an error is calculated based on the residual. In one embodiment,
the error is a root mean square (RMS) of the residual.
[0021] At step 20, the calculated RMS error for the non-linear fit is compared with
a determined RMS value. If the RMS error for the fitted peak is less than the
determined RMS error, the fitted curve is accepted (step 22).
[0022] If the RMS error is more than the determined RMS error, next non-linear fit
may be applied to the calorimetric data and steps 10, 14, 16, 18 and 20 may be
repeated whereby RMS error is calculated and compared to the determined RMS error
until the RMS error is equal to or less than the determined RMS error. The method is
repeated for finding subsequent peaks and providing non-linear fits for the subsequent
peaks. The process is repeated till the residual value is below a certain determined
residual value, and the peaks are identified and non-linear fits are provided for the
same. In one example, if the calculated RMS is greater than the determined RMS,
one more peak is fitted, if after fitting the peak, RMS is less than or equal to
determined RMS, the number of peaks is the number of peaks fitted with the RMS
value being at the lowest.
[0023] In another example, if no RMS threshold is set, the number of peaks is the
number of peaks fitted with the RMS value being at the lowest. Assuming that the
RMS value of any non-linear fit is not less than the standard deviation of the noise,
the determined RMS value may be selected by estimating the standard deviation over
a relatively flat (linear) portion of the data. In one example, the calculated RMS error
may be relatively greater than the determined RMS value (scaling factor > 1) but not
so large that less ideal fits may be accepted. The determined RMS value enables
providing a closest non-linear fit for the calorimetric data while avoiding unnecessary
inference of undesired peaks for the calorimetric data. The determined RMS value
prevents the algorithm from searching through several peaks if the required number of
peaks has already been discovered.
[0024] The determined RMS error value may be decided by the user.
Alternatively, the determined RMS may be selected by the system depending on the
type of DSC event.
[0025] In some embodiments, the algorithm may compare RMS values for
different non-linear fits and decide the total number of peaks in the calorimetric data.
In other embodiments, the user may input the number of maxima for the calorimetric
data. As illustrated in FIG. 2, if the calculated RMS error is greater than the
determined RMS, a second check may be performed for the non-linear fit at step 24,
whereby the total number of peaks in the non-linear fit may be compared with the
number of maxima inputted by the user. If the number of peaks in the non-linear fit is
equal to the number of maxima, the non-linear fit may be selected. In embodiments
where more than one non-linear fit have been attempted to be fitted in the calorimetric
data, the non-linear fit having the minimum RMS error may be selected (step 26).
The non-linear fit with the minimum RMS value may be then confirmed (step 22),
and subsequently displayed (step 28). However, if the number of peaks in the non
linear fit is not equal to the number of maxima, e.g., if the number of peaks is less
than the number of maxima, next peak may be determined in the calorimetric data
(step 30). At step 32, a non-linear fit may be provided for the next maxima. The non
linear fit is provided for the next maxima while retaining the non-linear fit for the
previous peak, i.e., the global maxima. Next, steps 10, 14, 16, 18 and 20 may be
repeated whereby RMS error is calculated and compared to the determined RMS
value until the RMS error is equal to or less than a determined RMS value.
Optionally, the number of peaks may be updated in the system after every non-linear
fit is confirmed. The non-linear fit is modified to fit a peak for the position
corresponding to the next maximum residual while retaining the earlier identified
peak location and shape.
[0026] The method may also comprise registering the peak locations for the
determined peaks. The method may further comprise identifying peaks introduced
due to impurities in the DSC sample. In one embodiment, the fitted peaks may be
compared with an existing library of calorimetric events. The comparison may be
used to identify events that may have been introduced due to impurities in the sample.
In one example, the system may have built-in intelligence to identify and discard
abnormally sharp peaks that usually occur due to presence of impurities in the sample.
In another example, such ambiguities (sharp peaks) may be pre-fed in the system.
The pre-fed information on ambiguities may be used to provide corrected information
to the user regarding the calorimetric events.
[0027] Optionally, the information related to the calorimetric data is provided to
the user. The data may be provided at different steps in the process. Alternatively or
additionally, the final outcome may comprise textual as well as graphical
representations of the number and locations of calorimetric peaks. The reporting may
be performed in numerous ways, e.g., via a visual display terminal, a paper printout,
or, indirectly for example, by outputting the parameter information to a database on a
storage medium for later retrieval by a user. The reporting step may comprise
reporting either textual or graphical information, or both. The parameters may be
provided to the user by displaying the same on a display, or generating a printout of
the parameters. Some methods of the invention may further comprise the action of
extracting, from the model spectral parameters, information related to or inferred to be
related to the physical functioning or operational state or an operational parameter of
the sample and reporting such information to a user. Additional steps of comparing
peak parameters (for instance, peak position) to a database and reporting, to a user,
the calorimetric events and their corresponding temperature and time for one or more
peaks may also be performed.
[0028] FIG. 3 illustrates an example of method of the invention. Calorimetric data
represented by curve 34 is provided. A non-linear fit 36 is provided for the global
maximum. A global maximum 38 is identified. RMS error is calculated and based on
the RMS error a suitable non-linear fit is provided for the global maximum.
Subsequently, if more than one peak exists, the subsequent peaks are non-linearly
fitted using the iterations. As illustrated in FIG. 4, the least RMS error occurs for two
peaks. The RMS value is higher for fitting one and three peaks, and the value of the
RMS error increases as the number of peaks increases beyond two. Referring back to
FIG. 3, the second peak is not easily visible to the human eye, however, using the
method of the invention, the number of peaks is correctly identified as two.
[0029] The methods of the invention may be applied in various applications where
DSC is used. For example, the method may be used to study liquid crystals, or
stability and/or optimum storage conditions for a material or compound for oxidation.
In one example, the presence of an exothermic event may be used to assess the
stability of a substance to heat. The method may be used for drug analysis in
pharmaceutical and polymer industries, or for studying curing processes, which
allows the fine tuning of polymer properties. The cross-linking of polymer molecules
that occurs in the curing process is exothermic, resulting in a positive peak in the DSC
curve that usually appears soon after the glass transition. In the pharmaceutical
industry it is desirable to have well-characterized drug compounds in order to define
processing parameters. For instance, if it is required to deliver a drug in the
amorphous form, it is desirable to process the drug at temperatures below those at
which crystallization can occur. The temperature range over which a mixture of
compounds melts is dependent on their relative amounts. Consequently, less pure
compounds will exhibit a broadened melting peak that begins at lower temperature
than a pure compound. In a chemical analysis, the method may be used as an analysis
tool to evaluate the purity levels of the samples.
[0030] The methods may be implemented in the existing software architecture
with no modifications to hardware. Therefore, a more reliable, higher productivity
calorimeter may be produced with no additional cost of goods.
[0031] While only certain features of the invention have been illustrated and
described herein, many modifications and changes will occur to those skilled in the
art. It is, therefore, to be understood that the appended claims are intended to cover
all such modifications and changes as fall within the scope of the invention.
CLAIMS:
1. A method for automatically determining a position of one or more
calorimetric peaks in a set of calorimetric data, comprising:
a) providing a non-linear fit for the calorimetric data;
b) calculating a residual by subtracting the non-linear fit from the calorimetric
data;
c) calculating an error based on the residual;
d) comparing the error with a predetermined error; and
e) providing another non-linear fit if the error is greater than the predetermined
error.
2 . The method of claim 1, further comprising, calculating a molar entropy
change or an area occupied by the calorimetric data.
3 . The method of claim 1 or 2, further comprising, determining whether
another peak exists in the calorimeter data based on the calculated error.
4 . The method of claim 1, 2 or 3, wherein calculating the error comprises
calculating a root mean square error.
5 . The method of any one of the preceding claims, further comprising,
determining a position of a maximum residual on the calorimetric data.
6 . The method of claim 5, further comprising automatically comparing
the maximum residual position with a library of calorimetric data.
7 . The method of claim 6, comprising accepting or rejecting the data
based on the comparison with the library of calorimetric data.
8 . The method of any one of the preceding claims, further comprising,
registering a position of the maximum residual.
9 . The method of claim 8, comprising displaying associated physical
phenomenon.
10. The method of any one of the preceding claims, comprising inputting a
determined number of peaks.
11. The method of any one of the preceding claims, wherein the non-linear
fit comprises a polynomial fit, or a Levenberg-Mar quardt algorithm.
12. The method of any one of the preceding claims, further comprising
displaying the non-linear fit at predefined stages.
13. The method of any one of the preceding claims, further comprising
repeating steps b), c), d) and e).
14. The method of any one of the preceding claims, further comprising
determining a number of peaks in the calorimetric data.
15. A method for automatically determining a position of one or more
calorimetric peaks in a set of calorimetric data, comprising:
a) providing a first non-linear fit for the calorimetric data;
b) determining a first residual by subtracting the first non-linear fit from the
calorimetric data;
c) calculating a first error based on the first residual;
d) providing a second non-linear fit for the calorimetric data;
e) determining a second residual by subtracting the second non-linear fit from
the calorimetric data;
f calculating a second error based on the second residual;
g) comparing the first and second errors; and
h) selecting the non-linear fit corresponding to a lower error.
16. The method of claim 15, further comprising repeating steps d) through
h) with one or more additional non-linear fits to confirm whether the selected non
linear fit provides the minimum error.
17. The method of claim 15 or 16, further comprising informing the user
whether the first or second error is below a determined value.
18. The method of claim 17, further comprising automatically selecting the
non-linear fit having an error which is below the determined value.
19. Thermal analysis of proteins including preforming the method of any
one of the preceding claims, wherein said non-linear fit of claim 1, or said first or
second non-linear fit of claim 15, is determined by any one or more of the equations
1,2 or 3 below:
AH (T) AHm +ACp (T -
m ) -Eq. 2
where B 0, B i are constants, subscript A refers to a domain in which proteins may
unfold, T is temperature, TmA is the temperature at which 50 percent of the proteins
have unfolded in domain A, Cp is a molar heat capacity, ACp is a change in molar
heat capacity, KA is an equilibrium constant for domain A, is a change in a molar
heat enthalpy for domain A, CPA is a change in a molar heat capacity for domain A,
and AHmA is a change in a molar heat enthalpy for domain A at temperature TmA.