Part VII. Verifying the Analytical Method’s Accuracy

Investigation 30

In Part V we found that the empirical model for the extraction of danshensu is

\[EY=0.575+0.0225A+0.00905B-0.00125A^2-0.000165B^2+0.000100AB\nonumber\]

where EY is the extraction yield (in mg/g), A is the extraction time (in min), and B is the solvent-to-solid ratio (in mL/g). Using this model, calculate danshensu’s predicted extraction yield for an extraction time of 7.50 min and a solvent-to-solid ratio of 35.0 mL/g. Is your predicted extraction yield consistent with the data in Table 2 and your response to Investigation 25?

Substituting into our empirical model for the extraction of danshensu an extraction time of 7.50 min and a solvent-to-solid ratio of 35.0 mL/g gives a predicted extraction yield of 0.814 μg/g. This results is consistent with the data in Table 2 for danshensu’s central-composite design, which suggests that its extraction yield is between 0.805 μg/g (for an extraction time of 7.00 min and a solvent-to-solid ratio of 35.0 mL/g) and 0.820 μg/g (for an extraction time of 7.82 min and a solvent-to-solid ratio of 25.0 mL/g), with its value closer to 0.805 μg/g.

Investigation 31

Figure 18 shows the chromatogram for a sample of Danshen extracted using the optimized conditions from Part VI. Using this chromatogram, calculate the actual extraction yield for each analyte and report its experimental extraction yield as a percentage of its predicted extraction yield from Table 3. Do your results provide confidence in our analytical method? Why or why not?

From Investigation 19, we know that the extraction yield, EY, is

\[\mathrm{\mathit{EY}\left(\dfrac{mg}{g}\right)=\dfrac{\mathit{A}\: (mAU)×\mathit{V}\:(mL)}{\mathit{k}\left(\dfrac{mAU•mL}{μg}\right)× \mathit{m}\: (g)}×\dfrac{1\: mg}{1000\: μg}}\nonumber\]

where A is the absorbance, V is the volume of solvent, k is an analyte-specific calibration constant, and m is the sample’s mass. The table below provides the absolute experimental extraction yields, EY, and the experimental extraction yields expressed as a percentage of the predicted extraction yield, %EY, using a volume of 35.0 mL and a sample of 1.000 g.

analyte	absorbance (mAU)	k (mAU•mL/μg)	EY (mg/g)	%EY
danshensu	36.4	1.605	0.794	97.5
rosmarinic acid	62.8	0.878	2.503	108.2
lithospermic acid	39.7	0.536	2.592	97.6
salvianolic acid A	26.4	1.585	0.583	97.2
dihydrotanshinone	33.1	2.841	0.408	96.2
cryptotanshinone	49.6	1.882	0.922	100.5
tanshinone I	59.4	1.599	1.300	97.3
tanshinone IIA	115.7	1.467	2.760	99.9

The percent extraction yields range from a low of 96.2% for dihydrotanshinone to a high of 108.2% for rosmarinic acid—the two analytes whose extraction yields could not be modeled—with an average percent extraction yield of 99.3%. These results suggest the empirical models for each analyte’s extraction yield provide a good estimation of the actual extraction yields.

Note: The predicted extraction yields are derived from Table 2 of the original paper. The chromatogram in Figure 18 is derived from Table 3 of the original paper.

Investigation 32

Compare your results from Investigation 31 with the results reported in Table 4. Do these results support a concern that heat-reflux extractions may distort the apparent composition of Danshen? As you consider this question, you may wish to review the chemical structures of these compounds, which are shown in Part I, and the HPLC data in Figure 19 for samples drawn at different times during an extended heat-reflux extraction of Danshen.

The table below reports the extraction yields for the three heat-reflux extractions as a percentage of the extraction yields from Investigation 30. With the exception of danshensu and lithospermic acid using HRE-1, the results for the remaining analytes are significantly less than 100%—suggesting that heat reflux extractions result in the thermal degradation of the analytes—ranging from a low of 62.0% for cryptotanshinone using HRE-1 to a high of 85.9% for dihydrotanshinone using HRE-2. The percentage extraction yield of 101.2% for lithospermic acid using HRE-1 is inconsistent with its results using HRE-2 and HRE-3 and most likely is an outlier.

	Extraction Yields as % of Extraction Yield for Microwave Extraction
analyte	HRE-1	HRE-2	HRE-3
danshensu	205.3	104.8	133.5
rosmarinic acid	81.1	80.4	64.6
lithospermic acid	101.2	67.6	85.7
salvianolic acid A	76.4	76.8	79.8
dihydrotanshinone	85.4	85.9	71.6
cryptotanshinone	62.0	65.0	59.0
tanshinone I	69.6	74.8	70.6
tanshinone IIA	72.1	84.2	64.2

The results for danshensu require a closer consideration as we need to determine if they represent an underreporting of danshensu when using a microwave-assisted extraction or if they are the result of thermal degradation of other compounds during a heat-reflux assisted extraction. Two observations lead us to the latter possibility. First, the HPLC chromatograms in Figure 19, which focus on danshensu’s peak, show an increase in its peak height and, therefore, an increase in danshensu’s concentration with longer exposures to an elevated temperature; this suggests that the concentration of danshensu may increase as a result of the thermal degradation of other compounds. The structures of rosmarinic acid, lithospermic acid, and salvianolic acid A support this possibility as each compound is an ester, one part of which is danshensu. It seems likely that hydrolysis of the ester bond releases danshensu; thus, as the concentrations of rosmarinic acid, lithospermic acid, and salvianolic acid A decrease, the concentration of danshensu increases. This further supports the concern that a heat-reflux extraction distorts our understanding of Danshen’s composition.

Note: The data in Table 4 is taken from Table 3 of the original paper.

Investigation 33

Explain why analyzing a sample before and after adding a known amount of an analyte allows you to evaluate a method’s accuracy. Figure 20 shows the chromatogram for a sample of Danshen spiked prior to the microwave extraction with known amounts of each analyte, the concentrations of which are shown in Table 5. Using this data and your results for the unspiked sample in Investigation 31, how confident are you in the accuracy of our analytical method?

The process of analyzing a sample before and after adding a known amount of analyte is called a spike recovery. We first analyze a sample and determine the concentration of analyte in the sample. Next, we spike an identical sample with a known amount of analyte and determine the concentration of analyte in the spiked sample. The percent recovery is defined as

\[\dfrac{C_\ce{spiked}-C_\ce{unspiked}}{C_\ce{spiked}} ×100\nonumber\]

where C_spiked is the analyte’s concentration in the spiked sample and C_unspiked is the analyte’s concentration in the original, unspiked sample. If we lose some analyte to thermal degradation during the extraction, then we will obtain a spike recovery significantly less than 100%, and if a different analyte converts to our analyte during the extraction (as is the case for the data in Table 4 and in Figure 19), then we will obtain a spike recovery significantly greater than 100%. Obtaining a spike recovery of 100% provides confidence that the analytes are not degraded during the extraction.

The table below summarizes results for the spike recoveries. The first column gives the absorbance values extracted from Figure 20. The concentrations of analytes in the spiked sample were calculated as in Investigation 30 and the concentrations of analytes in the unspiked sample are taken from Figure 18 and from Investigation 30. Individual spike recoveries range from a low of 93.7% for tanshinone I to a high of 103.4% for tanshinone IIA. The average spike recovery is 99.6%. With the possible exception of the spike recovery for tanshinone I, which is a bit low, these results provide confidence in our analytical method’s accuracy.

analyte	absorbance (mAU)	Cspiked (mg/g)	Cunspiked (mg/g)	Cadded (mg/g)	% Recovery
danshensu	59.3	1.293	0.794	0.500	99.8
rosmarinic acid	126.1	5.023	2.503	2.500	100.8
lithospermic acid	78.8	5.146	2.592	2.500	102.2
salvianolic acid A	49.4	1.091	0.583	0.500	101.6
dihydrotanshinone	73.3	0.903	0.408	0.500	99.0
cryptotanshinone	101.5	1.888	0.922	1.000	96.6
tanshinone I	102.2	2.237	1.300	1.000	93.7
tanshinone IIA	224.0	5.344	2.760	2.500	103.4

Note: The original paper reports that the spike recoveries range from a low of 94.6% to a high of 106.3%, but do not report the spike recoveries for individual analytes. The data for this investigation were generated artificially.