John gave me a scare with his link to a paper claiming that microwaving destroys of 97% of flavonoids in broccoli:
Research suggests that microwaving causes 97% loss of flavonoids in broccoli. Boiling caused 66% loss, high pressure boiling 47%. Steaming had minimal effect. 
Now I would be very reluctant to give up use of the microwave. We do a lot of cooking on weekends – soups, stews, lasagna, a pot of sweet potatoes, and the like – and eat those foods through the week. Stovetop warming is impossible at work, takes more time at home, and necessitates cleaning pots; so microwave warming is a central part of our lifestyle. We also make a pot of green tea every morning and use the microwave to re-heat cups through the day.
A Hard Result to Believe
The idea that flavonoids are so fragile that they are quickly destroyed by microwaves is extremely surprising. Flavonoids are partly responsible for the color of berries:
Yet I’ve never seen berries lose their color in the microwave. The cranberries in my Neo-Agutak (as Melissa dubbed it) may have darkened a bit, but they remained visibly red:
But who am I to believe my own eyes when published, peer-reviewed science says otherwise? So let’s look at the science.
The Vallejo et al paper
In the paper John cited, they submerged 1.2-inch diameter bunch of broccoli florets in tap water and cooked them “at full power (1000W) for 5 min.” 
The broccoli was then withdrawn from the cooking water, freeze-dried, powdered, after which 2 g of powder was homogenized three times in 50 ml of 70% methanol, and the homogenate filtered through cheesecloth to remove all solids. The resulting solution was evaporated in a vacuum at 30°C until it was reduced to 1 ml, after which they added 4 ml water. At this point the supernatant (the liquid on top) was taken and the bottom portion, containing any heavier solids, was discarded. The supernatant liquid was then filtered through a 0.45 µm polyethersulphone filter to remove any molecules or solids larger than about 4,000 atoms in diameter. 
Now I’m not a food chemist, and am not qualified to evaluate this procedure. But it seems clear that anything resembling “food” is rigorously removed from the water before measurement. There are many steps at which flavonoids could be lost.
The remaining filtered liquid was then analyzed with a Liquid Chromatography machine:
Phenolic acids were quantified as chlorogenic acid (5-caffeoylquinic acid; Sigma, St Louis, MO, USA), flavonols as quercetin 3-rutinoside (Sigma), and sinapic acid derivatives as sinapic acid (Sigma). 
The table of data for sinapic acid derivatives is detailed enough that we can get some idea of the variation across samples. Here is their data table:
Of the raw data – the top 9 rows and the 7 columns under “Sinapic and feruloyl derivatives” – 34 of the 63 data points read “0.0.” Every method of cooking has at least one 0.0 entry for edible parts, and for the watery part only 2 of the 28 data points are non-zero. Since each data point represents an average of three samples, it’s clear that the great majority of samples had no detectable nutrients at all by the time they reached the Liquid Chromatography machine.
Since nutrients dissolved in water were entirely lost, and the filtering and supernatant extraction were designed to remove everything that wasn’t dissolved in water, I think “0.0” is precisely what we should expect. If that’s the case, it’s very hard to be confident that the non-zero data points are measuring nutrients in the original food.
Here is their discussion of the results:
Microwave treatment led to the highest losses of phenolic compounds, similar to those found for glucosinolates.19 According to this, 97, 74 and 87% losses of total flavonoids, sinapics and caffeoylquinic derivatives respectively (Fig 2), were reached, probably owing to the high level of evaporation of water in which the leached compounds were dissolved. This flavonoid loss rate does not agree with that previously reported by other authors for microwaving.15,17 Also in this treatment, no compounds were detected in the cooking water (Fig 2). As previously mentioned in this work, it is suggested that components in the tissue are more stable than those in water, where they are more degraded. Probably a new microwave cooking treatment without water would lead to lower percentage losses, as previously reported for ascorbic acid,22 but it would also result in some flavor differences. 
I’m not a chemist, but it seems odd that evaporation of water would cause loss of flavonoids. Also, if the flavonoids were leached en masse from the broccoli into the “cooking water,” which then evaporated (turned to steam) due to microwave heating, then the microwaving must have been far more intense than most people’s kitchen heating.
These authors have also estimated flavonoid loss in other stages of food delivery:
- 60% loss of flavonoids in storage and shipping. 
- 84% loss of flavonoids in a model of intestinal digestion. 
So if our cranberries lost 60% of flavonoids in the supermarket, 97% in the microwave, and 84% in digestion, only 0.2% were left for the body. Perhaps.
What Do Other Researchers Find?
Fortunately for us, other groups have studied what happens when you microwave food.
Indeed, it seems that due to commercial products such as dried fruit and flavonoid supplements, there has been active research into microwaves as a means of drying berries and extracting flavonoids from various plants.
In these studies microwave heating often does better than other methods at preserving flavonoids!
Here is a sampling of papers. First, microwave drying preserved more anthocyanins in cranberries than hot air drying:
[C]ranberries were dried by vacuum-microwave drying (VMD), freeze-drying (FD), or hot air-drying (AD), to compare the effects of different drying processes on both physical changes as well as the retention of bioactive components in dried samples…. In general, vacuum-microwave drying and freeze-drying resulted in similar retention of anthocyanins and antioxidant activity, which were both relatively higher (P < 0.05) than that recovered from cranberries dried by hot air drying. 
There’s been a lot of work on green tea. Microwaving does better than standard methods for the extraction and preservation of catechin and epicatechin from green tea:
In this work, for the first time, microwave-assisted extraction (MAE) followed by CE was developed for the fast analysis of catechin and epicatechin in green tea. In the proposed method, catechin and epicatechin in green tea samples were rapidly extracted by MAE technique, and then analyzed by CE. The MAE conditions and the method’s validation were studied. It is found that the extraction time of 1 min with 400 W microwave irradiation is enough to completely extract catechin and epicatechin in green tea sample, whereas the conventional ultrasonic extraction (USE) technique needs long extraction time of 60 min…. The proposed method has good recoveries, which are 118% for catechin and 120% for epicatechin. The proposed method was successfully applied to determination of the catechin and epicatechin in different green tea samples. The experiment results have demonstrated that the MAE following CE is a simple, fast and reliable method for the determination of catechin and epicatechin in green tea. 
Another study used both low-power microwaves and conventional heating to keep green tea at 80°C for 30 minutes. Microwaved tea had a higher content of catechins, including the flavanol epigallocatechin gallate, than conventionally heated tea:
[M]icrowave-assisted water extraction (MWE) … appears more efficient than CWE [conventional water extraction] at both 80 and 100 degrees C, particularly for the extraction of flavanols and hydroxycinnamic acids. 
Microwaving tea leaf residues to temperatures as high as 230°C may not destroy polyphenols:
Microwave heating was used to produce aqueous-soluble components from green, oolong, and black tea residues. Heating at 200-230 degrees C for 2 min extracted 40-50% of polysaccharides and 60-70% of the polyphenols. 
In green tea, microwaves do destroy a natural chemical: the polyphenol-degrading enzyme polyphenol oxidase. Loss of polyphenol oxidase leads to higher levels of phenols and catechins. As a result, microwave pre-treatment of green tea leaves creates a tastier, higher quality tea:
Parched and sun-dried teas contained the lowest levels of total phenols and catechins, and their infusions were dull in color with a slightly burnt odor. Microwave-inactivated and-dried teas showed the highest levels of total phenols and catechins, and their infusions were bright in color and sweet in taste with a subtle pleasant odor. 
Onions are another frequently studied food. Microwaving onions causes about half the flavonoids to leach into water and half to remain in the onion. Only about 2% are lost:
[A]t optimized power (500W) [m]icrowave extraction resulted significant yield (81.5%) with 41.9% of flavonol contents, with better retain of remaining flavonoids (55.9%) in residues of onions. 
In a Japanese study, onions retained the highest fraction of flavonoids and vitamin C if they were cooked in a microwave, rather than fried or boiled:
We selected quercetin conjugates, total phenol compounds, and ascorbic acid to estimate the amount of flavonoid ingestion from onion. We examined the following cooking methods: boiling, frying with oil and butter, and microwave cooking. Microwave cooking without water better retains flavonoids and ascorbic acid. Frying does not affect flavonoid intake. The boiling of onion leads to about 30% loss of quercetin glycosides, which transfers to the boiling water. 
Vacuum microwaving seems to be the optimal way to dry and preserve strawberries:
This study has demonstrated that vacuum-microwave drying, especially at 240 W, can produce high-quality products, with the additional advantage of reduced processing times, compared to other processes such as freeze-drying. 
Microwaving causes no loss of anthocyanins from pigmented potatoes:
The analyses were carried out both on fresh tubers and after cooking treatments (boiling and microwaves)…. For the pigmented potatoes, the heating treatment did not cause any changes in the phenolic acids content, while anthocyanins showed only a small decrement (16-29%). The cv. Highland Burgundy Red showed anthocyanins and phenolic acid concentrations close to 1 g/kg and more than 1.1 g/kg, respectively. 
Olive oil polyphenols survive best under microwave heating:
Virgin olive oils were subjected to simulated common domestic processing, including frying, microwave heating, and boiling with water in a pressure cooker.… Microwave heating of oils for 10 min caused only minor losses in polyphenols, and the oil degradation was lower than that in thermoxidation assays. 
A Chinese group did a nice study comparing the flavonoid content of nine vegetables after microwaving, frying, boiling, and stewing. For flavonoid preservation, microwaving did better than boiling and stewing, worse than frying. Missing flavonoids were not destroyed, but transferred to the soup:
METHODS: Nine kinds of vegetables obtained from Tianjin market were cooked by frying, boiling, stewing, microwave cooking respectively, then the contents of flavonoids in vegetables and soups after cooking were determined by HPLC.
RESULTS: The reserving rates of flavonoids after frying, boiling, stewing and microwave cooking ranged from 54.6% to 115.6%, 33.6% to 107.8%, 31.7% to 100.5%, and 43.1% to 109.6% respectively. Parts of flavonoids were also transfered to the soup after cooking. The transferring rate ranged from 1.4% to 55.8%. 
I looked at a lot of papers and the Vallejo et al paper was the only one that found a substantial loss of nutrients in microwave cooking. A sizeable literature reports no significant loss of nutrients from microwave cooking, though microwaving like other cooking methods may cause significant leaching of flavonoids into cooking water or oils.
Indeed, if anything microwaves seem to be better at preserving nutritional value than most other cooking methods.
The scientists studying freeze-drying and polyphenol extraction seem to have settled on low-power settings – typically 200 to 500 W – as optimal. This fits with Anand’s suggestion to try low-power settings. However, I saw no evidence that high-power microwave settings destroy substantial amounts of nutrients.
Although they are a bit older, dating back to the 1980s, several review papers have been written on the effect of microwaves on the nutrient value of foods. Here are their conclusions:
Overall, the nutritional effects of microwaves on protein, lipid, and minerals appear minimal…. [T]here are only slight differences between microwave and conventional cooking on vitamin retention in foods. In conclusion, no significant nutritional differences exist between foods prepared by conventional and microwave methods. Any differences reported in the literature are minimal. 
Based on the information available in the literature, nutrient content and retention of microwave-cooked or reheated foods is equal to or better than the same product prepared conventionally or held hot in a foodservice operation. 
I’ve learned an important lesson from these papers. If you want your food to have a high nutrient content, DO NOT:
- Freeze dry it after cooking;
- Grind it to a powder and dissolve it in methanol;
- Filter the solution through a cheesecloth to remove all solids;
- Evaporate the filtered liquid in a vacuum;
- Dissolve any remaining food in water and extract the upper part of the water, leaving behind the lower part of the water which might contain anything heavy;
- Filter the remaining water through a 0.45 µm filter.
If you do these things you may find the nutrient content of your food has been diminished by 97% or more. So ignore any cookbooks that feature these steps at the end of recipes!
Finally: Congratulations, Jaminet family microwave!
You will live to re-heat again.
 Vallejo, F. et al. Phenolic compound contents in edible parts of broccoli inflorescences after domestic cooking. Journal of the Science of Food and Agriculture. Oct. 2003; 83(14):1511-1516 http://onlinelibrary.wiley.com/doi/10.1002/jsfa.1585/abstract.
 Vallejo F et al. Health-promoting compounds in broccoli as influenced by refrigerated transport and retail sale period. J Agric Food Chem. 2003 May 7;51(10):3029-34. http://pmid.us/12720387.
 Vallejo F et al. In vitro gastrointestinal digestion study of broccoli inflorescence phenolic compounds, glucosinolates, and vitamin C. J Agric Food Chem. 2004 Jan 14;52(1):135-8. http://www.ncbi.nlm.nih.gov/pubmed/14709026.
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