First let's be clear with the term apoptotic: It refers to apoptosis, the programmed activity of a cell's self destruction or suicide that is common with normal cells to make way for new replacement cells.
The problem with cancer cells is that they refuse to commit suicide; they're not programmed that way. So they either have to be killed by chemotoxic agents (synthetic or natural) or induced into programmed apoptosis.
The research summarized here examined chlorella's ability to induce apoptosis in cancer cells. The type of chlorella used for this study was Chlorella vulgaris extract, or CVE, extracted using hot water. 
Chlorella vulgaris extracts are available online; most, if not all, are extracted with hot water.
Summarizing a 2010 study of CVE's anticancer effects
This study was conducted at the Department of Biochemistry at the Universiti Kebangsaan Malaysia in Kuala Lumpur, Malaysia, and published in 2010 by the Sao Paulo, Brazil, journal Clinic.
This study was established to confirm the known reports of chlorella's anticancer properties and further analyze the mechanics of how it stops cancer from proliferating.
In order to achieve a specific analysis of the biochemical activities involved between Chlorella vulgaris and cancer cells, they used in vitro methods for the testing. "In vitro" is Latin for "in glass." So this trial was strictly a test tube and Petri dish matter.
They doused both cancerous liver cells and normal liver cells with CVE to examine the process of inducing apoptosis, which involves creating DNA damage as a precursor.
This was to determine whether or not the damaging effects on cancer cells would affect normal cells, which are already programmed normally for apoptosis. In other words, is the DNA damage cancer cell specific or does it affect normal cells too?
In layman's language, the results showed a 70% increased apoptotic rate in liver cancer cells compared to normal cells. Anti-apoptotic proteins in cancer cells were inhibited, while normal cells' apoptotic programming was left intact.
This demonstrates how chlorella can help stop cancer proliferation in the liver. But chlorella tends to generally help detox the liver and support liver regeneration. What about other cancers? Well, some say cancer is cancer, and others claim that some agents work on some cancers, while others don't.
But when it comes to food, which single-cell micro-algae chlorella is, most dietary approaches appear to work on several cancers.
Dr. Dietrich Klinghardt, MD, PhD, of the Klinghardt Academy explains that chlorella is a great preventative, but CVE should be used with plain chlorella for medicinal therapeutic purposes, especially regarding cancer. He even includes dosage recommendations in one of his newsletters. 
Chlorella as a daily supplement
Most prefer the tiny tablets, but the powder is the most cost effective if you can handle the taste, which is not as bad as spirulina for most. Mixing the powder with green smoothies or mixed well and with strong lemon water and gulped down, not sipped, worked for me. A tablespoon yields a little over five grams.
Chlorella's immune boosting and detoxification properties are well known. In our toxic, polluted environment, which includes what we eat and drink, we all need to be constantly detoxing and boosting our immune systems. 
Chlorella offers much in those areas at 3 to 5 grams daily (http://www.naturalnews.com).
Mike Adams, the Health Ranger, has personally had a lab test chlorella products for contaminants before including them in the Natural News store, as he explains here (http://www.naturalnews.com). 
Sources for this article include:
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