Chelation therapy, which is a very effective way to treat heavy-metal poisoning, is a chemical process in which a synthetic solution is injected into the bloodstream to remove heavy metals and/or minerals from the body. British Anti-Lewisite (BAL) was one of the first chelating agents to be developed as an anti-dote for war gas, dichlorovinyl arsine (Lewsite) during the Second World War. The breakthrough in the development in chelating therapy came after the introduction of ethylenediaminetetraacetic acid (EDTA), initially to combat lead intoxication (Ref.1).$^*$
$^*$During Second World War, dimercaprol (BAL), an organic dithiol compound, was developed as an experimental antidote against the arsenic-based poison gas Lewisite. After World War II, mass lead poisoning was observed in large number of navy personnel, later identified as a result of their jobs repainting the hulls of ships. This introduced the medical use of EDTA as a lead chelating agent. (Ref.2)

A specific salt of EDTA used to bind metal ions in the practice of chelation therapy is calcium disodium ethylenediaminetetraacetate (or sodium calcium edentate; $\ce{CaNa2EDTA}$), specifically treating mercury and lead poisoning. When this EDTA solution is injected into the veins, which is a slow process (administration must be intravenous because it has very law intestinal uptake), it chelates with (or "grabs") heavy metals and minerals such as lead, mercury, copper, zinc, iron, arsenic, aluminum, and calcium. The heavy metal-EDTA complex will be then removed from the body through urinary system.
For example, lead poisoning is generally treated by using the chelating salt, $\ce{CaNa2EDTA}$, which is the calcium chelate of EDTA. This chelating agent has a great affinity to heavy metals, the removing agents such as $\ce{Pb^2+}$. The point is this chelating agent has a greater affinity to lead than to calcium (see large $\log K_f$ values of heavy metals compared to that of $\ce{Ca^2+}$ in following table) and so the lead chelate is formed by exchange. Then, the lead chelate would be excreted in urine, leaving behind harmless calcium. The disadvantage of this therapy is though it removes only extracellular heavy metals.
$$
\begin{array}{c|ccc}
\text{metal} & \log K_f \text{ of EDTA} & \log K_f \text{ of DTPA} \\
\hline
\ce{Al(III)} & 16.13 & 18.40 \\
\ce{Ca(II)} & 10.96 & 10.74 \\
\ce{Cd(II)} & 16.46 & 19.31 \\
\ce{\color{red}{Cu(II)}} & \color{red}{18.80} & \color{red}{21.53} \\
\ce{Fe(III)} & 25.10 & 28.60 \\
\ce{Hg(II)} & 21.80 & 27.00 \\
\ce{\color{blue}{Li(III)}} & \color{blue}{2.79} & - \\
\ce{\color{blue}{Na(I)}} & \color{blue}{1.66} & - \\
\ce{\color{red}{Mn(II)}} & \color{red}{14.04} & \color{red}{15.60} \\
\ce{\color{red}{Mn(III)}} & \color{red}{24.80} & - \\
\ce{Pb(II)} & 18.04 & 18.80 \\
\ce{\color{red}{Zn(II)}} & \color{red}{16.50} & \color{red}{18.75} \\
\hline
\end{array}
$$
Further, $\mathrm{pH}$ also is an important factor influencing complex formation and stability. Most chelating agents are unstable at low $\mathrm{pH}$, whereas at high $\mathrm{pH}$ metals tend to form insoluble hydroxides which are less accessible to chelating agents. This feature becomes significant in pathological conditions leading to acidosis or alkalosis (Ref.2).
Note that the value of EDTA as clinical chelating agent was reduced by the need for slow intravenous administration, law intestinal uptake, exclusive extracellular action, and high stability constants with essential metals such as Zn, Cu, and Mn (Ref.1, Ref.3).
References:
- Kiran Kalia, Swaran J. S. Flora, “Strategies for Safe and Effective Treatment for Chronic Arsenic and Lead Poisoning,” Journal of Occupational Health 2005, 47(1), 1–21 (https://doi.org/10.1539/joh.47.1).
- Swaran J. S. Flora, Vidhu Pachauri, “Chelation in Metal Intoxication,” Int. J. Environ. Res. Public Health 2010, 7(7), 2745–2788 (doi: 10.3390/ijerph7072745).
- Sobrasua E.M. Ibim, Jason Trotman, Paul I. Musey, Wasswa E.B. Semafuko, “Depletion of essential elements by calcium disodium EDTA treatment in the dog,” Toxicology 1992, 73(2), 229-237 (https://doi.org/10.1016/0300-483X(92)90105-N).