During interplanetary missions (i.e., beyond the magnetic field of a planet), chronic low dose rate radiation exposures occur from galactic cosmic rays, solar event energetic particles and resulting secondary particles. US NASA employs individualized (age- and sex-dependent) permissible career limits in Sv [3% REID (risk of exposure induced death from cancer) at a 95% confidence level] for cancer mortality, and nominal (age- and sex-independent) dose limits in Gy or GyEq (30 day limit, one year limit or career limit) for non cancer effects (i.e., tissue reactions or formerly called deterministic effects) on the lens of the eye, skin, blood forming organ, circulatory system (more specifically, cardiovascular) and central nervous system. NASA considers acute effects as effects arising during a mission (e.g., a few years in Mars mission with exposure to >1 Sv), and late effects as effects occurring after the mission. Given this, what type of damage are you particularly interested in (e.g., damage at the level of DNA, cell, tissue, organ, a human individual, or even other animals such as tardigrades)?

Assuming you are interested in damage to humans, you might find this Wikipedia article a source of useful references (the article itself is in need of tidying up): https://en.wikipedia.org/wiki/Spaceflight_radiation_carcinogenesis

In terms of peer-reviewed articles, please have a look through the following:

On dose: Article Space: The Final Frontier—Research Relevant to Mars

An interesting article on biomarkers of carcinogenesis:

Article Evaluating biomarkers to model cancer risk post cosmic ray exposure

CV disease: Article Radiation-Induced Cardiovascular Disease: Mechanisms and Imp...

Immune system:

Article Impact of Particle Irradiation on the Immune System: From th...

Cataracts:

Article Cataractogenesis following high-LET radiation exposure

There are also neuroocular effects:

Article Space flight-associated neuro-ocular syndrome (SANS)

Hope that this is a useful start.

I think, thet the best metod of thin monitoring  for assessment of radiation damage is research of change in immune system and blood. The examination cytomorphology   of neutrophils and lymphocyte  give us  good resalts [Operchuk N.,Zadorozhna V., Raksha - Slusareva. O STUDY OF THE EFFECT OF LOW-INTENSITY NATURAL AND TECHNOGENIC INDUCED IONIZING RADIATION ON THE BLOOD PARAMETERS OF CHILDREN DEPENDING ON PLACES OF RESIDENCE, WITHIN THE SAME LOCATION // WORLD SCIENCE. – 2018. – № 4(32), Vol.4. – Р. 4 –7. (ISSN 2413-1032), Raksha-Slyusareva OA, Slyusarev OA, Tarasova IA, Yushchuk G Immunological support in infectology // "Infectious diseases of the present: etiology, epidemiology, diagnosis, treatment, prevention, biological safety": materials of the scientific and practical conference hall with international participation, dedicated to the annual "Reading" of the memory of academician L.V. Gromashevsky, confined to the 130th anniversary of the day of his birth, Kyiv, October 12-13, 2017 - Kyiv: "SPD FO" Kolomitsin V.Yu. ", 2017. - p.148 -150

You may want to apply a micronucleus test in various cells, including blood cells. If higher doses are expected, e.g. after solar events, as mentioned by Prof. Hamada, a y-H2AX assay might also be considered.

WD.

You may want to apply a micronucleus test in various cells, including blood cells. If higher doses are expected, e.g. after solar events, as mentioned by Prof. Hamada, a gamma-H2AX assay might also be considered.

WD.

You may want to apply a micronucleus test in various cells, including blood cells. If higher doses are expected, e.g. after solar events, as mentioned by Prof. Hamada, a gamma-H2AX assay might also be considered.

WD

If you looking for radiation dames in tumor cells the gold standard is colony formation assay, otherwise for normal cells other proliferation studies would be helpful.

I missed your explanation, for this purpose the chromosome analysis from peripheral blood lymphocytes is useful

When you say preliminary, what do you mean?

Choosing the assay to measure radiation damage depends on the dose range that you expect the subject was exposed to and the time point after the irradiation occurred.

For low dose and days after exposure, blood components could be a good test , as proposed in this article:

https://www.sciencedirect.com/science/article/pii/S1687850716000042

For a range of doses but immediate exposure assessment (for instance after a solar flare and to evaluate what dose the crew was exposed to - in case of other dose measure mechanisms fail) is yH2AX. It could be a useful triage tool to then proceed with counter measures (as proposed by Wolfgang Doerr ).

An good effort in this matter is being developed by RENEB:

https://biblio.ugent.be/publication/8136614/file/813663.pdf

It is also interesting to look into specific system damage as proposed by James Grellier