I am trying to plot a radiation dose response curve using graphpad prism. I an using a nonlinear regression (curve fit)> linear quadratic survival (Y is percentage). X is radiation dose in Grays (0, 1, 5, 10, 15, 20). The input equation is Y= 100*exp(-1*(A*X+B*X^2)). Rule for initial values of A = 1.0 amd B= 0.1. No constraints. No weighting. The best fit values for A obtained following analysis = 0.1687 and that of B= -0.005797 and A/B ratio = -29.10. This does not make any sense. Could some one help?
Try the Dose Estimate 5.2 software available on request fHealth Phys. 98(2):290 –295; 2010 doi: 10.1097/01.HP.0000346305.84577.b4 or the CABAS software at https://inis.iaea.org/collection/NCLCollectionStore/_Public/38/083/38083076.pdf
OriginLab Origin 8.5 or PAST 3.22 at https://folk.uio.no/ohammer/past/ software could also be used. Success !
The result sounds reasonable if obtained with Y= 100*exp(–A*X+B*X^2) instead of Y= 100*exp(–A*X–B*X^2) for Y= 100*exp(–1*(A*X+B*X^2)).
How does the fitted curve compare with the measured results? Does the fit appear plausible over the sample range? What are the uncertainties in the survival probability and the dosimetry?
Some nonlinear regressions can converge to a false minimum. In this case, re-starting the fit with different parameters might help.
Do your measured results show a monotonic decrease in survival with dose?
If there is significant scatter (measurement uncertainty) at intermediate doses, the fitting routine may find that the fit at 5-15 Gy is improved by making B negative, at the expense of an un-physical up-turn at 20 Gy.
An alternative approach is to fit the logarithm of the survival, which effectively gives more weight to lower survival probabilities and higher doses:
y = log(Y/100) = -(AX + BX2)
A simple linear regression can be used if you ignore the zero dose point
w = y/X = log(Y/100)/X = -(A + BX)
A quadratic dependence in the exponent results in a linear reduction of w with dose, X.
What is your Response data?
There are several available models, but without data we cannot help you.
This is likely because your data deviates from "linear-quadratic" (LQ) behavior. I'm assuming you've plotted your data with the y-axis on a logarithmic scale, and the x-axis on a linear scale. If the data is well characterized with the LQ model, it should appear concave downward -- otherwise, (e.g. if it is concave upward or there are inflection points, etc.) the best fit may well be achieved with a negative value for beta, as you have not imposed any constraints on it. As others have mentioned, seeing the data is really necessary to say for sure.
Thank you all for the comments. Really appreciate the help.
Yes I think my data deviates from the linear quadratic behaviour. But Y-axis is not on log scale. I have attached my data and the graph obtained with graphpad prism using the default parameters as I mentioned above. Thansk in advence for the help.
Your data appear unlikely to follow the LQ model. Given little difference at 1–20 Gy, is your endpoint mechanistically suitable to employ the LQ model? If this is clonogenic survival of mammalian cells, D10 (10% survival dose) >> 20 Gy is very rare.
I would suggest the paper:
Brenner, D. J., Hlatky, L. R., Hahnfeldt, et al. (1998) The Linear-Quadratic Model and Most Other Common Radiobiological Models Result in Similar Predictions of Time-Dose Relationships. Radiat. Res. 150,83-91
Success !!
Hi,
It seems that your cell lines have old passage number or may be fibroblast cells, which doesn't go for apoptosis and stay long in plates due to genomic instability or irreparable damage. Try to have more data points in less than 5 Gy and fit that results.
Dear all, Thanks for all the response. My data is not based on cell lines, this work was done using human cancer organoids which are not radiation naive, in fact these organoids are from patients with cancer recurrence. From the data, they seem to be radiation resilient (which is not surprising) and behave differently from the 2D cell-line culture and thus deviates from the classic LQ model. So the bottomline is, I cannot use LQ model. The classical LQ model is proposed based on clonogenic assay of 2D cell-line cultures, which is definitely not a reliable model to study cancers. Human cancer organoids are more relevant models that recapitulate most of the genetic and morphological signatures of human cancers. Do you have any suggestion on what to do next? Any other models that I can use to fit?
How did Dr Sasidharan S Lucky determine the survival of cancer organoids? LQ is a model for cellular clonogenic inactivation. Target theory was proposed in the 1940s based on experiments in bacteria, but the LQ model has broadly been used for clonogenic survival curve since mid-1970s ( Article The Effect of Multiple Small Doses of X Rays on Skin Reactio...
)
The shape of the dose response curve Dr Sasidharan S Lucky showed above is somewhat reminiscent of the clonogenic survival of Ku70–/– cells (albeit at a much lower dose range): please see open diamonds in Figure 3 of the following paper
https://www.ncbi.nlm.nih.gov/pubmed/11302764
If your data present a sigmoid shape, then you can use my ESE, EDE and their iterative versions BESE, BEDE in order ot find the inflection point, see here: Article On the Efficient Identification of an Inflection Point
R package inflection:
https://CRAN.R-project.org/package=inflection
I suggest you to invest in R and forget black box programs like Graphpad Prism (I have used it in the far past)
In R community your problem has a plethora of available solutions, check it!
Your data shows an abrupt fall in population to approximately 60% after only 1 Gy exposure. The response to additional exposure is much more gradual, dropping to around 33% at 20 Gy.
I am not familiar with the protocols and experimental procedures typically used for this type of study. Were the zero dose measurements made under identical conditions and at a similar time to those for the exposed samples? As @Krishnanand Mishra suggests, it would be useful to have additional data points at low doses - perhaps 0.1, 0.2, 0.5 Gy.
If the zero dose measurements are representative, then it appears that around 30% - 40% of the population are particularly susceptible to irradiation, with the remainder more tolerant. In a hardware failure analysis, this would be referred to as "infant mortality".
One possible model describes two or more populations with different exponential (or LQ) survival characteristics.
The figure attached plots the natural logarithm of the population as a function of dose. The mean of the three data sets is approximated by
S = 0.63 exp(-0.0312 x) + 0.37 exp(- K x)
where x is dose in Gy, and the exponent K is probably > 3, with insufficient low dose information for a more precise estimate.
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