Improving cancer detection through combinations of cancer and immune biomarkers: a modelling approach

Abstract

Background: Early cancer diagnosis is one of the most important challenges of cancer research, since in many cancers it can lead to cure for patients with early stage diseases. For epithelial ovarian cancer (which is the leading cause of death among gynaecologic malignancies) the classical detection approach is based on measurements of CA-125 biomarker. However, the poor sensitivity and specificity of this biomarker impacts the detection of early-stage cancers.

Methods: Here we use a computational approach to investigate the effect of combining multiple biomarkers for ovarian cancer (e.g., CA-125 and IL-7), to improve early cancer detection.

Results: We show that this combined biomarkers approach could lead indeed to earlier cancer detection. However, the immune response (which influences the level of secreted IL-7 biomarker) plays an important role in improving and/or delaying cancer detection. Moreover, the detection level of IL-7 immune biomarker could be in a range that would not allow to distinguish between a healthy state and a cancerous state. In this case, the construction of solution diagrams in the space generated by the IL-7 and CA-125 biomarkers could allow us predict the long-term evolution of cancer biomarkers, thus allowing us to make predictions on cancer detection times.

Conclusions: Combining cancer and immune biomarkers could improve cancer detection times, and any predictions that could be made (at least through the use of CA-125/IL-7 biomarkers) are patient specific.

Keywords: CA-125 biomarker; Cancer detection times; IL-7 biomarker; Mathematical model; Ovarian cancer.

Fig. 1

A schematic representation of the interactions between tumour cells and immune effector cells, as described by model (1)–(3)

Fig. 2

The dynamics of tumour cells and tumour biomarkers in the absence of any immune response (i.e., $N_{\text{I}}=B_{\text{I}}=0$), as investigated in [25]: a time-evolution of ovarian cancer cells; a′ tumour size (cell numbers) at the detection times $D_T$, when the CA-125 biomarkers reach the detection thresholds (as shown in b, c); b dynamics of CA-125 biomarker, when we assume only tumour shedding. Horizontal line shows the biomarker detection threshold $d_{CA125}$. In this case, the tumour detection threshold is $D_T=8.8$ years; see also [25]; c dynamics of CA-125 biomarker, when we assume both tumour and healthy cells shedding. Horizontal line shows the biomarker cut-off threshold $c_{CA125}$. In this case, the tumour detection threshold is $D_T=10.1$ years; see also [25]. The parameter values for these simulations are given in Table 1

Fig. 3

a Time-evolution of tumour cell population; b time-evolution of immune cell population; time-evolution of tumour biomarkers secreted by tumour cells alone (a′) or by tumour and healthy cells (a″); time-evolution of immune biomarkers secreted by immune cells alone (b′) or by immune and healthy cells (b″); c′, c″ tumour size at the detection times $D_T^t$ and $D_T^i$ (corresponding to a′, b′, and a″, b″ respectively). Parameter values for these simulations are given in Tables 1 and 2. The dotted horizontal lines in a′, b′ show detection thresholds for CA-125 and IL-7 calculated by multiplying $d_{CA125}$ and $d_{IL7}$ with $V_{\mathit{pl}}$ = the mean plasma volume in a 70-kg female patient. The dotted horizontal lines in panels a″, b″ show cut-off thresholds for CA-125 and IL-7 calculated by multiplying $c_{CA125}$ and $c_{IL7}$ with $V_{\mathit{pl}}$

Fig. 4

The time-evolution of immune biomarker concentration, for higher baseline IL-7 serum levels (i.e. $c_{IL7}=18$), as we increase the carrying capacity of immune cells (to allow the cells to reach higher numbers); a $M={10}^9$; b $M={10}^{10}$

Fig. 5

The effect of changing various immune-related parameters, namely a $d_t$, b $a_i$, c $d_i$, d M, e $h_i$, f $k_{\mathit{ei}}$, g $f_i{R}_i$, on the cancer detection times calculated based on the cut-off thresholds for the tumour biomarkers ($D_T^t$; blue circles) and the immune biomarkers ($D_T^i$; red diamonds). The vertical dashed lines denote the baseline parameter values, as listed in Table 2

Fig. 6

Tumour detection times, $D_T^t$ and $D_T^i$ for higher tumour lysis rate $d_t=5\times {10}^{-4}$, as we vary two immune parameters: a $a_i$ and b $d_i$

Fig. 7

The effect of changing various tumour-related parameters, namely a $k_{\mathit{gr}}$, b $f_{\mathit{ht}}{R}_{\mathit{ht}}{N}_h$, c $f_t$, d $R_t$, e $k_{\mathit{et}}$, on the cancer detection times calculated based on the cut-off thresholds for the tumour biomarkers ($D_T^i$; blue circles) and the immune biomarkers ($D_T^i$; red diamonds). The vertical dashed lines denote the baseline parameter values, as listed in Table 1

Fig. 8

Tumour size at the detection times $D_T^t$ (blue circles) and $D_T^i$ (red diamonds), as we vary: a–g the immune parameters corresponding to a–g in Fig. 5; and h the tumour growth rate, corresponding to Fig. 7a

Fig. 9

a Regions of malignant vs. benign tumour predictions in the (IL-7, CA-125) parameter space, as proposed in the clinical study by [14]. b(i) Regions of healthy vs. cancerous states in the (IL-7, CA-125) phase plane, as predicted by the numerical simulations; (ii) tumour size versus the immune biomarker (IL-7) level (the dotted vertical line shows the IL-7 detection threshold, while the dashed horizontal line shows tumour size at the detection time); (iii) tumour size versus the cancer biomarker (CA-125) level (the dotted horizontal line shows the CA-125 detection threshold, while the dashed vertical line shows tumour size at the detection time). The blue arrows on the solution curves show the increase in time