Incidence rates of SMM have increased in many countries during the study period and are subject to many variations (Dimitrov, 1993a; 1993b; Dimitrov and Komitov, 1995; Dimitrov et al., 1998; Ettler, 1987; Guering-Galaktionova and Kupriyanov, 1971; Houghton et al., 1978). Usually, forecasting of incidence trends relies on linear regression model over time but such simple extrapolation has very often shown big discrepancies between estimates and real values. Therefore, other approaches in forecasting are needed, at least the following: (1) non-linear regression model over time; (2) linear and non-linear regression models to independent variables with deterministic temporal patterns (seasonality, cyclicity, etc.). Currently the relationship of heliogeophysical cycles to disease dynamics is of increasing importance in view of the new 11-year solar cycle No. 24 that has just started on Jan. 4th, 2008 (http://www.physorg.com/news119271347.html).

Our previous time-series analyses have revealed different cycles in incidence rates for SMM in Bulgaria (period T=12.2 years), East Bohemia (T=7.5~7.63 years), Northwest region of England (T=11 years) and USA (white females, T=8.75 years) (Dimitrov, 1993a; 1993b; Dimitrov and Komitov, 1995). The present results have revealed also cycles in the incidence of SMM for Ontario (T=9.91 years) and USA total population (T=8.63 years, short arrow in Fig.​Fig.1).1). Hypercycles were also revealed. The long arrows on Fig.​Fig.11 show the hypercycles for Bulgaria (T _H=48.25 years) and USA (T _H=34.5 years).

Furthermore, both cycles in the incidence rates as above have been used in bi-cyclic cosine-sine model. Model curve estimates for Bulgaria and USA are presented in Fig.​Fig.2.2. The index PI indicating the forecasting power of SMM models shows a higher value for USA (PI=1.50) than for Bulgaria (PI=1.02). Cyclic patterns in estimated rates of SMM up to 1995 are clearly seen (3~6 years ahead within the rectangled areas for Bulgaria and USA).

On account of the eventually insufficient power of this cycle-based-only forecasting in particular (cyclic patterns alone by the above mentioned cosine-sine model), temporal associations of the sunspot index Rz and the planetary geomagnetic index aa, with rates for SMM, have been also analyzed. The latter approach may also give better insight into the aetiology of SMM (Table ​(Table2).2). The association of SMM in Bulgaria and USA with the index Rz is presented in Fig.​Fig.33 as an illustration of this approach. The lag-period dT is positive when the extremes of the incidence rate follow the extremes of the sunspot index Rz. Notably, the strongest relationships are most likely to occur on the descending slopes of the 11-year sunspot cycle—positive coefficients of correlation about 2~5 years after the peak of the present solar cycle (Fig.​(Fig.3,3, left short arrow as for SMM in Bulgaria) and about 1~2 years after the peak of the next one (Fig.​(Fig.3,3, right short arrow as for SMM in both Bulgaria and USA). A negative coefficient of correlation for USA described in Fig.​Fig.33 (long arrow) confirms the above findings. In conclusion, maximal rates for SMM are most likely to appear out of phase, in view of the 11-year sunspot cycle. The incidence rates oscillate with a linear-phase mode to the cyclic index Rz, which also confirms their cyclic patterns.

We summarized and validated the existence of cyclic patterns (cyclicity) in SMM incidence rates and/or their variations (when an existing main linear or cyclic trend is removed) across different regions and time intervals. The analyses have also confirmed the existence of ‘hypercycles’ as being similar to those found earlier in breast cancer incidence variations (Dimitrov et al., 1998). It should be noted that other authors (Houghton et al., 1978; Wigle, 1978) had previously presented cyclic patterns in SMM incidence rates, in Connecticut and New York (USA) and Alberta and Saskatchewan (Canada) by curves against the time of observation (8~11 year intervals between peaks), but these authors had neither analysed nor proved statistically any of the cycles they illustrated. Clearly, if proved and estimated statistically, such cyclic patterns may be successfully decomposed, reconstructed and used by trigonometric approximation and the time series could be forecasted ahead (e.g., rectangled areas in Fig.​Fig.3),3), thus providing better estimates of future incidence rates than those produced by linear models alone.

We also established lagged temporal associations of SMM incidence rates with the sunspot index Rz and planetary geomagnetic index aa. The latter approach may also give better insight into the aetiology of SMM and the time lag between an eventual first hit (initiating event) and the later clinical appearance of cancer. Notably, the strongest relationships are most likely to appear out of phase, that is, on the descending slopes of the 11-year sunspot cycle.

Last but not least, cyclic patterns for a number of cancers other than SMM were also described in different countries (breast cancer: Bulgaria, T=17.625 years; USA, T=20.5 years) (Dimitrov et al., 1998). On the other hand, earlier results (Houghton et al., 1978; Wigle, 1978) indicated that the appearance of SMM peaked about 1~3 years after sunspot peaks. An earlier study on data from Turkmenia (former USSR) has found that maximal rates for different cancers are most likely to appear also around the minima of the sunspot cycle (Guering-Galaktionova and Kupriyanov, 1971). It should be noted that the cyclic patterns for SMM differ in the length and level of significance across different countries. However, both the usual infra-annual cycles and infra-annual hypercycles as well as some statistical associations with Rz (dT=+11~+13 years, on average) are similar across different countries. The recent findings, from a time-series analysis on population exposure to UV radiation over a very long time interval from 1920 to 1995 in Finland (Kojo et al., 2006), confirmed our results by indicating that the most likely lag-period of +5~+19 years prior to melanoma appearance might be the most relevant “silent” period in the aetiology of melanoma as related to solar UV radiation.

Temporal distributions of cancer incidence peaks along the 11-year solar activity cyclic curves (i.e., lagged correlations) may give rise to interesting conjectures. Plausible biophysical pathways for these cyclic non-photic HGA influences in the later appearance of SMM may be direct, with a predominantly local receipt of the impact by UV irradiation, solar protons or heavy-charged particles (Cucinotta and Durante, 2006; Encinas et al., 2008) on the epidermal, adnexal and dermal cells or cutaneous nerve endings. The direct effect may be targeted, acting upon the melanocytes and interfering with their melanocytic defence system (MDS) (Dimitrov et al., 2007), or it may firstly be spread, initially intermediated by the surrounding microenvironment (e.g., bystander effect, skin neuroendocrine system (Slominski, 2005) signalling, and adjacent skin neuro-immunity impairment). Alternatively, or in parallel, these pathways may be also indirect, by impacts of solar coronal-related geomagnetic storms, gravitational field changes, low-frequency (LF) geophysical fluctuations or Schumann resonance signals (Cherry, 2002; Kamide, 2003; 2005) on the brain activity, neuro-endocrine axis modulations and haemato-immuno-logical variations (Kamide, 2005). For instance, a nonlinear resonant detection/absorption of Schumann resonance signals by LF brain waves (the same frequency ranges!), through interaction with neuronal calcium ions and subsequent melatonin/serotonin balance alterations, was suggested (i.e., the reduced melatonin may cause enhanced DNA damage that can initiate, promote and progress towards cancer) (Cherry, 2002). The spectral elements in physiological chronomes (time structures) may intermodulate with physical environmental chronomes. This could lead to rhythmically recurring and predictable phase responses (i.e., feedsidewards) at population level such as cancer incidence peaks as lagged to previous peaks of the original stimuli (phase-correlation), with or without inclusion of phylogenetic and ontogenetic memories (Halberg et al., 2004). It is interesting that during the declining phase of the 11-year solar cycle, coronal activity is reaching a peak causing geomagnetic disturbances near the Earth orbit (for example, an intense storm can result from the superposition of two successive moderate storms driven by two successive structures in the solar wind) (Kamide, 2003). The latter effects may interfere not only with the Schumann frequencies and provoke carcinogenic stimuli (e.g., via the LF resonance with brain waives) but may also intermodulate with other cyclic cosmic influences (e.g., galactic cosmic rays, solar proton flux) that have also been related to increased cancer risk (Cucinotta and Durante, 2006) or sensitivity of quiescent neural stem cells (Encinas et al., 2008). These impacts and mechanisms could be linked not only to SMM appearance but together with environmental light effects and melatonin disturbances, to breast (Srinivasan et al., 2008) or other solid cancer occurrences as well.