Theoretical analysis of comparative patient skin dose and exposure technique approaches in planar radiography

Transcription

1 Exposure technique Australian Institute of Radiography The Radiographer 2009; 56 (1): Theoretical analysis of comparative patient skin dose exposure technique approaches in planar radiography Faculty of Science, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia. Correspondence Abstract A theoretical analysis of patient skin dose changes with manipulation of technique factors (mas kv) was carried out in order to obtain a description of the relationship between patient dose the exposure technique approach employed. The stard exposure technique approaches in variable part thickness radiography of fixed kvp variable kvp the 15% rule in constant part thickness radiography were analysed in terms of the changes in patient skin dose. Analytical expressions describing the variation of dose change ratios have been developed in respect of each approach also in comparison between the two stard approaches. The resultant model is limited to essentially qualitative predictions due to its inherent limitation of neglecting secondary radiation at the entrance site of the beam, but nevertheless indicates some non intuitive benefits in utilisation of mas (only) changes in compensating for the thinner part for lower image densities, as well as indicating that most gain is to be had (in terms of lower skin dose), where only modest part thickness compensation is required. The model also describes the influence of the chosen voltage in a reference technique (upon which further compensatory changes in exposure factors are based) on the patient skin dose, when the variable kv approach is utilised. Keywords: exposure techniques, patient dose, planar radiography Introduction Elementary textbooks (for example 1,2,3 ) in radiography when discussing exposure technique in two-dimensional planar or common projection modes, whether screen-film or computed radiography versions commonly cite the 15% exposure rule as applicable to a constant part thickness. They also discuss stard approaches of variable kv fixed kv in order to compensate for changes in part thickness. In addition, it is generally pointed out in such texts that less absorption of x-ray energy occurs at higher kilovoltages (kv) this implies less patient dose occurs by using a higher kv rather than using a higher tube current (mas) where an exposure increase is required. Most radiography texts or works, old or new, do not actually explore to any significant degree the relationships between patient dose technique settings. One notable exception being that of van der Plaats 4 who examines the relationship between patient skin dose, tube loading, focus size in the context of higher kilovoltages exposure techniques. Automatic exposure control in planar radiography is being more widely used. As manual techniques in radiography have become less of a topic, naturally fundamental work in the area of radiographic exposure technique has also lessened. While much experimental work in computed radiography digital radiography has been published in regards to image quality patient dose, there still appears to be essentially no cohesive nor general theoretical/ analytical model that explicitly describes the relationship between the chosen employed exposure technique, patient dose. The basis of exposure technique as developed initially for screen film receptors hence consequently the ramifications in terms of patient dose have direct relevance to the use also of digital receptors, as indicated by Fauber. 3 This current study investigates this relationship. The aim of analysis was to develop a simple analytical model of dose change in terms of the operational quantities involved, that of tube voltage, tube charge, patient part thickness increase. The analysis used restricts itself to purely the consideration of patient skin absorbed dose, does not attempt to address the other consideration of image quality. Image quality is a consideration that is important in any actual imaging practice. However, if any understing of the balance between image quality patient dose is to be finally achieved, then it is necessary that each of these aspects be separately understood in terms of the relationships at play. Analysis The main points of the analysis are discussed in this section, however further mathematical details of the analysis are included in the appendices. Assumptions relevant quantities of consideration This analysis ignores, as is generally traditional to do so, the use of distance, focus to film distance (FFD) or source to image distance (SID), as a technique factor employed to manipulate the exposure value upon the image receptor. For simplicity, the patient skin absorbed dose, D, proximal to the x-ray tube is considered here as the measure of patient dose. The image density signal, S, as measured by a scale such as the optical density, or its equivalent on a digital receptor (e.g. the voltage output upon digital readout); is considered here (in this simple modelling exercise) in terms of its average value across the image receptor. The technique exposure quantities involved (that are under operator control) are the tube charge, q (or mas ), the tube voltage, V (or kv ). The part thickness, x, is also an

2 22 The Radiographer important quantity ( outside operator control). Last, there is an involvement of the beam area, A (as measured at some convenient location, such as the level of the image receptor or the patient entrance beam area), however for the most part the case of small area values will be considered, restricting analysis for simplicity to consideration of patient skin dose essentially to that component due to the primary beam. Some consideration is then later given to modification of the analytical model to embrace other than small beam areas evaluation of the patient skin dose considering backscatter radiation contribution. In a given case (whether constant part thickness technique or variable part thickness technique is being considered) these quantities exist as either variables or constant values. Throughout, a simple assumption will be made in the case of absorbed dose. The general relationship relating exposure, X, to absorbed dose, D, is given by the classic equation: The f factor, f, is actually a function of the photon energy, or more generally in the case of a multi-energetic x-ray beam, it will be a function of anything affecting the beam spectrum. In particular, for a given x-ray tube, this means that the f factor will strictly be a function of the tube voltage, V, used. In addition, as has already been shown 5, the image density can be usefully described for a given typical part thickness by the model: which simplifies to case of constant FFD, L, constant part thickness x: (3)...an expression which has been either implicitly or explicitly related by several authors. 4,6 (The exponent of 5 above agrees perfectly with the exposure rules 5 though some works cite the exponent of 4. In fact the exponent varies truly with part thickness at least, as indicated by van der Plaats 4 ) On the other h, the actual exposure value at some distance d from the focus is usefully given by: this reduces for the case of constant distance d to: (note each k in the above three expressions is a constant value) As can be seen from the following analysis, it is this difference in the power of the voltage (2 versus 5) describing the (skin) exposure the photographic effect respectively, that leads to notable differences in skin absorbed dose, according as to whether kv or mas is chosen to be varied. Now, in the case of soft tissue across the diagnostic energy range, there is some very slight decrease in the f factor, but this small change can be neglected for the purpose of the elementary treatment here. For the purposes that follow it is assumed that the f factor is essentially constant in value. Thus: where c is a constant for all systems (patients apparatus) (1) (2) (4) (5) (6) considered. For ease of presentation, further analysis is broken down under two main items of consideration, (a) constant part thickness technique (b) variable part thickness techniques. (a) Constant part thickness radiography Here, consider changing the average image density signal, S, by changing both q V together. This means that all of S, q, V are variables, whilst the part thickness, x, is a constant value. The so called 15% rule of radiography is generally related as applicable in cases where the part thickness is constant the image density is held constant. However, it is easily shown that this rule is mathematically equivalent to the statement:...where k is a constant whose value is determined by the system, that is the part radiographed, image receptor x-ray apparatus used. This realisation allows cases constant part thickness to be considered as radiography of the same part, but where now the image density is altered, utilising either q (mas) or V (kv) only. In doing so (see Appendix A) then in consideration of the assumptions relations already stated, the ratio change in skin absorbed dose ( new divided by old value) when using only a change in mas to change the average image density signal by a multiplicative factor of F, is given by: Likewise a similar skin dose change ratio where only kv is used to effect an increase in image density by a factor of F is given by: (9) These are further usefully compared by the further ratio this gives: (7) (8) (10) Equation (10) expresses effectively the ratio of the resultant skin absorbed dose to obtain an image density signal altered by a factor F using a change only in tube kv, to the skin absorbed dose value that results from using only mas to effect the same image density signal change. (b) Variable part thickness radiography. The stard approaches used here are embraced in the fixed kv variable kv approach rules. The fixed kv rule, typically expressed as a 25% increase in mas per cm, is easily shown to be equivalent to the mathematical statement: (11) where x r is some reference thickness where known settings of V (kv) q (mas) produce an acceptable average image density signal, m is the number of cm increments in part thickness. The variable kv rule is typically expressed as add 2 kv per cm increase in part thickness. This rule can be easily shown as equivalent to the expression: where V is measured in units of kv. (12)

3 Theoretical analysis of comparative patient skin dose exposure technique approaches in planar radiography The Radiographer 23 Both approaches confer that the average image density signal is held constant, which is the aim of these approaches. This is despite changes in part thickness, for example as in a thickness increase of m cm from some reference thickness x = x r to a thickness x = x r + m. Thus the part thickness x is a variable in both approaches. The only variable will in fact be either q(mas) in the fixed kv approach, or V(kV) in the variable kv approach. Again, conveniently for simplicity at this point tube to image distance beam area effects are ignored. Analogously to the previous case of constant part thickness, dose change ratios can be constructed (see Appendix B) related to the increase in part thickness, m. This gives dose change factors, old skin absorbed dose divided by new skin absorbed dose, of: (13) (14) for the cases of variable kv fixed kv approaches respectively. If t v is divided by t q then this gives the ratio of the skin absorbed dose as results from utilising increase in V (kv) only, using the variable kv approach, to the skin absorbed dose as results from changing only tube charge q (mas), using the fixed kv approach. This ratio, denoted T is shown (Appendix B) to be given by: (15) Discussion Equations (10) (15) above constitute a model of dose variation with exposure technique selection. In order to interpret the predictions of the first of these, it is convenient to consider graphical representations as shown in Figure 1 Figure 2 below: Figure 1 shows the variation of R with increase image density change factor F. This means that F naturally starts at the value of unity, signifying no alteration in image density, if just increases in image density values is consider. Since R <1 for all F> 1, then this means that there is always a lower skin absorbed dose utilising voltage increase to effect the increase in image density, than would result from using an increase in tube charge (mas) to effect the same increase in image density. The benefit, purely in terms of skin absorbed dose, is quantified by the value of R, which shows that since R is less for larger F, then the greater the increase required in average image density, the greater the benefit in terms of reduced skin dose in using tube voltage increases rather than tube charge increases. The rate of change of benefit, however clearly is greatest where the slope of the plot is descending most rapidly, in fact the rate of change of R with F is easily shown to be given by: (16) Using this gives that the value of R falls with F at a value of about 0.6 (at F = 1) the steepness of this fall decreases to half of this, 0.3, at about F = 1.5. Thus the rate of change of benefit is greatest for small changes in the image density increase factor, but decreases significantly for larger increases in F. Indeed between F = 5 F = 6 there is virtually no change in the value of R (~ 1% change only). This means that the greatest gains in terms of reduction of patient skin dose using tube voltage (kv) rather than tube charge (mas), will be had over quite small increases in image density. Nevertheless, there is always some benefit to be had in lesser comparative skin dose as a result of using kv increases in preference to mas increases. If values of F are considered where 0 <F <1, corresponding to a required decrease in the image density, then Figure 2 indicates the results. In this case R> 1 increases as the value of F is decreased further towards zero. Since R> 1, then there is now a relative increase in skin dose in the case of decreasing tube voltage, in comparison to the skin dose that would ensue using decreases in tube charge to obtain the required decreased image density. Of course the skin dose will be lessened if either V or q is decreased, but it will be a lesser value in the case of changing the tube charge, q(mas). Considering the cases of variable part thickness approaches, again pertinent results can be more easily seen by consulting a graph of T with thickness increase, m. [Note that the increment m assumes both negative positive values. The interpretation of this is that a negative increment is a decrement in thickness. Thus a value of m = -2 signifies a decrease in part thickness (from some reference technique thickness) by 2 cm. Also the plot shows the particular case whereby the reference technique voltage (at m = 0) is 50 kv]. Because of the definition of T, then if T <1, this means there is an advantage in terms of comparative skin dose in utilising a Figure 1. Figure 2.

4 24 The Radiographer Figure 3. Figure 4. change in voltage only through using the variable kv approach rule rather than utilising the fixed kv approach whereby only the mas is used to compensate for change in part thickness. Figure 3 indicates generally that there is always a skin dose benefit to be had in utilising the variable kv approach when compensation is required for the larger anatomical part or patient. Conversely, for m <0, there is benefit in choosing the fixed kv approach to compensate for the thinner part, lower skin doses will result in this case. The variation is now much less though than the former case (variation of R with F), thus the rate of change of the benefit here (dt/dm), whilst decreasing with increasing m, is not dramatic. T is a function not only of the change in thickness (m), but also the reference thickness voltage,, used (this corresponds to the value of V at m = 0). In fact simple consideration of the expression for T (Appendix C) shows that where a larger voltage is used for the stard thickness technique, then the values of T are correspondingly less, for positive increments in thickness. To illustrate this, Figure 4 shows T curves for reference voltages of 50 kv also 100 kv. Figure 4 also shows that the skin dose benefit to be had in using the fixed kv approach, in compensating for the thinner patient, is larger when larger tube voltages are used in the reference technique. To further illustrate the change in T with various choice of then it is possible to plot T against for some particular m value/s, as in Figure 5 for example. Figure 5 shows the variation of T with. In the case of compensating for a decrement in thickness, then decreasing the mas only, via the fixed kv rule, will always be of benefit (T> 1). However, more benefit is to be had where the reference technique voltage is larger, as shown by the gentle increase of the curve for m = -2 cm, from about 1.26 to 1.46 over the voltage interval from 40 to 120 kv. When the part to be imaged is thicker than the stard technique, then the solid curve of Figure 5 shows that an increased benefit occurs in terms of skin dose, where higher values of reference voltage are used within technique. In the case of thicker parts, the change of benefit, as evaluated using the ratio T, is though about half of that for the case of thinner parts, since there is now an average fall of about 0.1 in T over the same voltage interval. Limitations of the analysis: secondary radiation The simple model so far has not considered the effect of secondary, essentially scatter, radiation. This will alter the values of both R T as evaluated in the model here, though naturally, where beam area is smaller, then the simple model developed here is more applicable. The complication occurs in skin-absorbed dose by virtue of the Figure 5. necessity to consider the backscatter factor, B, that describes the variation of scatter radiation at the skin surface at beam entry. Since in general, B can be regarded as a function of tube voltage V, at least for a given system, then it should possible to incorporate this into a more general model using the same general approach. The inherent benefit in using changes of voltage, to accommodate for the larger part or to generate higher image density values, is essentially caused by the difference in the V 2 the V 5 terms within the analysis. V 2 V 5 refer respectively to the variation of absorbed dose the photographic effect (image density) with tube voltage V (kv). When the backscatter factor is considered, then the term for the absorbed dose will alter effectively increase the index or power above the value of 2. However, cursory consideration of the energy dependency of B (B values as listed in ICRU Report 74) 7 indicates this is unlikely to push the absorbed dose voltage dependency term much higher than the power of 2. This means there will still be a significant difference between any exponent chosen for the absorbed dose term the image density term. Thus the qualitative changes, if not the numerical values of R T, should be essentially unchanged. Consequently, the qualitative changes inferred by this model should also apply to the more general case where scatter radiation is significant. Conclusion A simple theoretical model has been constructed that describes the variation in proximal skin absorbed dose with technique factor changes, in both variable part radiography constant part thickness radiography. Qualitatively, accepting the limitations of the model, the model predicts importantly that patient dose benefits are gained by utilisation of increases in voltage where either larger image density

5 Theoretical analysis of comparative patient skin dose exposure technique approaches in planar radiography The Radiographer 25 values are sought, with a given radiographic part, also where compensation is required over a larger thickness. These predictions agree with the common sense intuitive notions of course using the basic reasoning of higher kv therefore higher transmission, less absorption. However, less intuitively, the predictions imply that major benefits are gained in compensating for modest part thickness increases, also that, where compensation is sought for the thinner part, then benefit is gained by utilising changes in tube charge (mas) rather than using the tube voltage. Improvement of this model by incorporation of secondary radiation effects should enable more general applicability more accurate predictions. This might be expected to reasonably extend the capabilities of the model from essentially purely qualitative predictions, into one that has a reasonable quantitative predictability, that can further be compared effectively with experimental or other empirically obtained data. The construction of such a model would be useful in further building a complete logistic approach to effecting the ALARA (As Low As Reasonably Achievable) dose principle of modern radiological protection by further consideration of the independent requirement of a necessary level of image quality. References 1 Fossbinder RA, Kelsey CA, Essentials Of Radiologic Science. New York: McGraw Hill; Bushong SC, Radiologic Science for Technologists: Physics, Biology, Protection. St Louis: Mosby; Fauber TL, Radiographic Imaging Exposure, 3 rd ed., St Louis, Mosby, van der Plaats GJ, Medical X ray techniques in diagnostic radiology. London & Basingstoke: Macmillan Press; pp & pp Garbett IT, Derivation of Exposure Rules In Conventional Radiographic Imaging, The Radiographer 1999; (46) 3: Johns HE, Cunningham JR. The physics of radiology, 4th ed. Springfield Illinois: Charles C Thomas; pp Journal of the ICRU Appendix A: Backscatter Factors, Table A1. Oxford University Press, 2005: 5 No 2 Report 74, pp 66. Appendix A Using the earlier related equations, then we consider the skin dose in two cases old new ( denoted here by subscripts o n ), so as to consider the change effected. Writing: Then for the case where q is used to change S (so V n = V o ): is similarly obtained as: Suppose an increase factor in image density, given by: Then, in general (A2) Substituting for the cases of changing q (mas) also changing V (kv) only leads to: For the case of changing only q (to effect the image density change): (A3) for the instance of increasing V only (to effect the change in image density): (A4) This allows the dose change ratio to be expressed in terms of the image density change factor in each case: (A5) (A6) The ratio R can now be constructed in order to compare these two change factors, where: This leads to the general result that: (A7) Then the ratio of change (from old to new) in skin absorbed dose, (denote as r q ) is: (A1)...a result that may be intuitively expected since the skin dose is the directly proportional to the value of mas used. For the case where the image density signal is changed using only tube voltage change then the equivalent dose change ratio r V Appendix B Again (as in Appendix A) we consider the skin dose in two cases old new (as denoted here by subscripts o n ), so as to consider the change effected. Using: Now generally: Then for the fixed kv approach (V n = ): X n = k 4 q n 2

6 26 The Radiographer Between old new cases we suppose a change in thickness by a positive amount m cm. Then in the fixed kv approach using equation (A7) we have: In the variable case we have: (B8) (B9) in the variable kv case a similar ratio change, denoted as t V : Defining now a new ratio T: (B13) Then for the skin absorbed dose in the fixed kv case: (B10) This gives the general result: (B14) For the variable kv case: (B11) The old skin absorbed dose values are c 3 q 0 c 4 2 for fixed variable cases respectively (these are necessarily the same value because in fact c 3 = c 2 2 c 4 = c 2 q 0 ) Then there is a skin dose change ratio (denote this as t q ) in the fixed kv case of: (B 12) Appendix C The voltage term in equation (B13) can be expressed as: (C15) thus as then this term reduces approaches unity. The smaller the value of, then the larger is this ratio (denoted as t V above). Thus for any chosen value of m, then the value of T will be smaller in the case of a larger choice for this reference technique voltage,.