### Hypothesis

The nephron number, which is estimated from the glomerular density in kidney biopsy specimens and the volume of the renal cortex, can predict the outcome of a CKD patient (Figure 1).

### Study design

In a multicenter, prospective (minimum 3 and maximum 5 years follow-up) study, approximately 600 patients with CKD who undergo a kidney biopsy for their diagnosis and will be enrolled from January 2011 to March 2013. These CKD patients will be recruited from 10 hospitals belonging to the National Hospital Organization of Japan. The hospitals participating in this study are spread throughout Japan (Hokkaido, Kanazawa, Chiba, Nagoya, Kyoto, Osaka, Fukuoka, and Nagasaki prefectures). This protocol was submitted to the UMIN-Clinical Trial Registration on January 1, 2011, and its unique trial number is UMIN000004784.

### Study participants

Participants will be eligible for inclusion if they (1) have CKD according to the K/DOQI CKD Guidelines [18], (2) are undergoing a needle biopsy of the kidney, (3) sign the acceptance letter for participating in this study, (4) are over 14 years old, (5) and their guardian has also signed the letter if they are under 20 years old. Participants will be excluded for any of the following reasons: (1) severe laterality in kidney size or function, for example, unilateral kidney, severe unilateral kidney atrophy, functionally unilateral kidney, and so on, (2) have had cancer, but the patients are eligible if they are free from the cancer for more than 1 year before the kidney biopsy.

In this study, the estimated glomerular filtration rate (GFR) will be calculated using the following formula, which was developed for Japanese subjects [19]:

\mathsf{\text{eGFR}}\left(\mathsf{\text{mL}}/min/1.73{\mathsf{\text{m}}}^{2}\right)=194\times \mathsf{\text{Ag}}{\mathsf{\text{e}}}^{-0.287}\times \mathsf{\text{Cr}}{\mathsf{\text{e}}}^{-1.094}\left(\times 0.739\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{infemals}}\right)

In this study, all attending CKD patients will undergo a needle biopsy of the kidney for their diagnosis. Therefore, although this protocol determines the exclusion criteria by the patients' CKD stage, most of the attending patients should not be in stage 4 or 5.

### Data collection at the enrollment

Enrollment should be performed at the time of the kidney biopsy after informed consent, followed by permission to participate in this study, is obtained. All patients will undergo: 1. a medical interview, 2. an ultrasound to measure the kidney size, 3. blood or urine tests, 4. a kidney biopsy to investigate the pathological findings data at the enrollment is shown in Figure 2. These examinations are performed routinely in the typical clinical setting for CKD patients receiving a kidney biopsy. In other words, no new or special examinations are included in this study.

In the medical interview, the question about birth weight may be difficult to answer, especially for elderly patients. If the subjects cannot answer the question about their birth weight, the question will be changed to whether their birth weight was normal (equal to or over 2500 g) or not, because LBW is defined as a newborn birth weight of less than 2500 g by the World Health Organization.

### Clinical follow-up and data collection

Patients will continue to have medical consultations and will receive examinations and/or treatment as usual. We will not direct physicians to prescribe any preferred drug, examination, or to give any specific medical advice. We will also not ban the physicians from prescribing any particular drugs.

The data for patients will be collected once a year after the kidney biopsy, and will be followed until March 2016. We will permit the data collected during the antero-posterior three months of the day of the kidney biopsy to be analyzed as well. The data collection plan is shown in Figure 3.

In this study, a cerebro-cardiovascular event was defined as an acute myocardial infarction, angina pectoris, and cerebro-vascular diseases. In addition, in order for a myocardial infarction to be reported in this study, it has to fulfill at least two of the following: (1) chest symptoms, (2) ECG changes, (3) elevated cardiac enzymes. Angina is defined as the presence of ECG abnormalities with chest symptoms and the need for catheter or surgical treatment. Furthermore, a cerebro-vascular event is defined as cases with neuropathy lasting more than 24 hours continuously and with proof of a causative lesion by CT scan or MRI (TIA and asymptomatic small infarction are not included). If no data is tracked during the follow-up, the reason will be recorded (stopped visiting the hospital, transferred to another hospital, moved to a new house, offered to stop the medical consultation, and so on).

### Parameters for the assessment

The primary parameter that will be assessed is the composite of the total mortality, renal death (starting maintenance hemodialysis and peritoneal dialysis, kidney transplantation), cerebro-cardiovascular events (ischemic heart disease, cerebral hemorrhage, cerebral infarction), and a 50% reduction in the eGFR. The secondary parameter is the rate of eGFR decline per year.

### Rationale for the number of patients

This study aims to predict the outcome of chronic kidney disease using the estimated nephron number. We assumed that the time from entry to event will be independently and exponentially distributed. The planned sample size was based on a two-tailed log-rank test with the significance level set to 0.05, and the power level set at 0.80. The ratio of low birth weight infants per total newborns in Japan was reported to be 0.086 in 1960 and 0.097 in 2007. During this period, the rate has been consistently increasing http://www.mhlw.go.jp/english/database/db-hw/vs01.html. The rate of LBW may be higher in the CKD patients than in normal subjects. We assumed that the rate of LBW would be 0.095 in the CKD patients in this study. This study is planned with an accrual interval of 2 years, and additional follow-up after the accrual interval of 3 years. The event rates were assumed to be 0.1 in the normal birth weight group and 0.2 in the low birth weight group by several studies [8, 20, 21]. The required sample size was therefore calculated to be 50 for the low birth weight group and 476 for the normal birth weight group [22]. Assuming that 10% of subjects would withdraw, we used the simple number of 600 as the target number of patients to recruit for this study.

### Measurement of the kidney size by ultrasound imaging

We will record the major and the minor axis of the longitudinal plane, and the diameter of the transverse plane of the kidney by ultrasound examination as shown in Figure 4. Only the size of the biopsied site will be registered at enrollment.

### Information from kidney biopsy specimens

As a general rule, sections stained by PAS or PAM-HE will be used for the measurement of the glomerular number and the length of the cortex (Figure 5). At the time of the measurement, squared grids will be set in an ocular lens, and thereafter, the length of the cortex will be measured. In the formal definition, the cortex and medulla are separated by the arcuate artery of the kidney. However, it is difficult to clearly discriminate between the cortex and medulla because of the frequent lack of the arcuate artery in the specimen. Therefore, we define the length of the cortex in the kidney biopsy specimen as shown in Figure 5. The needle gage number is also recorded, so that we will know the width of the specimen. The gross square area of the cortex in the specimens can be calculated by the total length of the cortex and the width. The total glomerular number and the number of glomeruli with global sclerosis will also be recorded. If the section has only one glomerulus, the section is ignored. If the total glomerular number in all sections obtained is under 8, such cases will be considered insufficient for the analysis. In line with the usual clinical procedure, the pathological diagnosis will be performed and registered.

### Estimation of the total nephron number in a kidney

Based on previous studies, we will first assume that there is 31% volume shrinkage in the paraffin-embedded specimens due to fixation in formalin [17, 23, 24]. Therefore, we will take the quotient of the actual measured values of the length by 0.883\phantom{\rule{0.3em}{0ex}}\left(=\sqrt[3]{1-0.31}\right) for the calculation below. Next, the volume of the glomerulus is thought to shrink 43% in the biopsied specimens because of the loss of arterial pressure and because of paraffin embedding after fixation in formalin [16, 17, 23, 24]. Therefore, the actual axis of the glomerulus is calculated by dividing the measurement axis by 0.829\left(=\sqrt[3]{1-0.43}\right), and the value is used for the numerical formula below.

The total number of glomeruli is estimated as follows:

The formula of the spherical volume can be derived using integral calculus, i.e. disk integration to sum the volumes \mathsf{\text{V}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{=}}\phantom{\rule{0.3em}{0ex}}{\int}_{-r}^{r}\pi \left({r}^{2}-{x}^{2}\right)dx=\frac{4}{3}\pi {r}^{3}, where r is radius of the sphere, and π is the constant pi.

Similarly, the average area of the observed glomeruli on one section in the biopsied specimen is estimated as follows:

We assume that glomeruli less than 5 micrometers in diameter cannot be counted. A sphere 2r in diameter is cut off at both ends in parallel so that the diameter of a section may be set to 2r_{o}(5 μm). We observe only circles parallel to the section of this solid, whose height is defined as 2 h. Considering a 2 h-high cylinder whose volume is equal to this solid, the cylindrical base area is equal to the average cross-sectional area of this solid cut at random parallel to the base of the solid (Figure 6).

{\mathsf{\text{A}}}_{\mathsf{\text{h}}}\times 2\mathsf{\text{h=}}{\int}_{-\mathsf{\text{h}}}^{\mathsf{\text{h}}}\pi \left({\mathsf{\text{r}}}^{2}\mathsf{\text{-}}\phantom{\rule{0.3em}{0ex}}{\mathsf{\text{x}}}^{2}\right)\mathsf{\text{dx}}

where A_{h} is the average rea of the observed circle. Hence, A_{h} is estimated by:

{\mathsf{\text{A}}}_{\mathsf{\text{h}}}=\frac{1}{2\mathsf{\text{h}}}{\int}_{-\mathsf{\text{h}}}^{\mathsf{\text{h}}}\pi \left({\mathsf{\text{r}}}^{2}\mathsf{\text{-}}{\mathsf{\text{x}}}^{2}\right)\mathsf{\text{dx=}}\frac{\pi}{2\mathsf{\text{h}}}{\left[{\mathsf{\text{r}}}^{2}\mathsf{\text{x-}}\frac{{\mathsf{\text{x}}}^{\mathsf{\text{3}}}}{3}\right]}_{-\mathsf{\text{h}}}^{\mathsf{\text{h}}}=\frac{\pi}{2\mathsf{\text{h}}}\left(2{r}^{2}\mathsf{\text{h-}}\frac{2}{3}{\mathsf{\text{h}}}^{3}\right)=\pi \left({\mathsf{\text{r}}}^{2}-\frac{{\mathsf{\text{h}}}^{2}}{3}\right)

Using the Pythagorean theorem, \text{h}=\sqrt{{\text{r}}^{2}-{\text{r}}_{\text{o}}{}^{2}}

Where r is the glomerular radius and r_{o} is the cut-off value of the observed glomerular radius (Figure 6).

Substituting h with a function of r and r_{o} gives:

{\mathsf{\text{A}}}_{\mathsf{\text{h}}}=\pi \left({\mathsf{\text{r}}}^{2}-\frac{\left({\mathsf{\text{r}}}^{\mathsf{\text{2}}}-{\mathsf{\text{r}}}_{\mathsf{\text{o}}}^{2}\right)}{3}\right)=\pi \left(\frac{2}{3}{\mathsf{\text{r}}}^{2}+\frac{1}{3}{\mathsf{\text{r}}}_{\mathsf{\text{o}}}^{2}\right)

A_{cortex_s} (Area of the cortex of the section in a biopsied specimen) is calculated as:

{\mathsf{\text{A}}}_{\mathsf{\text{cortex\_s}}}={\mathsf{\text{L}}}_{\mathsf{\text{a+b}}}\times {\mathsf{\text{d}}}_{\mathsf{\text{b}}}

Where d_{b} is the internal diameter of the biopsy needle and L_{a+b} is "a + b" in Figure 5 for the total cortex length in biopsied specimens.

VF _{glom/cortex} (Volume fraction of glomeruli/cortex) is equal to AF_{glom/cortex} (Area fraction of glomeruli/cortex on the section).

\mathsf{\text{V}}{\mathsf{\text{F}}}_{\mathsf{\text{glom}}/\mathsf{\text{cortex}}}=\mathsf{\text{A}}{\mathsf{\text{F}}}_{\mathsf{\text{glom}}/\mathsf{\text{cortex}}}=\frac{{\mathsf{\text{N}}}_{\mathsf{\text{s}}}\times {\mathsf{\text{A}}}_{\mathsf{\text{h}}}}{{\mathsf{\text{A}}}_{\mathsf{\text{cortex-b}}}}

Where N_{s} is the number of observed glomeruli in a biopsied specimen.

Finally, the total number of glomeruli (N_{total}) was calculated as:

{\mathsf{\text{N}}}_{\mathsf{\text{total}}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\frac{\mathsf{\text{Total}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{glomerular}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{volume}}}{\mathsf{\text{one}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{average}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{glomerular}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{volume}}\phantom{\rule{0.3em}{0ex}}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\frac{\mathsf{\text{V}}{\mathsf{\text{F}}}_{\mathsf{\text{glom/cortex}}}\phantom{\rule{0.3em}{0ex}}\times \phantom{\rule{0.3em}{0ex}}{\mathsf{\text{V}}}_{\mathsf{\text{Cortex}}}}{\frac{4}{3}\phantom{\rule{0.3em}{0ex}}\pi {\mathsf{\text{r}}}^{3}}

Where V_{cortex} is the volume of the cortex estimated by MRI.

In this study, the value of r will be decided after calculating the means of approximately 5% of the attending patients by random sampling. Therefore, "r" is not a variable in the final calculation.

### Statistical analysis

All data are expressed as the means (SD). The primary parameter for assessment is the composite of the total mortality, renal death, cerebro-cardiovascular events, and a 50% reduction in the eGFR. We will use a Cox proportional hazard model for the analysis. We will check for confounders, interactions and multicollinearity among the independent variables. The final models will be adjusted by all significant variables, as well as confounders and other baseline covariables judged to have clinical importance. The secondary parameter is the rate of eGFR decline per year. A multivariate regression analysis will be used for the analysis. The significance level on both sides in the hypothesis testing will be set at 0.05. The analyses will be performed using the SPSS statistics software program version 19.0. (IBM Corp.)

### Sub-cohort study to establish an equation for the renal cortex volume

Some of the participating patients will undergo MRI to measure the cortex volume of their kidney, because MRI is the safest procedure and has highest resolution to separate the cortex from the medulla, as reported in other studies [16, 17]. However, it is unrealistic to perform MRI for all CKD patients because of its high cost. Therefore, we will attempt to establish the equation to calculate an approximate value of the kidney cortex volume measured by MRI.

### Measurement of the cortex volume by MRI

While MR imaging sometimes does not provide sufficient contrast for the soft tissues, in many cases, it is possible to distinguish the cortex and the pith of the kidney by tomography. Therefore, we will image the entire kidney with axial MRI, and calculate the renal cortical volume by multiplying the slice thickness and the slice number of the kidney which we measured on each axis tomogram. For this purpose, we found that an MR image that provided the best contrast between the cortex and medulla of the kidney was obtained using the following sequence: 2D Turbo FLASH TR = 1570 ms, TE = 2.74 ms, TI = 1000 ms, Flip Angle = 15°, Fat sat (-). We will manually draw the ROI in the kidney, and the regional choice in the axial image of the kidney will be determined by specialized radiological technologists (with AZE virtual Place FUJIN workstation, AZE Co. Ltd., Tokyo).

The calculations used for the renal cortical and whole kidney volume are as follows:

\mathsf{\text{Whole}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{kidney}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{volume}}=\sum \mathsf{\text{Area}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{of}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{the}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{kidney}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{in}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{each}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{slice}}\times \mathsf{\text{slice}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{thickness}}\left(\mathsf{\text{slice}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{interval}}\right)

\mathsf{\text{Renal}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{cortex}}\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{volume}}=\sum \mathsf{\text{Area}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{of}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{the}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{cortex}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{in}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{each}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{slice}}\times \mathsf{\text{slice}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{thickness}}\left(\mathsf{\text{slice}}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{interval}}\right)